problem solving in heuristics

Heuristics: Definition, Examples, And How They Work

Benjamin Frimodig

Science Expert

B.A., History and Science, Harvard University

Ben Frimodig is a 2021 graduate of Harvard College, where he studied the History of Science.

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Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

On This Page:

Every day our brains must process and respond to thousands of problems, both large and small, at a moment’s notice. It might even be overwhelming to consider the sheer volume of complex problems we regularly face in need of a quick solution.

While one might wish there was time to methodically and thoughtfully evaluate the fine details of our everyday tasks, the cognitive demands of daily life often make such processing logistically impossible.

Therefore, the brain must develop reliable shortcuts to keep up with the stimulus-rich environments we inhabit. Psychologists refer to these efficient problem-solving techniques as heuristics.

Heuristics can be thought of as general cognitive frameworks humans rely on regularly to reach a solution quickly.

For example, if a student needs to decide what subject she will study at university, her intuition will likely be drawn toward the path that she envisions as most satisfying, practical, and interesting.

She may also think back on her strengths and weaknesses in secondary school or perhaps even write out a pros and cons list to facilitate her choice.

It’s important to note that these heuristics broadly apply to everyday problems, produce sound solutions, and helps simplify otherwise complicated mental tasks. These are the three defining features of a heuristic.

While the concept of heuristics dates back to Ancient Greece (the term is derived from the Greek word for “to discover”), most of the information known today on the subject comes from prominent twentieth-century social scientists.

Herbert Simon’s study of a notion he called “bounded rationality” focused on decision-making under restrictive cognitive conditions, such as limited time and information.

This concept of optimizing an inherently imperfect analysis frames the contemporary study of heuristics and leads many to credit Simon as a foundational figure in the field.

Kahneman’s Theory of Decision Making

The immense contributions of psychologist Daniel Kahneman to our understanding of cognitive problem-solving deserve special attention.

As context for his theory, Kahneman put forward the estimate that an individual makes around 35,000 decisions each day! To reach these resolutions, the mind relies on either “fast” or “slow” thinking.

The fast thinking pathway (system 1) operates mostly unconsciously and aims to reach reliable decisions with as minimal cognitive strain as possible.

While system 1 relies on broad observations and quick evaluative techniques (heuristics!), system 2 (slow thinking) requires conscious, continuous attention to carefully assess the details of a given problem and logically reach a solution.

Given the sheer volume of daily decisions, it’s no surprise that around 98% of problem-solving uses system 1.

Thus, it is crucial that the human mind develops a toolbox of effective, efficient heuristics to support this fast-thinking pathway.

Heuristics vs. Algorithms

Those who’ve studied the psychology of decision-making might notice similarities between heuristics and algorithms. However, remember that these are two distinct modes of cognition.

Heuristics are methods or strategies which often lead to problem solutions but are not guaranteed to succeed.

They can be distinguished from algorithms, which are methods or procedures that will always produce a solution sooner or later.

An algorithm is a step-by-step procedure that can be reliably used to solve a specific problem. While the concept of an algorithm is most commonly used in reference to technology and mathematics, our brains rely on algorithms every day to resolve issues (Kahneman, 2011).

The important thing to remember is that algorithms are a set of mental instructions unique to specific situations, while heuristics are general rules of thumb that can help the mind process and overcome various obstacles.

For example, if you are thoughtfully reading every line of this article, you are using an algorithm.

On the other hand, if you are quickly skimming each section for important information or perhaps focusing only on sections you don’t already understand, you are using a heuristic!

Why Heuristics Are Used

Heuristics usually occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind at the same moment

When studying heuristics, keep in mind both the benefits and unavoidable drawbacks of their application. The ubiquity of these techniques in human society makes such weaknesses especially worthy of evaluation.

More specifically, in expediting decision-making processes, heuristics also predispose us to a number of cognitive biases .

A cognitive bias is an incorrect but pervasive judgment derived from an illogical pattern of cognition. In simple terms, a cognitive bias occurs when one internalizes a subjective perception as a reliable and objective truth.

Heuristics are reliable but imperfect; In the application of broad decision-making “shortcuts” to guide one’s response to specific situations, occasional errors are both inevitable and have the potential to catalyze persistent mistakes.

For example, consider the risks of faulty applications of the representative heuristic discussed above. While the technique encourages one to assign situations into broad categories based on superficial characteristics and one’s past experiences for the sake of cognitive expediency, such thinking is also the basis of stereotypes and discrimination.

In practice, these errors result in the disproportionate favoring of one group and/or the oppression of other groups within a given society.

Indeed, the most impactful research relating to heuristics often centers on the connection between them and systematic discrimination.

The tradeoff between thoughtful rationality and cognitive efficiency encompasses both the benefits and pitfalls of heuristics and represents a foundational concept in psychological research.

When learning about heuristics, keep in mind their relevance to all areas of human interaction. After all, the study of social psychology is intrinsically interdisciplinary.

Many of the most important studies on heuristics relate to flawed decision-making processes in high-stakes fields like law, medicine, and politics.

Researchers often draw on a distinct set of already established heuristics in their analysis. While dozens of unique heuristics have been observed, brief descriptions of those most central to the field are included below:

Availability Heuristic

The availability heuristic describes the tendency to make choices based on information that comes to mind readily.

For example, children of divorced parents are more likely to have pessimistic views towards marriage as adults.

Of important note, this heuristic can also involve assigning more importance to more recently learned information, largely due to the easier recall of such information.

Representativeness Heuristic

This technique allows one to quickly assign probabilities to and predict the outcome of new scenarios using psychological prototypes derived from past experiences.

For example, juries are less likely to convict individuals who are well-groomed and wearing formal attire (under the assumption that stylish, well-kempt individuals typically do not commit crimes).

This is one of the most studied heuristics by social psychologists for its relevance to the development of stereotypes.

Scarcity Heuristic

This method of decision-making is predicated on the perception of less abundant, rarer items as inherently more valuable than more abundant items.

We rely on the scarcity heuristic when we must make a fast selection with incomplete information. For example, a student deciding between two universities may be drawn toward the option with the lower acceptance rate, assuming that this exclusivity indicates a more desirable experience.

The concept of scarcity is central to behavioral economists’ study of consumer behavior (a field that evaluates economics through the lens of human psychology).

Trial and Error

This is the most basic and perhaps frequently cited heuristic. Trial and error can be used to solve a problem that possesses a discrete number of possible solutions and involves simply attempting each possible option until the correct solution is identified.

For example, if an individual was putting together a jigsaw puzzle, he or she would try multiple pieces until locating a proper fit.

This technique is commonly taught in introductory psychology courses due to its simple representation of the central purpose of heuristics: the use of reliable problem-solving frameworks to reduce cognitive load.

Anchoring and Adjustment Heuristic

Anchoring refers to the tendency to formulate expectations relating to new scenarios relative to an already ingrained piece of information.

Put simply, this anchoring one to form reasonable estimations around uncertainties. For example, if asked to estimate the number of days in a year on Mars, many people would first call to mind the fact the Earth’s year is 365 days (the “anchor”) and adjust accordingly.

This tendency can also help explain the observation that ingrained information often hinders the learning of new information, a concept known as retroactive inhibition.

Familiarity Heuristic

This technique can be used to guide actions in cognitively demanding situations by simply reverting to previous behaviors successfully utilized under similar circumstances.

The familiarity heuristic is most useful in unfamiliar, stressful environments.

For example, a job seeker might recall behavioral standards in other high-stakes situations from her past (perhaps an important presentation at university) to guide her behavior in a job interview.

Many psychologists interpret this technique as a slightly more specific variation of the availability heuristic.

How to Make Better Decisions

Heuristics are ingrained cognitive processes utilized by all humans and can lead to various biases.

Both of these statements are established facts. However, this does not mean that the biases that heuristics produce are unavoidable. As the wide-ranging impacts of such biases on societal institutions have become a popular research topic, psychologists have emphasized techniques for reaching more sound, thoughtful and fair decisions in our daily lives.

Ironically, many of these techniques are themselves heuristics!

To focus on the key details of a given problem, one might create a mental list of explicit goals and values. To clearly identify the impacts of choice, one should imagine its impacts one year in the future and from the perspective of all parties involved.

Most importantly, one must gain a mindful understanding of the problem-solving techniques used by our minds and the common mistakes that result. Mindfulness of these flawed yet persistent pathways allows one to quickly identify and remedy the biases (or otherwise flawed thinking) they tend to create!

Further Information

• Shah, A. K., & Oppenheimer, D. M. (2008). Heuristics made easy: an effort-reduction framework. Psychological bulletin, 134(2), 207.
• Marewski, J. N., & Gigerenzer, G. (2012). Heuristic decision making in medicine. Dialogues in clinical neuroscience, 14(1), 77.
• Del Campo, C., Pauser, S., Steiner, E., & Vetschera, R. (2016). Decision making styles and the use of heuristics in decision making. Journal of Business Economics, 86(4), 389-412.

What is a heuristic in psychology?

A heuristic in psychology is a mental shortcut or rule of thumb that simplifies decision-making and problem-solving. Heuristics often speed up the process of finding a satisfactory solution, but they can also lead to cognitive biases.

Bobadilla-Suarez, S., & Love, B. C. (2017, May 29). Fast or Frugal, but Not Both: Decision Heuristics Under Time Pressure. Journal of Experimental Psychology: Learning, Memory, and Cognition .

Bowes, S. M., Ammirati, R. J., Costello, T. H., Basterfield, C., & Lilienfeld, S. O. (2020). Cognitive biases, heuristics, and logical fallacies in clinical practice: A brief field guide for practicing clinicians and supervisors. Professional Psychology: Research and Practice, 51 (5), 435–445.

Dietrich, C. (2010). “Decision Making: Factors that Influence Decision Making, Heuristics Used, and Decision Outcomes.” Inquiries Journal/Student Pulse, 2(02).

Groenewegen, A. (2021, September 1). Kahneman Fast and slow thinking: System 1 and 2 explained by Sue. SUE Behavioral Design. Retrieved March 26, 2022, from https://suebehaviouraldesign.com/kahneman-fast-slow-thinking/

Kahneman, D., Lovallo, D., & Sibony, O. (2011). Before you make that big decision .

Kahneman, D. (2011). Thinking, fast and slow . Macmillan.

Pratkanis, A. (1989). The cognitive representation of attitudes. In A. R. Pratkanis, S. J. Breckler, & A. G. Greenwald (Eds.), Attitude structure and function (pp. 71–98). Hillsdale, NJ: Erlbaum.

Simon, H.A., 1956. Rational choice and the structure of the environment. Psychological Review .

Tversky, A., & Kahneman, D. (1974). Judgment under Uncertainty: Heuristics and Biases. Science, 185 (4157), 1124–1131.

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What Are Heuristics?

These mental shortcuts lead to fast decisions—and biased thinking

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Steven Gans, MD is board-certified in psychiatry and is an active supervisor, teacher, and mentor at Massachusetts General Hospital.

Verywell / Cindy Chung 

• History and Origins
• Heuristics vs. Algorithms
• Heuristics and Bias

How to Make Better Decisions

If you need to make a quick decision, there's a good chance you'll rely on a heuristic to come up with a speedy solution. Heuristics are mental shortcuts that allow people to solve problems and make judgments quickly and efficiently. Common types of heuristics rely on availability, representativeness, familiarity, anchoring effects, mood, scarcity, and trial-and-error.

Think of these as mental "rule-of-thumb" strategies that shorten decision-making time. Such shortcuts allow us to function without constantly stopping to think about our next course of action.

However, heuristics have both benefits and drawbacks. These strategies can be handy in many situations but can also lead to  cognitive biases . Becoming aware of this might help you make better and more accurate decisions.

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History of the Research on Heuristics

Nobel-prize winning economist and cognitive psychologist Herbert Simon originally introduced the concept of heuristics in psychology in the 1950s. He suggested that while people strive to make rational choices, human judgment is subject to cognitive limitations. Purely rational decisions would involve weighing every alternative's potential costs and possible benefits.

However, people are limited by the amount of time they have to make a choice and the amount of information they have at their disposal. Other factors, such as overall intelligence and accuracy of perceptions, also influence the decision-making process.

In the 1970s, psychologists Amos Tversky and Daniel Kahneman presented their research on cognitive biases. They proposed that these biases influence how people think and make judgments.

Because of these limitations, we must rely on mental shortcuts to help us make sense of the world.

Simon's research demonstrated that humans were limited in their ability to make rational decisions, but it was Tversky and Kahneman's work that introduced the study of heuristics and the specific ways of thinking that people rely on to simplify the decision-making process.

How Heuristics Are Used

Heuristics play important roles in both  problem-solving  and  decision-making , as we often turn to these mental shortcuts when we need a quick solution.

Here are a few different theories from psychologists about why we rely on heuristics.

• Attribute substitution : People substitute simpler but related questions in place of more complex and difficult questions.
• Effort reduction : People use heuristics as a type of cognitive laziness to reduce the mental effort required to make choices and decisions.
• Fast and frugal : People use heuristics because they can be fast and correct in certain contexts. Some theories argue that heuristics are actually more accurate than they are biased.

In order to cope with the tremendous amount of information we encounter and to speed up the decision-making process, our brains rely on these mental strategies to simplify things so we don't have to spend endless amounts of time analyzing every detail.

You probably make hundreds or even thousands of decisions every day. What should you have for breakfast? What should you wear today? Should you drive or take the bus? Fortunately, heuristics allow you to make such decisions with relative ease and without a great deal of agonizing.

There are many heuristics examples in everyday life. When trying to decide if you should drive or ride the bus to work, for instance, you might remember that there is road construction along the bus route. You realize that this might slow the bus and cause you to be late for work. So you leave earlier and drive to work on an alternate route.

Heuristics allow you to think through the possible outcomes quickly and arrive at a solution.

Are Heuristics Good or Bad?

Heuristics aren't inherently good or bad, but there are pros and cons to using them to make decisions. While they can help us figure out a solution to a problem faster, they can also lead to inaccurate judgments about others or situations. Understanding these pros and cons may help you better use heuristics to make better decisions.

Types of Heuristics

There are many different kinds of heuristics. While each type plays a role in decision-making, they occur during different contexts. Understanding the types can help you better understand which one you are using and when.

Availability

The availability heuristic  involves making decisions based upon how easy it is to bring something to mind. When you are trying to make a decision, you might quickly remember a number of relevant examples.

Since these are more readily available in your memory, you will likely judge these outcomes as being more common or frequently occurring.

For example, imagine you are planning to fly somewhere on vacation. As you are preparing for your trip, you might start to think of a number of recent airline accidents. You might feel like air travel is too dangerous and decide to travel by car instead. Because those examples of air disasters came to mind so easily, the availability heuristic leads you to think that plane crashes are more common than they really are.

Familiarity

The familiarity heuristic refers to how people tend to have more favorable opinions of things, people, or places they've experienced before as opposed to new ones. In fact, given two options, people may choose something they're more familiar with even if the new option provides more benefits.

Representativeness

The representativeness heuristic  involves making a decision by comparing the present situation to the most representative mental prototype. When you are trying to decide if someone is trustworthy, you might compare aspects of the individual to other mental examples you hold.

A soft-spoken older woman might remind you of your grandmother, so you might immediately assume she is kind, gentle, and trustworthy. However, this is an example of a heuristic bias, as you can't know someone trustworthy based on their age alone.

The affect heuristic involves making choices that are influenced by an individual's emotions at that moment. For example, research has shown that people are more likely to see decisions as having benefits and lower risks when in a positive mood.

Negative emotions, on the other hand, lead people to focus on the potential downsides of a decision rather than the possible benefits.

The anchoring bias involves the tendency to be overly influenced by the first bit of information we hear or learn. This can make it more difficult to consider other factors and lead to poor choices. For example, anchoring bias can influence how much you are willing to pay for something, causing you to jump at the first offer without shopping around for a better deal.

Scarcity is a heuristic principle in which we view things that are scarce or less available to us as inherently more valuable. Marketers often use the scarcity heuristic to influence people to buy certain products. This is why you'll often see signs that advertise "limited time only," or that tell you to "get yours while supplies last."

Trial and Error

Trial and error is another type of heuristic in which people use a number of different strategies to solve something until they find what works. Examples of this type of heuristic are evident in everyday life.

People use trial and error when playing video games, finding the fastest driving route to work, or learning to ride a bike (or any new skill).

Difference Between Heuristics and Algorithms

Though the terms are often confused, heuristics and algorithms are two distinct terms in psychology.

Algorithms are step-by-step instructions that lead to predictable, reliable outcomes, whereas heuristics are mental shortcuts that are basically best guesses. Algorithms always lead to accurate outcomes, whereas, heuristics do not.

Examples of algorithms include instructions for how to put together a piece of furniture or a recipe for cooking a certain dish. Health professionals also create algorithms or processes to follow in order to determine what type of treatment to use on a patient.

How Heuristics Can Lead to Bias

Heuristics can certainly help us solve problems and speed up our decision-making process, but that doesn't mean they are always a good thing. They can also introduce errors, bias, and irrational decision-making. As in the examples above, heuristics can lead to inaccurate judgments about how commonly things occur and how representative certain things may be.

Just because something has worked in the past does not mean that it will work again, and relying on a heuristic can make it difficult to see alternative solutions or come up with new ideas.

Heuristics can also contribute to stereotypes and  prejudice . Because people use mental shortcuts to classify and categorize people, they often overlook more relevant information and create stereotyped categorizations that are not in tune with reality.

While heuristics can be a useful tool, there are ways you can improve your decision-making and avoid cognitive bias at the same time.

We are more likely to make an error in judgment if we are trying to make a decision quickly or are under pressure to do so. Taking a little more time to make a decision can help you see things more clearly—and make better choices.

Whenever possible, take a few deep breaths and do something to distract yourself from the decision at hand. When you return to it, you may find a fresh perspective or notice something you didn't before.

Identify the Goal

We tend to focus automatically on what works for us and make decisions that serve our best interest. But take a moment to know what you're trying to achieve. Consider some of the following questions:

• Are there other people who will be affected by this decision?
• What's best for them?
• Is there a common goal that can be achieved that will serve all parties?

Thinking through these questions can help you figure out your goals and the impact that these decisions may have.

Process Your Emotions

Fast decision-making is often influenced by emotions from past experiences that bubble to the surface. Anger, sadness, love, and other powerful feelings can sometimes lead us to decisions we might not otherwise make.

Is your decision based on facts or emotions? While emotions can be helpful, they may affect decisions in a negative way if they prevent us from seeing the full picture.

Recognize All-or-Nothing Thinking

When making a decision, it's a common tendency to believe you have to pick a single, well-defined path, and there's no going back. In reality, this often isn't the case.

Sometimes there are compromises involving two choices, or a third or fourth option that we didn't even think of at first. Try to recognize the nuances and possibilities of all choices involved, instead of using all-or-nothing thinking .

Heuristics are common and often useful. We need this type of decision-making strategy to help reduce cognitive load and speed up many of the small, everyday choices we must make as we live, work, and interact with others.

But it pays to remember that heuristics can also be flawed and lead to irrational choices if we rely too heavily on them. If you are making a big decision, give yourself a little extra time to consider your options and try to consider the situation from someone else's perspective. Thinking things through a bit instead of relying on your mental shortcuts can help ensure you're making the right choice.

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Hjeij M, Vilks A. A brief history of heuristics: how did research on heuristics evolve? Humanit Soc Sci Commun . 2023;10(1):64. doi:10.1057/s41599-023-01542-z

Brighton H, Gigerenzer G. Homo heuristicus: Less-is-more effects in adaptive cognition .  Malays J Med Sci . 2012;19(4):6-16.

Schwartz PH. Comparative risk: Good or bad heuristic?   Am J Bioeth . 2016;16(5):20-22. doi:10.1080/15265161.2016.1159765

Schwikert SR, Curran T. Familiarity and recollection in heuristic decision making .  J Exp Psychol Gen . 2014;143(6):2341-2365. doi:10.1037/xge0000024

AlKhars M, Evangelopoulos N, Pavur R, Kulkarni S. Cognitive biases resulting from the representativeness heuristic in operations management: an experimental investigation .  Psychol Res Behav Manag . 2019;12:263-276. doi:10.2147/PRBM.S193092

Finucane M, Alhakami A, Slovic P, Johnson S. The affect heuristic in judgments of risks and benefits . J Behav Decis Mak . 2000; 13(1):1-17. doi:10.1002/(SICI)1099-0771(200001/03)13:1<1::AID-BDM333>3.0.CO;2-S

Teovanović P. Individual differences in anchoring effect: Evidence for the role of insufficient adjustment .  Eur J Psychol . 2019;15(1):8-24. doi:10.5964/ejop.v15i1.1691

Cheung TT, Kroese FM, Fennis BM, De Ridder DT. Put a limit on it: The protective effects of scarcity heuristics when self-control is low . Health Psychol Open . 2015;2(2):2055102915615046. doi:10.1177/2055102915615046

Mohr H, Zwosta K, Markovic D, Bitzer S, Wolfensteller U, Ruge H. Deterministic response strategies in a trial-and-error learning task . Inman C, ed. PLoS Comput Biol. 2018;14(11):e1006621. doi:10.1371/journal.pcbi.1006621

Grote T, Berens P. On the ethics of algorithmic decision-making in healthcare .  J Med Ethics . 2020;46(3):205-211. doi:10.1136/medethics-2019-105586

Bigler RS, Clark C. The inherence heuristic: A key theoretical addition to understanding social stereotyping and prejudice. Behav Brain Sci . 2014;37(5):483-4. doi:10.1017/S0140525X1300366X

del Campo C, Pauser S, Steiner E, et al.  Decision making styles and the use of heuristics in decision making .  J Bus Econ.  2016;86:389–412. doi:10.1007/s11573-016-0811-y

Marewski JN, Gigerenzer G. Heuristic decision making in medicine .  Dialogues Clin Neurosci . 2012;14(1):77-89. doi:10.31887/DCNS.2012.14.1/jmarewski

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By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Heuristic Problem Solving: A comprehensive guide with 5 Examples

What are heuristics, advantages of using heuristic problem solving, disadvantages of using heuristic problem solving, heuristic problem solving examples, frequently asked questions.

• Speed: Heuristics are designed to find solutions quickly, saving time in problem solving tasks. Rather than spending a lot of time analyzing every possible solution, heuristics help to narrow down the options and focus on the most promising ones.
• Flexibility: Heuristics are not rigid, step-by-step procedures. They allow for flexibility and creativity in problem solving, leading to innovative solutions. They encourage thinking outside the box and can generate unexpected and valuable ideas.
• Simplicity: Heuristics are often easy to understand and apply, making them accessible to anyone regardless of their expertise or background. They don’t require specialized knowledge or training, which means they can be used in various contexts and by different people.
• Cost-effective: Because heuristics are simple and efficient, they can save time, money, and effort in finding solutions. They also don’t require expensive software or equipment, making them a cost-effective approach to problem solving.
• Real-world applicability: Heuristics are often based on practical experience and knowledge, making them relevant to real-world situations. They can help solve complex, messy, or ill-defined problems where other problem solving methods may not be practical.
• Potential for errors: Heuristic problem solving relies on generalizations and assumptions, which may lead to errors or incorrect conclusions. This is especially true if the heuristic is not based on a solid understanding of the problem or the underlying principles.
• Limited scope: Heuristic problem solving may only consider a limited number of potential solutions and may not identify the most optimal or effective solution.
• Lack of creativity: Heuristic problem solving may rely on pre-existing solutions or approaches, limiting creativity and innovation in problem-solving.
• Over-reliance: Heuristic problem solving may lead to over-reliance on a specific approach or heuristic, which can be problematic if the heuristic is flawed or ineffective.
• Lack of transparency: Heuristic problem solving may not be transparent or explainable, as the decision-making process may not be explicitly articulated or understood.
• Trial and error: This heuristic involves trying different solutions to a problem and learning from mistakes until a successful solution is found. A software developer encountering a bug in their code may try other solutions and test each one until they find the one that solves the issue.
• Working backward: This heuristic involves starting at the goal and then figuring out what steps are needed to reach that goal. For example, a project manager may begin by setting a project deadline and then work backward to determine the necessary steps and deadlines for each team member to ensure the project is completed on time.
• Breaking a problem into smaller parts: This heuristic involves breaking down a complex problem into smaller, more manageable pieces that can be tackled individually. For example, an HR manager tasked with implementing a new employee benefits program may break the project into smaller parts, such as researching options, getting quotes from vendors, and communicating the unique benefits to employees.
• Using analogies: This heuristic involves finding similarities between a current problem and a similar problem that has been solved before and using the solution to the previous issue to help solve the current one. For example, a salesperson struggling to close a deal may use an analogy to a successful sales pitch they made to help guide their approach to the current pitch.
• Simplifying the problem: This heuristic involves simplifying a complex problem by ignoring details that are not necessary for solving it. This allows the problem solver to focus on the most critical aspects of the problem. For example, a customer service representative dealing with a complex issue may simplify it by breaking it down into smaller components and addressing them individually rather than simultaneously trying to solve the entire problem.

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Heuristic Method

Heuristic Method: this article explains the concept of the Heuristic Method , developed by George Pólya in a practical way. After reading it, you will understand the basics of this powerful Problem Solving tool.

What is the Heuristic Method?

A heuristic method is an approach to finding a solution to a problem that originates from the ancient Greek word ‘eurisko’, meaning to ‘find’, ‘search’ or ‘discover’. It is about using a practical method that doesn’t necessarily need to be perfect. Heuristic methods speed up the process of reaching a satisfactory solution.

Previous experiences with comparable problems are used that can concern problem situations for people, machines or abstract issues. One of the founders of heuristics is the Hungarian mathematician György (George) Pólya , who published a book about the subject in 1945 called ‘How to Solve It’. He used four principles that form the basis for problem solving.

Heuristic method: Four principles

Pólya describes the following four principles in his book:

• try to understand the problem
• make a plan
• carry out this plan
• evaluate and adapt

If this sequence doesn’t lead to the right solution, Pólya advises to first look for a simpler problem.

A solution may potentially be found by first looking at a similar problem that was possible to solve. With this experience, it’s possible to look at the current problem in another way.

First principle of the heuristic method: understand the problem

It’s more difficult than it seems, because it seems obvious. In truth, people are hindered when it comes to finding an initially suitable approach to the problem.

It can help to draw the problem and to look at it from another angle. What is the problem, what is happening, can the problem be explained in other words, is there enough information available, etc. Such questions can help with the first evaluation of a problem issue.

Second principle of the heuristic method: make a plan

There are many ways to solve problems. This section is about choosing the right strategy that best fits the problem at hand. The reversed ‘working backwards’ can help with this; people assume to have a solution and use this as a starting point to work towards the problem.

It can also be useful to make an overview of the possibilities, delete some of them immediately, work with comparisons, or to apply symmetry. Creativity comes into play here and will improve the ability to judge.

Third principle of the heuristic method: carry out the plan

Once a strategy has been chosen, the plan can quickly be implemented. However, it is important to pay attention to time and be patient, because the solution will not simply appear.

If the plan doesn’t go anywhere, the advice is to throw it overboard and find a new way.

Fourth principle of the heuristic method: evaluate and adapt

Take the time to carefully consider and reflect upon the work that’s already been done. The things that are going well should be maintained, those leading to a lesser solution, should be adjusted. Some things simply work, while others simply don’t.

There are many different heuristic methods, which Pólya also used. The most well-known heuristics are found below:

1. Dividing technique

The original problem is divided into smaller sub-problems that can be solved more easily. These sub-problems can be linked to each other and combined, which will eventually lead to the solving of the original problem.

2. Inductive method

This involves a problem that has already been solved, but is smaller than the original problem. Generalisation can be derived from the previously solved problem, which can help in solving the bigger, original problem.

3. Reduction method

Because problems are often larger than assumed and deal with different causes and factors, this method sets limits for the problem in advance. This reduces the leeway of the original problem, making it easier to solve.

4. Constructive method

This is about working on the problem step by step. The smallest solution is seen as a victory and from that point consecutive steps are taken. This way, the best choices keep being made, which will eventually lead to a successful end result.

5. Local search method

This is about the search for the most attainable solution to the problem. This solution is improved along the way. This method ends when improvement is no longer possible.

Exact solutions versus the heuristic method

The heuristic approach is a mathmatical method with which proof of a good solution to a problem is delivered. There is a large number of different problems that could use good solutions. When the processing speed is equally as important as the obtained solution, we speak of a heuristic method.

The Heuristic Method only tries to find a good, but not necessarily optimal, solution. This is what differentiates heuristics from exact solution methods, which are about finding the optimal solution to a problem. However, that’s very time consuming, which is why a heuristic method may prove preferable. This is much quicker and more flexible than an exact method, but does have to satisfy a number of criteria.

It’s Your Turn

What do you think? Is the Heuristic Method applicable in your personal or professional environment? Do you recognize the practical explanation or do you have more suggestions? What are your success factors for solving problems

Share your experience and knowledge in the comments box below.

More information

• Groner, R., Groner, M., & Bischof, W. F. (2014). Methods of heuristics . Routledge .
• Newell, A. (1983). The heuristic of George Polya and its relation to artificial intelligence . Methods of heuristics, 195-243.
• Polya, G. (2014, 1945). How to solve it: A new aspect of mathematical method . Princeton university press .

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Patty Mulder is an Dutch expert on Management Skills, Personal Effectiveness and Business Communication. She is also a Content writer, Business Coach and Company Trainer and lives in the Netherlands (Europe). Note: all her articles are written in Dutch and we translated her articles to English!

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Heuristics and Problem Solving

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Definitions

In a general sense heuristics are guidelines or methods for problem solving. Therefore, we will first define problem solving before presenting a specific definition of heuristics.

Problem Solving

In contrast to a routine task, a problem is a situation in which a person is trying to attain a goal but does not dispose of a ready-made solution or solution method. Problem solving involves then “cognitive processing directed at transforming the given situation into a goal situation when no obvious method of solution is available” (Mayer and Wittrock 2006 , p. 287). An implication is that a task can be a problem for one person, but not for someone else. For instance, the task “divide 120 marbles equally among 8 children” may be a problem for beginning elementary school children, but not for people who master the algorithm for long division, or know how to use a calculator.

The term “heuristic” originates from the Greek word heuriskein which means “to find.” Heuristics ...

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De Corte, E., Verschaffel, L., & Op’t Eynde, P. (2000). Self-regulation: a characteristic and a goal of mathematics education. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of self-regulation (pp. 687–726). San Diego, CA: Academic.

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Groner, R., Groner, M., & Bischof, W. F. (Eds.). (1983). Methods of heuristics . Hillsdale, NJ: Erlbaum.

Mayer, R. E., & Wittrock, M. C. (2006). Problem solving. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (pp. 287–303). New York: Macmillan.

Polya, G. (1945). How to solve it . Princeton, NJ: Princeton University Press.

Schoenfeld, A. H. (1985). Mathematical problem solving . New York: Academic.

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Some Helpful Problem-Solving Heuristics

A  heuristic  is a thinking strategy, something that can be used to tease out further information about a problem and thus help you figure out what to do when you don’t know what to do. Here are 25 heuristics that can be useful in solving problems. They help you monitor your thought processes, to step back and watch yourself at work, and thus keep your cool in a challenging situation.

• Ask somebody else  how to do the problem. This strategy is probably the most used world-wide, though it is not one we encourage our students to use, at least not initially.
• Guess and try  (guess, check, and revise). Your first guess might be right! But incorrect guesses can often suggest a direction toward a solution. (N.B. A spreadsheet is a powerful aid in guessing and trying. Set up the relationships and plug in a number to see if you get what you want. If you don’t, it is easy to try another number. And another.)
• Restate the problem  using words that make sense to you. One way to do this is to explain the problem to someone else. Often this is all it takes for the light to dawn.
• Organize information  into a table or chart. Having it laid out clearly in front of you frees up your mind for thinking. And perhaps you can use the organized data to generate more information.
• Draw a picture  of the problem. Translate problem information into pictures, diagrams, sketches, glyphs, arrows, or some other kind of representation.
• Make a model  of the problem. The model might be a physical or mental model, perhaps using a computer. You might vary the problem information to see whether and how the model may be affected.
• Look for patterns , any kind of patterns: number patterns, verbal patterns, spatial/visual patterns, patterns in time, patterns in sound. (Some people define mathematics as the science of patterns.)
• Act out the problem , if it is stated in a narrative form. Acting it out can have the same effect as drawing a picture. What’s more, acting out the problem might disclose incorrect assumptions you are making.
• Invent notation . Name things in the problem (known or unknown) using words or symbols, including relationships between problem components.
• Write equations . An equation is simply the same thing named two different ways.
• Check all possibilities  in a systematic way. A table or chart may help you to be systematic.
• Work backwards  from the end condition to the beginning condition. Working backwards is particularly helpful when letting a variable (letter) represent an unknown.
• Identify subgoals  in the problem. Break up the problem into a sequence of smaller problems (“If I knew this, then I could get that”).
• Simplify the problem . Use easier or smaller numbers, or look at extreme cases (e.g., use the minimum or maximum value of one of the varying quantities).
• Restate the problem again . After working on the problem for a time, back off a bit and put it into your own words in still a different way, since now you know more about it.
• Change your point of view . Use your imagination to change the way you are looking at the problem. Turn it upside down, or pull it inside out.
• Check for hidden assumptions  you may be making (you might be making the problem harder than it really is). These assumptions are often found by changing the given numbers or conditions and looking to see what happens.
• Identify needed and given information clearly . You may not need to find everything you think you need to find, for instance.
• Make up your own technique . It is your mind, after all; use mental actions that make sense to you. The key is to do something that engages you with the problem.
• Try combinations of the above heuristics .

These heuristics can be readily pointed out to students as they engage problems in the classroom. However, real-world problems are often confronted many times over or on increasingly complex levels. For those kinds of problems, George Polya, the father of modern problem-solving heuristics, identified a fifth class (E) of looking-back heuristics. We include these here for completeness, but also with the teaching caveat that solutions often improve and insights grow deeper after the initial pressure to produce a solution has been resolved. Subsequent considerations of a problem situation are invariably deeper than the first attempt.

• Check your solution . Substitute your answer or results back into the problem. Are all of the conditions satisfied?
• Find another solution . There may be more than one answer. Make sure you have them all.
• Solve the problem a different way . Your first solution will seldom be the best solution. Now that the pressure is off, you may readily find other ways to solve the problem.
• Solve a related problem . Steve Brown and Marion Walter in their book,  The Art of Problem Posing , suggest the “What if not?” technique. What if the train goes at a different speed? What if there are 8 children, instead of 9? What if . . .? Fascinating discoveries can be made in this way, leading to:
• Generalize the solution . Can you glean from your solution how it can be made to fit a whole class of related situations? Can you prove your result?

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What are heuristics and how do they help us make decisions?

Heuristics are simple rules of thumb that our brains use to make decisions. When you choose a work outfit that looks professional instead of sweatpants, you’re making a decision based on past information. That's not intuition; it’s heuristics. Instead of weighing all the information available to make a data-backed choice, heuristics enable us to move quickly into action—mostly without us even realizing it. In this article, you’ll learn what heuristics are, their common types, and how we use them in different scenarios.

Green means go. Most of us accept this as common knowledge, but it’s actually an example of a micro-decision—in this case, your brain is deciding to go when you see the color green.

You make countless of these subconscious decisions every day. Many things that you might think just come naturally to you are actually caused by heuristics—mental shortcuts that allow you to quickly process information and take action. Heuristics help you make smaller, almost unnoticeable decisions using past information, without much rational input from your brain.

Heuristics are helpful for getting things done more quickly, but they can also lead to biases and irrational choices if you’re not aware of them. Luckily, you can use heuristics to your advantage once you recognize them, and make better decisions in the workplace.

What is a heuristic?

Heuristics are mental shortcuts that your brain uses to make decisions. When we make rational choices, our brains weigh all the information, pros and cons, and any relevant data. But it’s not possible to do this for every single decision we make on a day-to-day basis. For the smaller ones, your brain uses heuristics to infer information and take almost-immediate action.

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How heuristics work

For example, if you’re making a larger decision about whether to accept a new job or stay with your current one, your brain will process this information slowly. For decisions like this, you collect data by referencing sources—chatting with mentors, reading company reviews, and comparing salaries. Then, you use that information to make your decision. Meanwhile, your brain is also using heuristics to help you speed along that track. In this example, you might use something called the “availability heuristic” to reference things you’ve recently seen about the new job. The availability heuristic makes it more likely that you’ll remember a news story about the company’s higher stock prices. Without realizing it, this can make you think the new job will be more lucrative.

On the flip side, you can recognize that the new job has had some great press recently, but that might be just a great PR team at work. Instead of “buying in” to what the availability heuristic is trying to tell you—that positive news means it’s the right job—you can acknowledge that this is a bias at work. In this case, comparing compensation and work-life balance between the two companies is a much more effective way to choose which job is right for you.

History of heuristics

The term "heuristics," originating from the Greek word meaning “to discover,” has ancient roots, but much of today's understanding comes from twentieth-century social scientists. Herbert Simon's research into "bounded rationality" highlighted the use of heuristics in decision-making, particularly under constraints like limited time and information.

Daniel Kahneman was one of the first researchers to study heuristics in his behavioral economics work in the 1970’s, along with fellow psychologist Amos Tversky. They theorized that many of the decisions and judgments we make aren’t rational—meaning we don’t move through a series of decision-making steps to come to a solution. Instead, the human brain uses mental shortcuts to form seemingly irrational, “fast and frugal” decisions—quick choices that don’t require a lot of mental energy.

Kahneman’s work showed that heuristics lead to systematic errors (or biases), which act as the driving force for our decisions. He was able to apply this research to economic theory, leading to the formation of behavioral economics and a Nobel Prize for Kahneman in 2002.

In the years since, the study of heuristics has grown in popularity with economists and in cognitive psychology. Gerd Gigerenzer’s research , for example, challenges the idea that heuristics lead to errors or flawed thinking. He argues that heuristics are actually indicators that human beings are able to make decisions more effectively without following the traditional rules of logic. His research seems to indicate that heuristics lead us to the right answer most of the time.

Types of heuristics

Heuristics are everywhere, whether we notice them or not. There are hundreds of heuristics at play in the human brain, and they interact with one another constantly. To understand how these heuristics can help you, start by learning some of the more common types of heuristics.

Recognition heuristic

The recognition heuristic uses what we already know (or recognize) as a criterion for decisions. The concept is simple: When faced with two choices, you’re more likely to choose the item you recognize versus the one you don’t.

This is the very base-level concept behind branding your business, and we see it in all well-known companies. Businesses develop a brand messaging strategy in the hopes that when you’re faced with buying their product or buying someone else's, you recognize their product, have a positive association with it, and choose that one. For example, if you’re going to grab a soda and there are two different cans in the fridge, one a Coca-Cola, and the other a soda you’ve never heard of, you are more likely to choose the Coca-Cola simply because you know the name.

Familiarity heuristic

The familiarity heuristic is a mental shortcut where individuals prefer options or information that is familiar to them. This heuristic is based on the notion that familiar items are seen as safer or superior. It differs from the recognition heuristic, which relies solely on whether an item is recognized. The familiarity heuristic involves a deeper sense of comfort and understanding, as opposed to just recognizing something.

An example of this heuristic is seen in investment decisions. Investors might favor well-known companies over lesser-known ones, influenced more by brand familiarity than by an objective assessment of the investment's potential. This tendency showcases how the familiarity heuristic can lead to suboptimal choices, as it prioritizes comfort and recognition over a thorough evaluation of all available options.

Availability heuristic

The availability heuristic is a cognitive bias where people judge the frequency or likelihood of events based on how easily similar instances come to mind. This mental shortcut depends on the most immediate examples that pop into one's mind when considering a topic or decision. The ease of recalling these instances often leads to a distorted perception of their actual frequency, as recent, dramatic, or emotionally charged memories tend to be more memorable.

A notable example of the availability heuristic is the public's reaction to shark attacks. When the media reports on shark attacks, these incidents become highly memorable due to their dramatic nature, leading people to overestimate the risk of such events. This heightened perception is despite statistical evidence showing the rarity of shark attacks. The result is an exaggerated fear and a skewed perception of the actual danger of swimming in the ocean.

Representativeness heuristic

The representativeness heuristic is when we try to assign an object to a specific category or idea based on past experiences. Oftentimes, this comes up when we meet people—our first impression. We expect certain things (such as clothing and credentials) to indicate that a person behaves or lives a certain way.

Without proper awareness, this heuristic can lead to discrimination in the workplace. For example, representativeness heuristics might lead us to believe that a job candidate from an Ivy League school is more qualified than one from a state university, even if their qualifications show us otherwise. This is because we expect Ivy League graduates to act a certain way, such as by being more hard-working or intelligent. Of course, in our rational brains, we know this isn’t the case. That’s why it’s important to be aware of this heuristic, so you can use logical thinking to combat potential biases.

Anchoring and adjustment heuristic

Used in finance for economic forecasting, anchoring and adjustment is when you start with an initial piece of information (the anchor) and continue adjusting until you reach an acceptable decision. The challenge is that sometimes the anchor ends up not being a good enough value to begin with. In other words, you choose the anchor based on unknown biases and then make further decisions based on this faulty assumption.

Anchoring and adjustment are often used in pricing, especially with SaaS companies. For example, a displayed, three-tiered pricing model shows you how much you get for each price point. The layout is designed to make it look like you won’t get much for the lower price, and you don’t necessarily need the highest price, so you choose the mid-level option (the original target). The anchors are the low price (suggesting there’s not much value here) and the high price (which shows that you’re getting a "discount" if you choose another option). Thanks to those two anchors, you feel like you’re getting a lot of value, no matter what you spend.

Affect heuristic

You know the advice; think with your heart. That’s the affect heuristic in action, where you make a decision based on what you’re feeling. Emotions are important ways to understand the world around us, but using them to make decisions is irrational and can impact your work.

For example, let’s say you’re about to ask your boss for a promotion. As a product marketer, you’ve made a huge impact on the company by helping to build a community of enthusiastic, loyal customers. But the day before you have your performance review , you find out that a small project you led for a new product feature failed. You decide to skip the conversation asking for a raise and instead double down on how you can improve.

In this example, you’re using the affect heuristic to base your entire performance on the failure of one small project—even though the rest of your performance (building that profitable community) is much more impactful than a new product feature. If you weighed the options rationally, you would see that asking for a raise is still a logical choice. But instead, the fear of asking for a raise after a failure felt like too big a trade-off.

Satisficing

Satisficing is when you accept an available option that’s satisfactory (i.e., just fine) instead of trying to find the best possible solution. In other words, you’re settling. This creates a “bounded rationality,” where you’re constrained by the choices that are good-enough, instead of pushing past the limits to discover more. This isn’t always negative—for lower-impact scenarios, it might not make sense to invest time and energy into finding the optimal choice. But there are also times when this heuristic kicks in and you end up settling for less than what’s possible.

For example, let’s say you’re a project manager planning the budget for the next fiscal year. Instead of looking at previous spend and revenue, you satisfice and base the budget off projections, assuming that will be good enough. But without factoring in historical data, your budget isn’t going to be as equipped to manage hiccups or unexpected changes. In this case, you can mitigate satisficing with a logically-based data review that, while longer, will produce a more accurate and thoughtful budget plan.

Trial and error heuristic

The trial and error heuristic is a problem-solving method where solutions are found through repeated experimentation. It's used when a clear path to the solution isn't known, relying on iterative learning from failures and adjustments.

For example, a chef might experiment with various ingredient combinations and techniques to perfect a new recipe. Each attempt informs the next, demonstrating how trial and error facilitates discovery in situations without formal guidelines.

Pros and cons of heuristics

Heuristics are effective at helping you get more done quickly, but they also have downsides. Psychologists don’t necessarily agree on whether heuristics and biases are positive or negative. But the argument seems to boil down to these two pros and cons:

Heuristics pros:

Simple heuristics reduce cognitive load, allowing you to accomplish more in less time with fast and frugal decisions. For example, the satisficing heuristic helps you find a "good enough" choice. So if you’re making a complex decision between whether to cut costs or invest in employee well-being , you can use satisficing to find a solution that’s a compromise. The result might not be perfect, but it allows you to take action and get started—you can always adjust later on.

Heuristics cons:

Heuristics create biases. While these cognitive biases enable us to make rapid-fire decisions, they can also lead to rigid, unhelpful beliefs. For example, confirmation bias makes it more likely that you’ll seek out other opinions that agree with your own. This makes it harder to keep an open mind, hear from the other side, and ultimately change your mind—which doesn’t help you build the flexibility and adaptability so important for succeeding in the workplace.

Heuristics and psychology

Heuristics play a pivotal role in psychology, especially in understanding how people make decisions within their cognitive limitations. These mental shortcuts allow for quicker decisions, often necessary in a fast-paced world, but they can sometimes lead to errors in judgment.

The study of heuristics bridges various aspects of psychology, from cognitive processes to behavioral outcomes, and highlights the balance between efficient decision-making and the potential for bias.

Stereotypes and heuristic thinking

Stereotypes are a form of heuristic where individuals make assumptions based on group characteristics, a process analyzed in both English and American psychology.

While these generalizations can lead to rapid conclusions and rational decisions under certain circumstances, they can also oversimplify complex human behaviors and contribute to prejudiced attitudes. Understanding stereotypes as a heuristic offers insight into the cognitive limitations of the human mind and their impact on social perceptions and interactions.

How heuristics lead to bias

Because heuristics rely on shortcuts and stereotypes, they can often lead to bias. This is especially true in scenarios where cognitive limitations restrict the processing of all relevant information. So how do you combat bias? If you acknowledge your biases, you can usually undo them and maybe even use them to your advantage. There are ways you can hack heuristics, so that they work for you (not against you):

Be aware. Heuristics often operate like a knee-jerk reaction—they’re automatic. The more aware you are, the more you can identify and acknowledge the heuristic at play. From there, you can decide if it’s useful for the current situation, or if a logical decision-making process is best.

Flip the script. When you notice a negative bias, turn it around. For example, confirmation bias is when we look for things to be as we expect. So if we expect our boss to assign us more work than our colleagues, we might always experience our work tasks as unfair. Instead, turn this around by repeating that your boss has your team’s best interests at heart, and you know everyone is working hard. This will re-train your confirmation bias to look for all the ways that your boss is treating you just like everyone else.

Practice mindfulness. Mindfulness helps to build self-awareness, so you know when heuristics are impacting your decisions. For example, when we tap into the empathy gap heuristic, we’re unable to empathize with someone else or a specific situation. However, if we’re mindful, we can be aware of how we’re feeling before we engage. This helps us to see that the judgment stems from our own emotions and probably has nothing to do with the other person.

Examples of heuristics in business

This is all well and good in theory, but how do heuristic decision-making and thought processes show up in the real world? One reason researchers have invested so much time and energy into learning about heuristics is so that they can use them, like in these scenarios:

How heuristics are used in marketing

Effective marketing does so much for a business—it attracts new customers, makes a brand a household name, and converts interest into sales, to name a few. One way marketing teams are able to accomplish all this is by applying heuristics.

Let’s use ambiguity aversion as an example. Ambiguity aversion means you're less likely to choose an item you don’t know. Marketing teams combat this by working to become familiar to their customers. This could include the social media team engaging in a more empathetic or conversational way, or employing technology like chat-bots to show that there’s always someone available to help. Making the business feel more approachable helps the customer feel like they know the brand personally—which lessens ambiguity aversion.

How heuristics are used in business strategy

Have you ever noticed how your CEO seems to know things before they happen? Or that the CFO listens more than they speak? These are indications that they understand people in a deeper way, and are able to engage with their employees and predict outcomes because of it. C-suite level executives are often experts in behavioral science, even if they didn’t study it. They tend to get what makes people tick, and know how to communicate based on these biases. In short, they use heuristics for higher-level decision-making processes and execution. 

This includes business strategy . For example, a startup CEO might be aware of their representativeness bias towards investors—they always look for the person in the room with the  fancy suit or car. But after years in the field, they know logically that this isn’t always true—plenty of their investors have shown up in shorts and sandals. Now, because they’re aware of their bias, they can build it into their investment strategy. Instead of only attending expensive, luxury events, they also attend conferences with like-minded individuals and network among peers. This approach can lead them to a greater variety of investors and more potential opportunities.

Heuristics vs algorithms

Heuristics and algorithms are both used by the brain to reduce the mental effort of decision-making, but they operate a bit differently. Algorithms act as guidelines for specific scenarios. They have a structured process designed to solve that specific problem. Heuristics, on the other hand, are general rules of thumb that help the brain process information and may or may not reach a solution.

For example, let's say you’re cooking a well-loved family recipe. You know the steps inside and out, and you no longer need to reference the instructions. If you’re following a recipe step-by-step, you’re using an algorithm. If, however, you decide on a whim to sub in some of your fresh garden vegetables because you think it will taste better, you’re using a heuristic.

How to use heuristics to make better decisions

Heuristics can help us make decisions quickly and with less cognitive strain. While they can be efficient, they sometimes lead to errors in judgment. Understanding how to use heuristics effectively can improve decision-making, especially in complex or uncertain situations.

Take time to think

Rushing often leads to reliance on automatic heuristics, which might not always be suitable. To make better decisions, slow down your thinking process. Take a step back, breathe, and allow yourself a moment of distraction. This pause can provide a fresh perspective and help you notice details or angles you might have missed initially.

Clarify your objectives

When making a decision, it's important to understand the ultimate goal. Our automatic decision-making processes tend to favor immediate benefits, sometimes overlooking long-term impacts or the needs of others involved. Consider the broader implications of your decision. Who else is affected? Is there a common objective that benefits all parties? Such considerations can lead to more holistic and effective decisions.

Manage your emotional influences

Emotions significantly influence our decision-making, often without our awareness. Fast decisions are particularly prone to emotional biases. Acknowledge your feelings, but also separate them from the facts at hand. Are you making a decision based on solid information or emotional reactions? Distinguishing between the two can lead to more rational and balanced choices.

Beware of binary thinking

All-or-nothing thinking is a common heuristic trap, where we see decisions as black or white with no middle ground. However, real-life decisions often have multiple paths and possibilities. It's important to recognize this complexity. There might be compromises or alternative options that weren't initially considered. By acknowledging the spectrum of possibilities, you can make more nuanced and effective decisions.

Heuristic FAQs

What is heuristic thinking.

Heuristic thinking refers to a method of problem-solving, learning, or discovery that employs a practical approach—often termed a "rule of thumb"—to make decisions quickly. Heuristic thinking is a type of cognition that humans use subconsciously to make decisions and judgments with limited time.

What is a heuristic evaluation?

A heuristic evaluation is a usability inspection method used in the fields of user interface (UI) and user experience (UX) design. It involves evaluators examining the interface and judging its compliance with recognized usability principles, known as heuristics. These heuristics serve as guidelines to identify usability problems in a design, making the evaluation process more systematic and comprehensive.

What are computer heuristics?

Computer heuristics are algorithms used to solve complex problems or make decisions where an exhaustive search is impractical. In fields like artificial intelligence and cybersecurity, these heuristic methods allow for efficient problem-solving and decision-making, often based on trial and error or rule-of-thumb strategies.

What are heuristics in psychology?

In psychology, heuristics are quick mental rules for making decisions. They are important in social psychology for understanding how we think and decide. Figures like Kahneman and Tversky, particularly in their work "Judgment Under Uncertainty: Heuristics and Biases," have influenced the study of heuristics in psychology.

Learn heuristics, de-mystify your brain

Your brain doesn’t actually work in mysterious ways. In reality, researchers know why we do a lot of the things we do. Heuristics help us to understand the choices we make that don’t make much sense. Once you understand heuristics, you can also learn to use them to your advantage—both in business, and in life. 

Related resources

How Asana streamlines strategic planning with work management

How to create a CRM strategy: 6 steps (with examples)

What is management by objectives (MBO)?

Write better AI prompts: A 4-sentence framework

7.3 Problem-Solving

Learning objectives.

By the end of this section, you will be able to:

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving

   People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.

PROBLEM-SOLVING STRATEGIES

   When people are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them (table below). For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

   Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.

Additional Problem Solving Strategies :

• Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
• Analogy – is using a solution that solves a similar problem.
• Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
• Divide and conquer – breaking down large complex problems into smaller more manageable problems.
• Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
• Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
• Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
• Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
• Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
• Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
• Reduction – adapting the problem to be as similar problems where a solution exists.
• Research – using existing knowledge or solutions to similar problems to solve the problem.
• Root cause analysis – trying to identify the cause of the problem.

The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.

One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :

Missionary-Cannibal Problem

Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.

Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.

The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:

• 1. Only one disk can be moved at a time.
• 2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
• 3. No disc may be placed on top of a smaller disk.

  Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.

Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.

The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.

As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage  (1990) suggesting that while collecting data for what would later be his book  The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.

While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as  insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).

While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.

Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground.  Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).

Solving puzzles.

   Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

   Here is another popular type of puzzle (figure below) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

   Take a look at the “Puzzling Scales” logic puzzle below (figure below). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

What steps did you take to solve this puzzle? You can read the solution at the end of this section.

Pitfalls to problem solving.

   Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

   Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in the table below.

Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.

   Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

References:

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology

Review Questions:

1. A specific formula for solving a problem is called ________.

a. an algorithm

b. a heuristic

c. a mental set

d. trial and error

2. Solving the Tower of Hanoi problem tends to utilize a  ________ strategy of problem solving.

a. divide and conquer

b. means-end analysis

d. experiment

3. A mental shortcut in the form of a general problem-solving framework is called ________.

4. Which type of bias involves becoming fixated on a single trait of a problem?

a. anchoring bias

b. confirmation bias

c. representative bias

d. availability bias

5. Which type of bias involves relying on a false stereotype to make a decision?

6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.

a. social adjustment

b. student load payment options

c. emotional learning

d. insight learning

7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.

a. functional fixedness

c. working memory

Critical Thinking Questions:

1. What is functional fixedness and how can overcoming it help you solve problems?

2. How does an algorithm save you time and energy when solving a problem?

Personal Application Question:

1. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

anchoring bias

availability heuristic

confirmation bias

functional fixedness

hindsight bias

problem-solving strategy

representative bias

trial and error

working backwards

Answers to Exercises

algorithm:  problem-solving strategy characterized by a specific set of instructions

anchoring bias:  faulty heuristic in which you fixate on a single aspect of a problem to find a solution

availability heuristic:  faulty heuristic in which you make a decision based on information readily available to you

confirmation bias:  faulty heuristic in which you focus on information that confirms your beliefs

functional fixedness:  inability to see an object as useful for any other use other than the one for which it was intended

heuristic:  mental shortcut that saves time when solving a problem

hindsight bias:  belief that the event just experienced was predictable, even though it really wasn’t

mental set:  continually using an old solution to a problem without results

problem-solving strategy:  method for solving problems

representative bias:  faulty heuristic in which you stereotype someone or something without a valid basis for your judgment

trial and error:  problem-solving strategy in which multiple solutions are attempted until the correct one is found

working backwards:  heuristic in which you begin to solve a problem by focusing on the end result

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8.2 Problem-Solving: Heuristics and Algorithms

Learning objectives.

• Describe the differences between heuristics and algorithms in information processing.

When faced with a problem to solve, should you go with intuition or with more measured, logical reasoning? Obviously, we use both of these approaches. Some of the decisions we make are rapid, emotional, and automatic. Daniel Kahneman (2011) calls this “fast” thinking. By definition, fast thinking saves time. For example, you may quickly decide to buy something because it is on sale; your fast brain has perceived a bargain, and you go for it quickly. On the other hand, “slow” thinking requires more effort; applying this in the same scenario might cause us not to buy the item because we have reasoned that we don’t really need it, that it is still too expensive, and so on. Using slow and fast thinking does not guarantee good decision-making if they are employed at the wrong time. Sometimes it is not clear which is called for, because many decisions have a level of uncertainty built into them. In this section, we will explore some of the applications of these tendencies to think fast or slow.

We will look further into our thought processes, more specifically, into some of the problem-solving strategies that we use. Heuristics are information-processing strategies that are useful in many cases but may lead to errors when misapplied. A heuristic is a principle with broad application, essentially an educated guess about something. We use heuristics all the time, for example, when deciding what groceries to buy from the supermarket, when looking for a library book, when choosing the best route to drive through town to avoid traffic congestion, and so on. Heuristics can be thought of as aids to decision making; they allow us to reach a solution without a lot of cognitive effort or time.

The benefit of heuristics in helping us reach decisions fairly easily is also the potential downfall: the solution provided by the use of heuristics is not necessarily the best one. Let’s consider some of the most frequently applied, and misapplied, heuristics in the table below.

In many cases, we base our judgments on information that seems to represent, or match, what we expect will happen, while ignoring other potentially more relevant statistical information. When we do so, we are using the representativeness heuristic . Consider, for instance, the data presented in the table below. Let’s say that you went to a hospital, and you checked the records of the babies that were born on that given day. Which pattern of births do you think you are most likely to find?

Most people think that list B is more likely, probably because list B looks more random, and matches — or is “representative of” — our ideas about randomness, but statisticians know that any pattern of four girls and four boys is mathematically equally likely. Whether a boy or girl is born first has no bearing on what sex will be born second; these are independent events, each with a 50:50 chance of being a boy or a girl. The problem is that we have a schema of what randomness should be like, which does not always match what is mathematically the case. Similarly, people who see a flipped coin come up “heads” five times in a row will frequently predict, and perhaps even wager money, that “tails” will be next. This behaviour is known as the gambler’s fallacy . Mathematically, the gambler’s fallacy is an error: the likelihood of any single coin flip being “tails” is always 50%, regardless of how many times it has come up “heads” in the past.

The representativeness heuristic may explain why we judge people on the basis of appearance. Suppose you meet your new next-door neighbour, who drives a loud motorcycle, has many tattoos, wears leather, and has long hair. Later, you try to guess their occupation. What comes to mind most readily? Are they a teacher? Insurance salesman? IT specialist? Librarian? Drug dealer? The representativeness heuristic will lead you to compare your neighbour to the prototypes you have for these occupations and choose the one that they seem to represent the best. Thus, your judgment is affected by how much your neibour seems to resemble each of these groups. Sometimes these judgments are accurate, but they often fail because they do not account for base rates , which is the actual frequency with which these groups exist. In this case, the group with the lowest base rate is probably drug dealer.

Our judgments can also be influenced by how easy it is to retrieve a memory. The tendency to make judgments of the frequency or likelihood that an event occurs on the basis of the ease with which it can be retrieved from memory is known as the availability heuristic (MacLeod & Campbell, 1992; Tversky & Kahneman, 1973). Imagine, for instance, that I asked you to indicate whether there are more words in the English language that begin with the letter “R” or that have the letter “R” as the third letter. You would probably answer this question by trying to think of words that have each of the characteristics, thinking of all the words you know that begin with “R” and all that have “R” in the third position. Because it is much easier to retrieve words by their first letter than by their third, we may incorrectly guess that there are more words that begin with “R,” even though there are in fact more words that have “R” as the third letter.

The availability heuristic may explain why we tend to overestimate the likelihood of crimes or disasters; those that are reported widely in the news are more readily imaginable, and therefore, we tend to overestimate how often they occur. Things that we find easy to imagine, or to remember from watching the news, are estimated to occur frequently. Anything that gets a lot of news coverage is easy to imagine. Availability bias does not just affect our thinking. It can change behaviour. For example, homicides are usually widely reported in the news, leading people to make inaccurate assumptions about the frequency of murder. In Canada, the murder rate has dropped steadily since the 1970s (Statistics Canada, 2018), but this information tends not to be reported, leading people to overestimate the probability of being affected by violent crime. In another example, doctors who recently treated patients suffering from a particular condition were more likely to diagnose the condition in subsequent patients because they overestimated the prevalence of the condition (Poses & Anthony, 1991).

The anchoring and adjustment heuristic is another example of how fast thinking can lead to a decision that might not be optimal. Anchoring and adjustment is easily seen when we are faced with buying something that does not have a fixed price. For example, if you are interested in a used car, and the asking price is $10,000, what price do you think you might offer? Using $10,000 as an anchor, you are likely to adjust your offer from there, and perhaps offer $9000 or $9500. Never mind that $10,000 may not be a reasonable anchoring price. Anchoring and adjustment does not just happen when we’re buying something. It can also be used in any situation that calls for judgment under uncertainty, such as sentencing decisions in criminal cases (Bennett, 2014), and it applies to groups as well as individuals (Rutledge, 1993).

In contrast to heuristics, which can be thought of as problem-solving strategies based on educated guesses, algorithms are problem-solving strategies that use rules. Algorithms are generally a logical set of steps that, if applied correctly, should be accurate. For example, you could make a cake using heuristics — relying on your previous baking experience and guessing at the number and amount of ingredients, baking time, and so on — or using an algorithm. The latter would require a recipe which would provide step-by-step instructions; the recipe is the algorithm. Unless you are an extremely accomplished baker, the algorithm should provide you with a better cake than using heuristics would. While heuristics offer a solution that might be correct, a correctly applied algorithm is guaranteed to provide a correct solution. Of course, not all problems can be solved by algorithms.

As with heuristics, the use of algorithmic processing interacts with behaviour and emotion. Understanding what strategy might provide the best solution requires knowledge and experience. As we will see in the next section, we are prone to a number of cognitive biases that persist despite knowledge and experience.

Key Takeaways

• We use a variety of shortcuts in our information processing, such as the representativeness, availability, and anchoring and adjustment heuristics. These help us to make fast judgments but may lead to errors.
• Algorithms are problem-solving strategies that are based on rules rather than guesses. Algorithms, if applied correctly, are far less likely to result in errors or incorrect solutions than heuristics. Algorithms are based on logic.

Bennett, M. W. (2014). Confronting cognitive ‘anchoring effect’ and ‘blind spot’ biases in federal sentencing: A modest solution for reforming and fundamental flaw. Journal of Criminal Law and Criminology , 104 (3), 489-534.

Kahneman, D. (2011). Thinking, fast and slow. New York, NY: Farrar, Straus and Giroux.

MacLeod, C., & Campbell, L. (1992). Memory accessibility and probability judgments: An experimental evaluation of the availability heuristic.  Journal of Personality and Social Psychology, 63 (6), 890–902.

Poses, R. M., & Anthony, M. (1991). Availability, wishful thinking, and physicians’ diagnostic judgments for patients with suspected bacteremia.  Medical Decision Making,  11 , 159-68.

Rutledge, R. W. (1993). The effects of group decisions and group-shifts on use of the anchoring and adjustment heuristic. Social Behavior and Personality, 21 (3), 215-226.

Statistics Canada. (2018). Ho micide in Canada, 2017 . Retrieved from https://www150.statcan.gc.ca/n1/en/daily-quotidien/181121/dq181121a-eng.pdf

Tversky, A., & Kahneman, D. (1973). Availability: A heuristic for judging frequency and probability.  Cognitive Psychology, 5 , 207–232.

Psychology - 1st Canadian Edition Copyright © 2020 by Sally Walters is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Why do we take mental shortcuts?

What are heuristics.

Heuristics are mental shortcuts that can facilitate problem-solving and probability judgments. These strategies are generalizations, or rules-of-thumb, that reduce cognitive load. They can be effective for making immediate judgments, however, they often result in irrational or inaccurate conclusions.

Where this bias occurs

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We use heuristics in all sorts of situations. One type of heuristic, the availability heuristic , often happens when we’re attempting to judge the frequency with which a certain event occurs. Say, for example, someone asked you whether more tornadoes occur in Kansas or Nebraska. Most of us can easily call to mind an example of a tornado in Kansas: the tornado that whisked Dorothy Gale off to Oz in Frank L. Baum’s The Wizard of Oz . Although it’s fictional, this example comes to us easily. On the other hand, most people have a lot of trouble calling to mind an example of a tornado in Nebraska. This leads us to believe that tornadoes are more common in Kansas than in Nebraska. However, the states actually report similar levels. 1

Individual effects

The thing about heuristics is that they aren’t always wrong. As generalizations, there are many situations where they can yield accurate predictions or result in good decision-making. However, even if the outcome is favorable, it was not achieved through logical means. When we use heuristics, we risk ignoring important information and overvaluing what is less relevant. There’s no guarantee that using  heuristics will work out and, even if it does, we’ll be making the decision for the wrong reason. Instead of basing it on reason, our behavior is resulting from a mental shortcut with no real rationale to support it.

Systemic effects

Heuristics become more concerning when applied to politics, academia, and economics. We may all resort to heuristics from time to time, something that is true even of members of important institutions who are tasked with making large, influential decisions. It is necessary for these figures to have a comprehensive understanding of the biases and heuristics that can affect our behavior, so as to promote accuracy on their part.

How it affects product

Heuristics can be useful in product design. Specifically, because heuristics are intuitive to us, they can be applied to create a more user-friendly experience and one that is more valuable to the customer. For example, color psychology is a phenomenon explaining how our experiences with different colors and color families can prime certain emotions or behaviors. Taking advantage of the representativeness heuristic, one could choose to use passive colors (blue or green) or more active colors (red, yellow, orange) depending on the goals of the application or product. 18 For example, if a developer is trying to evoke a feeling of calm for their app that provides guided meditations, they may choose to make the primary colors of the program light blues and greens. Colors like red and orange are more emotionally energizing and may be useful in settings like gyms or crossfit programs. 

By integrating heuristics into products we can enhance the user experience. If an application, device, or item includes features that make it feel intuitive, easy to navigate and familiar, customers will be more inclined to continue to use it and recommend it to others. Appealing to those mental shortcuts we can minimize the chances of user error or frustration with a product that is overly complicated.

Heuristics and AI

Artificial intelligence and machine learning tools already use the power of heuristics to inform its output. In a nutshell, simple AI tools operate based on a set of built in rules and sometimes heuristics! These are encoded within the system thus aiding in decision-making and the presentation of learning material. Heuristic algorithms can be used to solve advanced computational problems, providing efficient and approximate solutions.  Like in humans, the use of heuristics can result in error, and thus must be used with caution. However, machine learning tools and AI can be useful in supporting human decision-making, especially when clouded by emotion, bias or irrationality due to our own susceptibility to heuristics. 

Why it happens

In their paper “Judgment Under Uncertainty: Heuristics and Biases” 2 , Daniel Kahneman and Amos Tversky identified three different kinds of heuristics: availability, representativeness, as well as anchoring and adjustment. Each type of heuristic is used for the purpose of reducing the mental effort needed to make a decision, but they occur in different contexts.

Availability heuristic

The availability heuristic, as defined by Kahneman and Tversky, is the mental shortcut used for making frequency or probability judgments based on “the ease with which instances or occurrences can be brought to mind”. 3 This was touched upon in the previous example, judging the frequency with which tornadoes occur in Kansas relative to Nebraska. 3

The availability heuristic occurs because certain memories come to mind more easily than others. In Kahneman and Tversky’s example participants were asked if more words in the English language start with the letter K or have K as the third letter  Interestingly, most participants responded with the former when in actuality, it is the latter that is true. The idea being that it is much more difficult to think of words that have K as the third letter than it is to think of words that start with K. 4 In this case,  words that begin with K are more readily available to us than words with the K as the third letter.

Representativeness heuristic

Individuals tend to classify events into categories, which, as illustrated by Kahneman and Tversky, can result in our use of the representativeness heuristic. When we use this heuristic, we categorize events or objects based on how they relate to instances we are already familiar with.  Essentially, we have built our own categories, which we use to make predictions about novel situations or people. 5 For example, if someone we meet in one of our university lectures looks and acts like what we believe to be a stereotypical medical student, we may judge the probability that they are studying medicine as highly likely, even without any hard evidence to support that assumption.

The representativeness heuristic is associated with prototype theory. 6 This prominent theory in cognitive science, the prototype theory explains object and identity recognition. It suggests that we categorize different objects and identities in our memory. For example, we may have a category for chairs, a category for fish, a category for books, and so on. Prototype theory posits that we develop prototypical examples for these categories by averaging every example of a given category we encounter. As such, our prototype of a chair should be the most average example of a chair possible, based on our experience with that object. This process aids in object identification because we compare every object we encounter against the prototypes stored in our memory. The more the object resembles the prototype, the more confident we are that it belongs in that category. 

Prototype theory may give rise to the representativeness heuristic as it is in situations when a particular object or event is viewed as similar to the prototype stored in our memory, which leads us to classify the object or event into the category represented by that prototype. To go back to the previous example, if your peer closely resembles your prototypical example of a med student, you may place them into that category based on the prototype theory of object and identity recognition. This, however, causes you to commit the representativeness heuristic.

Anchoring and adjustment heuristic

Another heuristic put forth by Kahneman and Tversky in their initial paper is the anchoring and adjustment heuristic. 7 This heuristic describes how, when estimating a certain value, we tend to give an initial value, then adjust it by increasing or decreasing our estimation. However, we often get stuck on that initial value – which is referred to as anchoring – this results in us making insufficient adjustments. Thus, the adjusted value is biased in favor of the initial value we have anchored to.

In an example of the anchoring and adjustment heuristic, Kahneman and Tversky gave participants questions such as “estimate the number of African countries in the United Nations (UN).” A wheel labeled with numbers from 0-100 was spun, and participants were asked to say whether or not the number the wheel landed on was higher or lower than their answer to the question. Then, participants were asked to estimate the number of African countries in the UN, independent from the number they had spun. Regardless, Kahneman and Tversky found that participants tended to anchor onto the random number obtained by spinning the wheel. The results showed that  when the number obtained by spinning the wheel was 10, the median estimate given by participants was 25, while, when the number obtained from the wheel was 65, participants’ median estimate was 45.8.

A 2006 study by Epley and Gilovich, “The Anchoring and Adjustment Heuristic: Why the Adjustments are Insufficient” 9 investigated the causes of this heuristic. They illustrated that anchoring often occurs because the new information that we anchor to is more accessible than other information Furthermore, they provided empirical evidence to demonstrate that our adjustments tend to be insufficient because they require significant mental effort, which we are not always motivated to dedicate to the task. They also found that providing incentives for accuracy led participants to make more sufficient adjustments. So, this particular heuristic generally occurs when there is no real incentive to provide an accurate response.

Quick and easy

Though different in their explanations, these three types of heuristics allow us to respond automatically without much effortful thought. They provide an immediate response and do not use up much of our mental energy, which allows us to dedicate mental resources to other matters that may be more pressing. In that way, heuristics are efficient, which is a big reason why we continue to use them. That being said, we should be mindful of how much we rely on them because there is no guarantee of their accuracy.

Why it is important

As illustrated by Tversky and Kahneman, using heuristics can cause us to engage in various cognitive biases and commit certain fallacies. 10 As a result, we may make poor decisions, as well as inaccurate judgments and predictions. Awareness of heuristics can aid us in avoiding them, which will ultimately lead us to engage in more adaptive behaviors.

How to avoid it

Heuristics arise from automatic System 1 thinking. It is a common misconception that errors in judgment can be avoided by relying exclusively on System 2 thinking. However, as pointed out by Kahneman, neither System 2 nor System 1 are infallible. 11   While System 1 can result in relying on heuristics leading to certain biases, System 2 can give rise to other biases, such as the confirmation bias . 12 In truth, Systems 1 and 2 complement each other, and using them together can lead to more rational decision-making. That is, we shouldn’t make judgments automatically, without a second thought, but we shouldn’t overthink things to the point where we’re looking for specific evidence to support our stance. Thus, heuristics can be avoided by making judgments more effortfully, but in doing so, we should attempt not to overanalyze the situation.

How it all started

The first three heuristics – availability, representativeness, as well as anchoring and adjustment – were identified by Tverksy and Kahneman in their 1974 paper, “Judgment Under Uncertainty: Heuristics and Biases”. 13 In addition to presenting these heuristics and their relevant experiments, they listed the respective biases each can lead to.

For instance, upon defining the availability heuristic, they demonstrated how it may lead to illusory correlation , which is the erroneous belief that two events frequently co-occur. Kahneman and Tversky made the connection by illustrating how the availability heuristic can cause us to over- or under-estimate the frequency with which certain events occur. This may result in drawing correlations between variables when in reality there are none.  

Referring to our tendency to overestimate our accuracy making probability judgments, Kahneman and Tversky also discussed how the illusion of validity is facilitated by the representativeness heuristic. The more representative an object or event is, the more confident we feel in predicting certain outcomes. The illusion of validity, as it works with the representativeness heuristic, can be demonstrated by our assumptions of others based on past experiences. If you have only ever had good experiences with people from Canada, you will be inclined to judge most Canadians as pleasant. In reality, your small sample size cannot account for the whole population. Representativeness is not the only factor in determining the probability of an outcome or event, meaning we should not be as confident in our predictive abilities.

Example 1 – Advertising

Those in the field of advertising should have a working understanding of heuristics as consumers often rely on these shortcuts when making decisions about purchases. One heuristic that frequently comes into play in the realm of advertising is the scarcity heuristic . When assessing the value of something, we often fall back on this heuristic, leading us to believe that the rarity or exclusiveness of an object contributes to its value.

A 2011 study by Praveen Aggarwal, Sung Yul Jun, and Jong Ho Huh evaluated the impact of “scarcity messages” on consumer behavior. They found that both “limited quantity” and “limited time” advertisements influence consumers’ intentions to purchase, but “limited quantity” messages are more effective. This explains why people get so excited over the one-day-only Black Friday sales, and why the countdowns of units available on home shopping television frequently lead to impulse buys. 14

Knowledge of the scarcity heuristic can help businesses thrive, as “limited quantity” messages make potential consumers competitive and increase their intentions to purchase. 15 This marketing technique can be a useful tool for bolstering sales and bringing attention to your business.

Example 2 – Stereotypes

One of the downfalls of heuristics is that they have the potential to lead to stereotyping, which is often harmful. Kahneman and Tversky illustrated how the representativeness heuristic might result in the propagation of stereotypes. The researchers presented participants with a personality sketch of a fictional man named Steve followed by a list of possible occupations. Participants were tasked with ranking the likelihood of each occupation being Steve’s. Since the personality sketch described Steve as shy, helpful, introverted, and organized, participants tended to indicate that it was probable that he was a  librarian. 16 In this particular case the stereotype is less harmful than many others, however it accurately illustrates the link between heuristics and stereotypes.

Published in 1989, Patricia Devine’s paper “Stereotypes and Prejudice: Their Automatic and Controlled Components” illustrates how, even among people who are low in prejudice, rejecting stereotypes requires a certain level of motivation and cognitive capacity. 17 We typically use heuristics in order to avoid exerting too much mental energy, specifically when we are not sufficiently motivated to dedicate mental resources to the task at hand. Thus, when we lack the mental capacity to make a judgment or decision effortfully, we may rely upon automatic heuristic responses and, in doing so, risk propagating stereotypes.

Stereotypes are an example of how heuristics can go wrong. Broad generalizations do not always apply, and their continued use can have serious consequences. This underscores the importance of effortful judgment and decision-making, as opposed to automatic.

Heuristics are mental shortcuts that allow us to make quick judgment calls based on generalizations or rules of thumb.

Heuristics, in general, occur because they are efficient ways of responding when we are faced with problems or decisions. They come about automatically, allowing us to allocate our mental energy elsewhere. Specific heuristics occur in different contexts; the availability heuristic happens because we remember certain memories better than others, the representativeness heuristic can be explained by prototype theory, and the anchoring and adjustment heuristic occurs due to lack of incentive to put in the effort required for sufficient adjustment.

The scarcity heuristic, which refers to how we value items more when they are limited, can be used to the advantage of businesses looking to increase sales. Research has shown that advertising objects as “limited quantity” increases consumers' competitiveness and their intentions to buy the item.

While heuristics can be useful, we should exert caution, as they are generalizations that may lead us to propagate stereotypes ranging from inaccurate to harmful.

Putting more effort into decision-making instead of making decisions automatically can help us avoid heuristics. Doing so requires more mental resources, but it will lead to more rational choices.

Related TDL articles

What are heuristics.

This interview with The Decision Lab’s Managing Director Sekoul Krastev delves into the history of heuristics, their applications in the real world, and their consequences, both positive and negative.

10 Decision-Making Errors that Hold Us Back at Work

In this article, Dr. Melina Moleskis examines the common decision-making errors that occur in the workplace. Everything from taking in feedback provided by customers to cracking the problems of on-the-fly decision-making, Dr. Moleskis delivers workable solutions that anyone can implement. 

• Gilovich, T., Keltner, D., Chen. S, and Nisbett, R. (2015).  Social Psychology  (4th edition). W.W. Norton and Co. Inc.
• Tversky, A. and Kahneman, D. (1974). Judgment Under Uncertainty: Heuristics and Biases.  Science . 185(4157), 1124-1131.
• Mervis, C. B., & Rosch, E. (1981). Categorization of natural objects.  Annual Review of Psychology ,  32 (1), 89–115. https://doi.org/10.1146/annurev.ps.32.020181.000513
• Epley, N., & Gilovich, T. (2006). The anchoring-and-adjustment heuristic.  Psychological Science -Cambridge- ,  17 (4), 311–318.
• System 1 and System 2 Thinking.  The Marketing Society.  https://www.marketingsociety.com/think-piece/system-1-and-system-2-thinking
• Aggarwal, P., Jun, S. Y., & Huh, J. H. (2011). Scarcity messages.  Journal of Advertising ,  40 (3), 19–30.
• Devine, P. G. (1989). Stereotypes and prejudice: their automatic and controlled components.  Journal of Personality and Social Psychology ,  56 (1), 5–18. https://doi.org/10.1037/0022-3514.56.1.5
• Kuo, L., Chang, T., &amp; Lai, C.-C. (2022). Research on product design modeling image and color psychological test. Displays, 71, 102108. https://doi.org/10.1016/j.displa.2021.102108

About the Authors

Dan is a Co-Founder and Managing Director at The Decision Lab. He is a bestselling author of Intention - a book he wrote with Wiley on the mindful application of behavioral science in organizations. Dan has a background in organizational decision making, with a BComm in Decision & Information Systems from McGill University. He has worked on enterprise-level behavioral architecture at TD Securities and BMO Capital Markets, where he advised management on the implementation of systems processing billions of dollars per week. Driven by an appetite for the latest in technology, Dan created a course on business intelligence and lectured at McGill University, and has applied behavioral science to topics such as augmented and virtual reality.

Dr. Sekoul Krastev

Sekoul is a Co-Founder and Managing Director at The Decision Lab. He is a bestselling author of Intention - a book he wrote with Wiley on the mindful application of behavioral science in organizations. A decision scientist with a PhD in Decision Neuroscience from McGill University, Sekoul's work has been featured in peer-reviewed journals and has been presented at conferences around the world. Sekoul previously advised management on innovation and engagement strategy at The Boston Consulting Group as well as on online media strategy at Google. He has a deep interest in the applications of behavioral science to new technology and has published on these topics in places such as the Huffington Post and Strategy & Business.

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Table of Contents

What is heuristics, history of heuristics, types of heuristics, advantages of heuristics, heuristics & cognitive bias, making quick decisions with heuristics, heuristics at a glance.

Heuristics are mental shortcut techniques used to solve problems and make decisions efficiently. These techniques are used to reduce the decision making time and allow the individual to function without interrupting their next course of action.

Heuristics are a time-saving approach to solving problems and making decisions efficiently. Heuristics processes are usually used to find quick answers and solutions to problems. However, decisions based on this mindset are not always accurate. They serve as quick mental references that are used for everyday problems and experiences.

Humans and animals resort to this mindset because processing every information that comes into the brain takes time and effort. With the help of these shortcut techniques, the brain can make faster and efficient decisions despite the consequences. This is known as the accuracy effort trade-off theory. This theory works because not every decision requires the same amount of time and energy.

Hence, people use it as a means to save time. Another reason why people resort to heuristics is that the brain simply doesn’t have the capacity to process everything and so they must resort to these mental shortcuts to make quick decisions. A 2014 study 1 Mousavi, S., & Gigerenzer, G. (2014). Risk, uncertainty, and heuristics.  Journal of Business Research ,  67 (8), 1671-1678.  https://doi.org/10.1016/j.jbusres.2014.02.013 demonstrated that in case of uncertainty and a lack of information, heuristics allows a “less is more effect” wherein less information leads to more accuracy. It is worth mentioning that the applicability and usefulness of heuristics depend on the situation.

A 2011 study 2 Gigerenzer G, Gaissmaier W. Heuristic decision making. Annu Rev Psychol. 2011;62:451-82. doi: 10.1146/annurev-psych-120709-145346. PMID: 21126183. pointed out that there may be two reasons for relying on heuristics. They are:

• Individuals and organizations often rely on simple heuristics in an adaptive way
• Ignoring part of the information can lead to more accurate judgments than weighing and adding all information

Although heuristics are useful, sometimes they can be inaccurate. In case an individual relies on it too heavily, it may result in incorrect judgments or cognitive biases. Understanding commonly unfavorable heuristics and identifying situations that may affect behavior can help individuals avoid mental pitfalls. It is important to assess major problems by making a list of pros and cons. In order to avoid inaccurate decisions, you can consult trusted individuals, take time to think through things where quick decisions may cause significant problems such as catching an important flight. Hence, it is important to be mindful of the information that is being processed in the brain to make accurate decisions.

Nobel prize-winning psychologist, Herbert Simon suggested that although people attempt to make rational decisions, humans are subject to cognitive limitations. A 2013 study 3 Rachlin, H. (2003). Rational thought and rational behavior: A review of bounded rationality: The adaptive toolbox. Journal of the Experimental Analysis of Behavior, 79(3), 409-412. https://doi.org/10.1901/jeab.2003.79-409 pointed out that rational decisions involve weighing different factors such as potential costs against potential benefits. People are often limited by time to make choices as well as the amount of information we have at our disposal. Other factors that influence our thinking are overall intelligence and accuracy of perceptions.

Psychologists Amos Tversky and Daniel Kahneman proposed that cognitive biases influence how people think and the judgements people make about events. Due to these limitations, we are often forced to rely on our instinctive shortcuts i.e heuristics to make sense of the world. Simon’s research indicated that humans have a limited ability to make rational decisions. On the other hand, Tversky and Kahneman’s research 4 Kahneman, D., & Tversky, A. (1977). Prospect theory. An analysis of decision making under risk. https://doi.org/10.21236/ada045771 represented how people have specific ways to simplify the decision-making process.

Read More About Decision-Making Here

Some of the common heuristics may include the following:

1. Availability Heuristics

This involves making decisions based on the information that is readily available in one’s mind. When an individual makes a decision, they immediately refer to a number of relevant examples. Since the relevant information is readily available in their memory, they are more likely to conclude that these outcomes are common. For example, dramatic, violent deaths are usually more highly publicized and hence have higher availability.

Another instance where availability heuristics may work is if an individual is thinking about taking a trip and thinks of a number of recent airline accidents. This may lead them to think that air travel is dangerous. This may also enable them to resort to traveling by car instead. Since airline disasters came to their mind easily, the availability heuristics lead them to think that plane crashes are more common even though it may not be entirely true.

2. Representative Heuristics

This involves making a decision based on the comparison of the present situation and the most relevant mental prototype. In case an individual is trying to decide if someone is trustworthy they may compare the incident with other mental examples. For instance, an older woman sitting beside you at a train station may remind you of your grandmother. You may immediately assume that she may be kind, gentle, and trustworthy. People tend to believe in the existing mental information since the traits match up to the individual’s mental prototype.

3. Affect Heuristics

This involves making choices that are influenced by emotions that an individual is experiencing at that moment. Research 5 Finucane, M. L., Alhakami, A., Slovic, P., & Johnson, S. M. (2000). The affect heuristic in judgments of risks and benefits. Journal of Behavioral Decision Making, 13(1), 1-17. https://doi.org/10.1002/(sici)1099-0771(200001/03)13:1<1::aid-bdm333>3.0.co;2-s has demonstrated that people are more likely to view decisions as having benefits and lower risks when their mood is positive. However, negative emotions lead people to focus on the potential downfall of a decision rather than the possible benefits.

4. Satisficing Heuristics

This is a decision making strategy wherein the first option that fulfills the criteria is selected even if there are better alternatives available. Hebert Simon formulated the concept of satisficing. This theory 6 Simon, H. A. (1955). A behavioral model of rational choice. The Quarterly Journal of Economics, 69(1), 99. https://doi.org/10.2307/1884852 is used to choose one alternative from a set of alternatives in situations of uncertainty. In this case, uncertainty refers to the total set of alternatives and their consequences that cannot be known or foreseen. For instance, professional real estate entrepreneurs rely on this theory to decide where they should invest to develop new commercial areas. Although there may be better alternatives available, they resort to the first option that fulfills their criteria.

Some of the most common advantages of using this cognitive approach are:

• Facilitates timely decisions
• Makes decision making simpler
• Less information, more accuracy
• Quick answers to problems
• Reduces complex information into simple and manageable set of choices
• Frees up cognitive resources for more complex planning

Although heuristics can advance our problems and decision-making process, it can even cause errors. It can often lead to inaccurate judgments based on how common things can occur and how certain events influence our decisions. It is important to realize that even though something worked in the past, it doesn’t necessarily mean that it will work again. Relying on existing heuristics can make it difficult to see alternatives or brainstorm new ideas. A 2014 study pointed out that heuristics can also contribute to other things such as stereotypes and prejudice. Due to this people often overlook more relevant information and create stereotypical categorization that is not entirely true.

Read More About Cognitive Bias Here

Heuristics allow us to make quick decisions and make our life easier. It is often accurate. However, it is important to be aware of what is influencing our decisions in order to avoid potential cognitive biases. This will allow us to make more accurate decisions.

• Heuristics are mental shortcut techniques used to solve problems and make decisions efficiently.
• Heuristics processes are usually used to find quick answers and solutions to problems.
• They serve as quick mental references that are used for everyday problems and experiences.
• With the help of these shortcut techniques, the brain can make faster and efficient decisions despite the consequences.
• Sometimes it may result in incorrect judgments or cognitive biases.
• It is important to be aware of what is influencing our decisions in order to avoid potential cognitive biases.

References:

• 1 Mousavi, S., & Gigerenzer, G. (2014). Risk, uncertainty, and heuristics.  Journal of Business Research ,  67 (8), 1671-1678.  https://doi.org/10.1016/j.jbusres.2014.02.013
• 2 Gigerenzer G, Gaissmaier W. Heuristic decision making. Annu Rev Psychol. 2011;62:451-82. doi: 10.1146/annurev-psych-120709-145346. PMID: 21126183.
• 3 Rachlin, H. (2003). Rational thought and rational behavior: A review of bounded rationality: The adaptive toolbox. Journal of the Experimental Analysis of Behavior, 79(3), 409-412. https://doi.org/10.1901/jeab.2003.79-409
• 4 Kahneman, D., & Tversky, A. (1977). Prospect theory. An analysis of decision making under risk. https://doi.org/10.21236/ada045771
• 5 Finucane, M. L., Alhakami, A., Slovic, P., & Johnson, S. M. (2000). The affect heuristic in judgments of risks and benefits. Journal of Behavioral Decision Making, 13(1), 1-17. https://doi.org/10.1002/(sici)1099-0771(200001/03)13:1<1::aid-bdm333>3.0.co;2-s
• 6 Simon, H. A. (1955). A behavioral model of rational choice. The Quarterly Journal of Economics, 69(1), 99. https://doi.org/10.2307/1884852

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Heuristics Are the Building Blocks of Human Behavior

Though heuristics are often seen as flawed, they are effective most of the time..

Posted October 5, 2020 | Reviewed by Lybi Ma

Consider the following scenario: you are watching a movie in your living room. One of the supporting characters is played by someone who looks familiar, but you can’t quite put your finger on where you’ve seen that person before. It will drive you crazy until you figure it out, so what do you do?

If you’re like most people, you’d probably go straight to the internet to find the answer. In a matter of moments, you’ve likely satisfied your curiosity and acquired more information about that actor than you ever wanted to know.

When such situations arise, most people don’t expend much effort thinking through where to find the information they’re looking for. They behave as if they instinctively know the answer will be on the internet (and most likely Wikipedia).

But it isn’t instinctual at all. Instincts are inborn, but the nearly automatic decision to search the internet is learned – and by a lot of people. In fact, the decision to search Google [1] is made more than 3.5 billion times per day . Though that decision largely occurs without much conscious effort, it isn’t because of instinct. It’s because most people have developed a heuristic – a mental shortcut used to solve problems – in which searching the internet becomes a nearly automatic solution to answer a myriad of questions. Gigerenzer and Gaissmaier (2011) defined a heuristic as “a strategy that ignores part of the information, with the goal of making decisions more quickly, frugally, and/or accurately than more complex methods” (p. 454).

We rely on heuristics a lot. They help us make most of the decisions in our daily lives. Decisions such as what time we get up, the route we take to work, even how we work all generally rely heavily on heuristics. But heuristics don’t just operate when things go according to plan. If surprises pop up, such as slow traffic due to an accident, many people have developed heuristics that guide them in selecting an alternative route.

So, it stands to reason that without heuristics, we would run into a lot of problems trying to make decisions. Unfortunately, heuristics, like biases , are often discussed in a very negative way. The negativity toward heuristics largely stems from academic research focusing on the ways they can result in suboptimal decisions [2] . Yet, how suboptimal those decisions are can be quite subjective. Therefore, the utility of heuristics requires a little bit more of a nuanced discussion.

What Heuristics Are and How They Benefit Us

The word heuristic comes from the Greek word heuriskein , which means to discover. Any problem-solving shortcut that is learned or discovered can be aptly dubbed a heuristic. It doesn’t matter if the shortcut is formally taught to us, one we learn from experience, one we develop via trial and error, or one we learn some other way. Essentially, heuristics allow us to take what we’ve learned and apply it without having to consciously decide how to do so (which frees up cognitive resources for other activities).

Shah and Oppenheimer (2008) argued that heuristics allow us to make decisions with incomplete information, thus giving us the ability to make decisions more quickly and frugally than if we attempted to apply more effortful decision-making approaches [3] . They can also, as Gigerenzer and Gaissmaier pointed out, result in more accurate decision making [4] , especially in situations (1) that are overly complex or (2) where information quality is low. This is why many heuristics can be said to be ecologically rational .

Some formal models of heuristics we use include satisficing , recognition , take-the-best , and fast and frugal trees , all of which can be applied to many situations. But heuristics don’t just exist, they are constantly revised and refined as we learn from our experiences. For example, when people first learn to drive a car, their heuristics are based more on what they’re taught than their own experiences. However, as more driving experience is acquired – and new situations are encountered – those heuristics are updated. This is one reason why younger drivers are more likely to get into accidents. They do not yet have established experience-based heuristics to help refine what they have been taught.

When Heuristics Can Go Awry

Heuristics, though, like any other decision-making strategy, don’t always lead to more accurate conclusions. In fact, we can develop heuristics that, while they appear to work with some reliability, are actually flawed.

For example, many people are health conscious and are drawn to healthier food choices when shopping at the grocery store. Yet, making those healthier choices is not necessarily an easy task because the difference between “healthy” and “unhealthy” is quite complex [5] . They can then choose between expending a great deal of cognitive effort to accomplish a trip to the grocery store and developing more cognitively frugal decision-making strategies to help them make choices.

Enter the use of heuristics. Rather than relying on all the available information, health-conscious buyers can develop shortcuts to help inform their decisions. One such shortcut is to look for information that indicates the food is healthier. Terms like low-fat, low-sodium, or lite can serve this purpose. The problem is that, at least in the case of foods labelled “lite,” it would be mistaken to assume that a food labelled as such is healthier .

Information quality influences the validity of a given heuristic. When our heuristic is reliant on insufficient (not enough information available) or erroneous (paying attention to the wrong information) information, then it may be less accurate than would a decision derived using more effortful decision making [6] or using a more well-refined heuristic.

In keeping with our healthier food choice heuristic, the word “lite” is both insufficient and erroneous information on which to make the determination of a healthier food choice. Hence, to include that in our heuristic would result in reduced accuracy, especially if that is the sole basis for making the decision to buy a given product.

Sometimes, though, a heuristic is accurate when used in the right situation but becomes inaccurate when applied to situations where it doesn’t work. For example, when shopping through the produce department of a grocery store, it is easy to categorize various fruits and vegetables based on pattern recognition . We don’t need to know all the different varieties of apples in order to recognize that a piece of produce that looks like an apple, even if it is a variety we have never seen before, is indeed an apple.

Similarly, we can easily identify arugula, oregano, and basil as herbs. Most people probably wouldn’t classify a banana as an herb because it doesn’t fit the pattern, but, indeed, it is actually an herb . Therefore, we can make mistakes when we apply a heuristic that works most of the time but doesn’t apply all the time or doesn’t apply in every situation. Almost all heuristics – even those that can be quite useful – have limitations to their utility. In fact, learning when and where to apply heuristics most effectively can itself be a useful heuristic to develop.

Key Takeaways

While heuristics are often criticized for being lower-quality decision-making strategies, they are quite useful in many situations. Without heuristics, we would have difficulty navigating our daily environment. In cases where heuristics would result in the same (or a close enough) answer as more complex strategies, it would be irrational to rely on a less efficient strategy to derive a decision. However, it is important to remember that heuristics can also lead us astray. When the heuristic doesn’t fit the situation, ignores important information, or relies on low-quality information, then decision making can suffer. The challenge is in developing heuristics that effectively guide our use of heuristics.

[1] Which is only one of the available search engines, though by far the most popular one.

[2] And the implication that this happens quite often.

[3] A rational approach to decision making involve considering all alternatives, attempting to locate all available information, deciding which information is most important, and assessing each alternative before reaching a conclusion. This set of tasks is quite demanding, both in terms of effort and time and, thus, is impossible in many, maybe most, situations.

[4] Or at least just as accurate as using a more deliberative and time-consuming process.

[5] Calories, fat, sodium, sugar, nutrient density are all factors that could be considered.

[6] It may, but this is dependent on the degree to which (1) more information is available on which to make our decision, (2) higher-quality information exists on which we could rely, and (3) enough certainty exists that a more accurate decision is likely given more time and/or cognitive effort.

Matt Grawitch, Ph.D. , is a professor at Saint Louis University (SLU), serving within the School for Professional Studies (SPS).

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Home Blog Business Using Heuristic Problem-Solving Methods for Effective Decision-Making

Using Heuristic Problem-Solving Methods for Effective Decision-Making

Problem-solving capability and effective decision making are two of the most prized capabilities of any leader. However, one cannot expect these traits to be simply present by default in an individual, as both require extensive analysis of the root cause of issues and to know what to look for when anticipating a gain. In a previous article, we brought you  5 Problem-Solving Strategies to Become a Better Problem Solver . This time we have something that can help you dig deep to resolve problems, i.e. using heuristic problem-solving methods for effective decision-making.

What are Heuristics?

Heuristics are essentially problem-solving tools that can be used for solving non-routine and challenging problems. A heuristic method is a practical approach for a short-term goal, such as solving a problem. The approach might not be perfect but can help find a quick solution to help move towards a reasonable way to resolve a problem.

Example: A computer that is to be used for an event to allow presenters to play PowerPoint presentations via a projector malfunctions due to an operating system problem. In such a case a system administrator might quickly refresh the system using a backup to make it functional for the event. Once the event concludes the system administrator can run detailed diagnostic tests to see if there are any further underlying problems that need to be resolved.

In this example, restoring the system using a backup was a short-term solution to solve the immediate problem, i.e. to make the system functional for the event that was to start in a few hours. There are a number of heuristic methods that can lead to such a decision to resolve a problem. These are explained in more detail in the sections below.

Examples of Heuristic Methods Used for Challenging and Non-Routine Problems

Heuristic methods can help ease the cognitive load by making it easy to process decisions. These include various basic methods that aren’t rooted in any theory per se but rather rely on past experiences and common sense. Using heuristics one can, therefore, resolve challenging and non-routine problems. Let’s take a look at some examples.

A Rule of Thumb

This includes using a method based on practical experience. A rule of thumb can be applied to find a short-term solution to a problem to quickly resolve an issue during a situation where one might be pressed for time.

Example: In the case of the operating system failure mentioned earlier, we assume that the PC on which PowerPoint presentations are to be run by presenters during an event is getting stuck on the start screen. Considering that the event is about to start in 2 hours, it is not practical for the system administrator to reinstall the operating system and all associated applications, hotfixes and updates, as it might take several hours. Using a rule of thumb, he might try to use various tried and tested methods, such as trying to use a system restore point to restore the PC without deleting essential files or to use a backup to restore the PC to an earlier environment.

An Educated Guess

An educated guess or guess and check can help resolve a problem by using knowledge and experience. Based on your knowledge of a subject, you can make an educated guess to resolve a problem.

Example: In the example of the malfunctioning PC, the system administrator will have to make an educated guess regarding the best possible way to resolve the problem. The educated guess, in this case, can be to restore the system to a backup instead of using system restore, both of which might take a similar amount of time; however, the former is likely to work better as a quick fix based on past experience and knowledge of the system administrator.

Trial and Error

This is another heuristic method to problem-solving where one might try various things that are expected to work until a solution is achieved.

Example: The system administrator might try various techniques to fix the PC using trial and error. He might start with checking if the system is accessible in safe mode. And if so, does removing a newly installed software or update solve the problem? If he can’t access the system at all, he might proceed with restoring it from a backup. If that too fails, he might need to quickly opt for a wipe and load installation and only install PowerPoint to ensure that at least presenters can run presentations on the PC. In this case he can perform other required software installations after the event.

An Intuitive Judgment

Intuitive judgment does not result from a rational analysis of a situation or based on reasoning. It is more of a feeling one has which may or may not lead to the desired outcome. Sometimes, intuitive judgement can help resolve problems. Perhaps the most rational way to describe an intuition is that it is some type of calculation at the subconscious level, where you can’t put your finger on the reason why you think something might be the way it is.

Example: The system administrator might have a feeling that the PC is not working because the hard drive has failed. This might be an intuitive judgment without hard evidence. He might quickly replace the hard drive to resolve the problem. Later, after he runs diagnostics on the old hard drive, he might realize that it was indeed that hard drive that was faulty and trying to fix it would have been a waste of time. In this case, he might be able to solve a problem using intuitive judgment.

Stereotyping

A stereotype is an opinion which is judgmental rather than rational. Certain types of possessions for example create a stereotype of social status. A person who wears an expensive watch might be deemed rich, although he might simply have received it as a gift from someone, instead of being rich himself.

Example: A certain company might have developed a bad reputation of developing faulty hard drives. If the systems administrator sees the name of that company on the hard drive when opening the faulty PC, he might think that the hard drive is faulty based on stereotyping and decide to replace it.

Profiling is used to systematically analyze data to understand its dynamics. Profiling as a heuristic method for problem-solving might entail analyzing data to understand and resolve a problem or to look for patterns, just like a root cause analysis .

Example: To solve the issue of the faulty PC, a system administrator might look for similar patterns which might have led to the problem. He might search online for solutions via online forums to understand what might have caused the issue. He might also look at the information associated with recently installed software and updates to see if something conflicted with the operating system. During the profiling process, he might realize that software he installed yesterday before shutting down the PC is the cause of the problem, since similar issues have been reported by other users. He might try to remove the software using Safe Mode or by removing its files by running the computer from a bootable disc drive.

Common Sense

Common sense is the use of practical judgment to understand something. The use of common sense is also a heuristic method used for problem-solving.

Example: When dealing with a faulty PC the system administrator sees smoke coming out of the PC. In this case, it is common sense that a hardware component is faulty. He shuts down the PC, removes the power cord and investigates the issue further based on common sense. This is because keeping the system linked to a power socket amidst smoke emitting from the PC can only make things worse. It is common sense to turn off everything and take the necessary precautions to investigate the issue further.

How are Heuristic Methods Used in Decision-Making?

There are a number of formal and informal models of heuristics used for decision making. Let’s take a look at a few of the formal models of heuristics used for decision making.

Formal Models of Heuristics

Fast-and-frugal tree.

A fast-and-frugal tree is a classification or decision tree. It is a graphical form that helps make decisions. For example, a fast-and-frugal tree might help doctors determine if a patient should be sent to a regular ward or for an emergency procedure. fast-and-frugal trees are methods for making decisions based on hierarchical models, where one has to make a decision based on little information.

Fluency Heuristic

In psychology, fluency heuristic implies an object that can be easily processed and deemed to have a higher value, even if it is not logical to assume this. Understanding the application of fluency heuristic can help make better decisions in a variety of fields. Fluency heuristic is more like sunk cost fallacy .

For example, a designer might design a user interface that is easier for users to process, with fewer buttons and easily labeled options. This can help them think fast, work quicker and improve productivity. Similarly, the concept might be used in marketing to sell products using effective marketing techniques. Even if two products are identical, a consumer might pick one over the other based on fluency heuristic. The consumer might deem the product to be better for his needs, even if it is the same as the other one.

Gaze Heuristic

Assume that you aim to catch a ball. Based on your judgment you would leap to catch the ball. If you were to leave yourself to instinct, you will end up at the same spot to catch the ball at a spot you would predict it to fall. This is essentially gaze heuristic. The concept of gaze heuristic is thought to be applied for simple situations and its applications are somewhat limited.

Recognition Heuristic

If there are two objects, one recognizable and the one isn’t, the person is likely to deem the former to be of greater value. A simple example of recognition heuristic is branding. People get used to brand logos, assuming them to be of high quality. This helps brands to sell multiple products using recognition heuristic. So, if you are looking to buy an air conditioner and come across two products, A and B, where A is a brand you know and B is a new company you don’t recognize, you might opt for A. Even if B is of better quality, you might simply trust A because you have been buying electronics from the brand for many years and they have been of good quality.

Satisficing

Satisficing entails looking for alternatives until an acceptable threshold can be ensured. Satisficing in decision making implies selecting an option which meets most needs or the first option which can meet a need, even if it is not the optimal solution. For example, when choosing between early retirement or continuing service for 2 or 3 more years, one might opt for early retirement assuming that it would meet the individual’s needs.

Similarity Heuristic

Similarity heuristic is judgment based on which is deemed similar, if something reminds someone of good or bad days, something similar might be considered the same. Similarity heuristics is often used by brands to remind people of something that they might have sentimental value for.

Someone might buy a limited-edition bottle of perfume that is being sold in a packaging style that was replaced 20 years ago. Assuming that sales were great in those days, the company might sell such limited-edition perfume bottles in the hope of boosting sales. Consumers might buy them simply because they remind them of the ‘good old days’, even though the product inside might not even be of the same but rather similar to what it used to be. Many consumers claim to buy these types of products claiming that it reminds them of a fond memory, such as their youth, marriage or  first job, when they used the product back in the day.

Final Words

Heuristics play a key role in decision making and affect the way we make decisions. Understanding heuristics can not only help resolve problems but also understand biases that affect effective decision making. A business decision or one that affects one’s health, life, or well-being cannot rely merely on a hunch. Understanding heuristics and applying them effectively can therefore help make the best possible decisions. Heuristic methods are not only used in different professions and personal decision making but are also used in artificial intelligence and programming.

Modern anti-virus software for instance uses heuristic methods to dig out the most elusive malware. The same rule can be essentially applied to decision making, by effectively using heuristics to resolve problems and to make decisions based on better judgment.

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Common Sense, Decision Making, Educated Guess, Heuristics, Judgment, Problem Solving, Profiling, Rule of Thumb, Stereotyping, Trial and Error Filed under Business

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AP®︎/College Computer Science Principles

Course: ap®︎/college computer science principles   >   unit 4, using heuristics.

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Heuristic Approaches to Problem Solving

“A heuristic technique, often called simply a heuristic, is any approach to problem solving, learning, or discovery that employs a practical method not guaranteed to be optimal or perfect, but sufficient for the immediate goals. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision. Examples of this method include using a rule of thumb, an educated guess, an intuitive judgement, guesstimate, stereotyping, profiling, or common sense.” (Source: Wikipedia )

“In computer science, a heuristic is a technique designed for solving a problem more quickly when classic methods are too slow, or for finding an approximate solution when classic methods fail to find any exact solution. This is achieved by trading optimality, completeness, accuracy, or precision for speed. In a way, it can be considered a shortcut.” (Source: Wikipedia )

The objective of a heuristic algorithm is to apply a rule of thumb approach to produce a solution in a reasonable time frame that is good enough for solving the problem at hand. There is no guarantee that the solution found will be the most accurate or optimal solution for the given problem. We often refer the solution as “good enough” in most cases.

Heuristic Algorithms? Heuristic Algorithms can be found in:

Let’s investigate a few basic examples where a heuristic algorithm can be used:

Based on this approach, can you think of how a similar approach could be used for an algorithm to play:

• Othello (a.k.a. Reversi Game)
• A Battleship game?
• Rock/Paper/Scissors?

It is hence essential to use a heuristic approach to quickly discard some moves which would most likely lead to a defeat while focusing on moves that would seem to be a good step towards a win!

Let’s consider the above scenario when investigating all the possible moves for this white pawn. Can the computer make a quick decision as to what would most likely be the best option?

Alternatively, a machine learning algorithm could play the game and record and update statistics after playing each card to progressively learn which criteria is more likely to win the round for each card in the deck. You can investigate how machine learning can be used in a game of Top Trumps by reading this blog post. Heuristic methods can be used when developing algorithms which try to understand what the user is saying, or asking for. For instance, by looking for words associations, an algorithm can narrow down the meaning of words especially when a word can have two different meanings:

e.g. When using Google search a user types: “Raspeberry Pi Hardware” We can deduct that in this case Raspberry has nothing to do with the piece of fruit, so there is no need to give results on healthy eating, cooking recipes or grocery stores…

However if the user searches for “Raspeberry Pie ingredients” , we can deduct that the user is searching for a recipe and is less likely to be interested in programming blogs or computer hardware online shops. Short Path Algorithms used by GPS systems and self-driving cars also use a heuristic approach to decide on the best route to go from A to Z. This is for instance the case for the A* Search algorithm which takes into consideration the distance as the crow flies between two nodes to decide which paths to explore first and hence more effectively find the shortest path between two nodes.

You can compare two different algorithms used to find the shortest route from two nodes of a graph:

• Dijkstra’s Shortest Path Algorithm (Without using a heuristic approach)
• A* Search Algorithm (Using a heuristic approach)

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Meet our Mid-Valley: Salem resident, UO grad inspired about solving city's problems

This is part of a weekly series introducing readers to individuals who are passionate about our Mid-Valley community.

Throughout the school year, University of Oregon students in more than 20 courses set their focus on a singular goal — solving problems in Salem.

Students and faculty in the Sustainable City Year Program visited and studied the city, talked with residents and city staff, and set their sights on proposing solutions on a variety of topics, including the role of AI in city government, safe bicycle infrastructure, housing, climate action plans, equity and parks management.

For south Salem resident and recent UO grad Sulwyn De Crozuc, the topic she tackled was personal. De Crozuc earned a degree in planning, public policy and management, and worked on a team led by co-founder and co-director of the Sustainable Cities Initiative Marc Schlossberg to improve the safety and usability of the bike corridor in Salem.

De Crozuc previously worked on the Sustainable City Year Program in Sisters and jumped at the chance to work on a project in her hometown.

She worked on a redesign of Front Street from Commercial Street to Union Street to north of Marion Square Park. The corridor, which passes along Riverfront Park and downtown, is a bustling spot for cyclists, pedestrians and vehicles.

"I grew up going to the park, and I grew up cycling to the park when I was a teenager," she said. "At that time, I was really, really, really frustrated with just how hard it was to bike around Salem."

The ride from Bush's Pasture Park to Riverfront Park was frequently plagued by near misses with cars due to the design of the streets, she said.

De Crozuc said she wanted to work on Front Street because of her experiences and because she cares about safety and making the spaces able to accommodate people as little as a baby to as old as someone in a care home.

"Front Street currently does not do that, but with the design me and my team proposed, we at least made it so people could bike better and be more comfortable entering and exiting the park," she said.

Proposals included widening bike lanes, installing bike foot rests at intersections and improving sidewalks near Riverfront Park.

Students get real-life experience, cities get ideas

De Crozuc and other students presented their projects to community leaders at the Center 50+ in June as part of the program's end-of-year celebration.

The Sustainable City Year Program is in its 14th year in partnering with Oregon communities. Every year, 200 to 500 students focus on a different city or transit district, contributing more than 60,000 hours of work. The nationally recognized program has been adopted throughout the world by other universities.

Courtney Knox Busch, Salem's chief strategy officer, said the program's contributions to the city are massive.

"We were at a point where there was just so much that we wanted to get done, and we were really struggling with capacity," she said. "Being able to invite the students in to help us further the council and the community goals was also a tremendous opportunity for this year."

City staff and leaders can use the proposals and framework for city projects and initiatives. Knox Busch pointed to implementing a project to discourage vehicle idling as part of the city's Climate Action Plan to reduce emissions. Students developed the low-cost idea of having elementary school students design stickers to spread awareness and post them near schools.

"It's just this huge opportunity and we had never considered (it)," she said. "In 10 weeks, the students produced that for us and the budget. It made it so easy."

Knox Busch also highlighted the bicycle corridor project as something to help further city goals.

"We're in the throes of updating our transportation systems plan, and the bicycle planning course turned out to be a great way to move some of that thinking forward," Knox Busch said.

Salem is the first city to participate twice in the program.

Students in the 2010-2011 school year provided input into the Minto-Brown Island Park Master Plan, proposing trail connections to Riverfront Park, crafting police facility designs, encouraging neighborhood associations to create social media pages to connect with residents and recommending projects to increase revenue and reuse at the city's wastewater treatment facility.

Many of the impacts of those proposals can be seen today, Knox Busch said. Facebook pages have become major hubs for neighborhood engagement, new signs were added to Minto and the Pringle Creek path was undercover and restored and is on the way to becoming a connection to Riverfront Park.

After the 2010-2011 program, then-Salem City Manager Linda Norris said the project was successful beyond her wildest dreams.

"I know we will be using the work for years and years to come," she said.

'These are our future leaders'

This year's participation was made possible through federal funding secured by U.S. Sens. Ron Wyden and Jeff Merkley, both Oregon Democrats.

Mayor Chris Hoy lauded the partnership and expressed gratitude for the students' insights.

“The ideas and collaboration these students bring to the city are instrumental in helping us tackle a variety of local problems," Hoy said.

Program leaders said the benefits are far from one-sided.

"What we found through the Sustainable City Year Program and our work with cities around Oregon is that students are just a lot more motivated when they're working on a real project in a real city," program director Megan Banks said.

Instead of a hypothetical question from their professor, students can tackle a real-life problem and see their ideas implemented, she said.

Knox Busch said many students can use her as a reference and put their experience on their resume.

De Crozuc said her experience gave her clarity and confidence about her post-grad plans. She wants to be a transportation planner, growing public transportation networks and pedestrian and cyclist infrastructure while working to solve climate change.

"The fact that all of these wonderful fresh ideas are being given to the like city officials and the city planners of Salem is just so rewarding," she said. "It also makes me feel really confident as someone who's going into the planning field to know that the cities in Oregon — where I'm from — want to seek out ideas to improve and better themselves."

Banks said students don't want to wait until they graduate to start real-life learning and make the world a better place to live.

"These are our future leaders," she said. "We want them to be engaged with communities and think about how to make Oregon a better place to live, so we love that they're doing that while they're in school."

If you have an idea for someone we should profile for this series, please email Statesman Journal executive editor Cherrill Crosby at  [email protected]  

For questions, comments and news tips, email reporter Whitney Woodworth at  [email protected]  call 503-910-6616 or follow on X at  @wmwoodworth .

This article originally appeared on Salem Statesman Journal: Sulwyn De Crozuc passionate about solving Salem's problems

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Behind every emerging technology is a great idea propelling it forward. In the new Microsoft Research Podcast series, Ideas, members of the research community at Microsoft discuss the beliefs that animate their research, the experiences and thinkers that inform it, and the positive human impact it targets. In this episode, host Gretchen Huizinga talks with Principal Researcher Behnaz Arzani (https://www.microsoft.com/en-us/research/people/bearzani/). Arzani has always been attracted to hard problems, and there’s no shortage of them in her field of choice—network management—where her contributions to heuristic analysis and incident diagnostics are helping the networks people use today run more smoothly. But the criteria she uses to determine whether a challenge deserves her time has evolved. These days, a problem must appeal across several dimensions: Does it answer a hard technical question? Would the solution be useful to people? And … would she enjoy solving it?Learn more:* Solving Max-Min Fair Resource Allocations Quickly on Large Graphs (https://www.microsoft.com/en-us/research/publication/solving-max-min-fair-resource-allocations-quickly-on-large-graphs/) | Publication, February 2024* Finding Adversarial Inputs for Heuristics using Multi-level Optimization (https://www.microsoft.com/en-us/research/publication/finding-adversarial-inputs-for-heuristics-using-multi-level-optimization/) | Publication, February 2024* MetaOpt: Examining, explaining, and improving heuristic performance (https://www.microsoft.com/en-us/research/blog/metaopt-examining-explaining-and-improving-heuristic-performance/) | Microsoft Research blog, January 2024* A Holistic View of AI-driven Network Incident Management (https://www.microsoft.com/en-us/research/publication/a-holistic-view-of-ai-driven-network-incident-management/) | Publication, October 2023* Behnaz Arzani: Painting, storytelling, and other hobbies (https://www.microsoft.com/en-us/research/people/bearzani/painting-and-other-hobbies/) | Microsoft Research bio page

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ORIGINAL RESEARCH article

Numerical methods for solving second-order initial value problems of ordinary differential equations with euler and runge-kutta fourth-order methods.

• Department of Mathematics, College of Natural and Computational Sciences, Mekdela Amba University, Tulu Awuliya, Ethiopia

This paper presents two standard numerical methods for solving second order initial value problems for ordinary differential equations (ODEs). The Euler and the Runge-Kutta fourth-order methods are applied without any discretization or restrictive assumptions for solving ODEs. The numerical solutions obtained by the two methods are in good agreement with the exact solutions. The convergence and error analysis which are discussed demonstrate the effectiveness of the methods. The results obtained from the two numerical methods show that the RK4 method is appropriate, consistent, convergent, quite stable, and more accurate than the Euler's method.

1 Introduction

Ordinary differential equations (ODEs) are mathematical equations that describe the relationship between a function and its derivatives. They are widely used in various fields of science, engineering and mathematics to model physical, biological, and dynamical systems [ 1 – 5 ]. Solving ODEs analytically can often be challenging or even impossible for complex differential equations [ 6 – 8 ]. Therefore, numerical methods play a crucial role in approximating solutions to these equations. The initial value problem (IVP) is a specific type of ODE problem where the values of the unknown function and its derivative(s) are specified at a given initial point. Many researchers developed different methods for solving ordinary differential equations (ODEs) with the initial value problem. Many authors have attempted to solve initial value problems (IVPs) to obtain high accuracy rapidly by using different methods such as the spactral method, the, the Euler's method and Runge Kutta fourth (RK4) order method and some other methods.

Jhnson and Lee explored the application of spectral methods to solve second-order IVP ODEs [ 9 ]. The authors employed Legendre polynomials as basis functions and developed spectral schemes to approximate the solution with high accuracy and rapid convergence rates. The advantages of spectral methods in terms of solution accuracy and numerical examples to validate their approach are discussed. Spectral methods are based on representing the solution as a series of basis functions, such as Legendre polynomials, Fourier series or Chebyshev polynomials [ 6 , 10 , 11 ]. By discretizing the problem on a set of collocation points, the unknown function can be approximated by a truncated Legendre polynomial series. These methods provide exponential convergence and are particularly effective for smooth or periodic solutions. It is worth noting that spectral methods, such as the Fourier or Chebyshev methods, have their own advantages for solving ODEs. They are typically more accurate, rapid convergence rates and efficient for problems with only smooth and periodic solutions. Euler's method is straightforward to implement and understand, making it a popular choice for beginners in numerical analysis [ 5 , 11 ]. It involves only simple arithmetic operations. Euler's method requires fewer computations compared to more complex methods, such as RK4. Hence, it can be computationally more efficient for simple and low-dimensional problems. Since Euler's method only uses information from the previous step to approximate the next step, it can provide a quick estimate of the solution, especially when speed is prioritized over accuracy. RK4 is a higher-order method, which means it provides more accurate approximations compared to Euler's method for a given step size [ 6 , 11 , 12 ]. It achieves this by using multiple evaluations of the derivative at different points within the step, resulting in a smaller truncation error. RK4 is a versatile method that can handle various types of problem, including those with stiff equations and irregular behavior [ 9 ]. It is widely used and considered to be one of the most accurate and reliable numerical methods for solving ODEs. Compared to Euler's method, RK4 exhibits better stability properties, making it more suitable for problems that require higher accuracy over longer integration intervals [ 6 , 12 ]. While there are more advanced and sophisticated numerical methods available, Euler's method and the Runge-Kutta fourth-order method strike a balance between simplicity, efficiency, accuracy, and stability when solving second-order IVPs of ODEs. Euler's method is a basic, easy-to-implement method, while the Runge-Kutta fourth-order method provides higher accuracy, numerical stability, and better control over the solution's accuracy. The choice between these methods depends on the specific problem characteristics, accuracy requirements, available computational resources, and desired trade-offs between accuracy and computational efficiency. Euler's method and Runge-Kutta methods provide a practical and reliable alternative for general second order IVPs of ODEs but spectral methods are accurate and efficient for problems with smooth and periodic solutions. Although extensive research has been conducted on numerical methods for solving first-order IVPs of ODEs, there is a noticeable gap in the literature regarding specialized methods for solving second-order IVPs. Second-order IVPs are more complex due to their involving second derivatives, and applying first-order methods may result in inaccurate solutions or numerical instability. The lack of comprehensive studies on numerical methods tailored for second-order IVPs highlights the need to bridge this gap in the literature. It is crucial to develop and evaluate specialized numerical methods that can reliably and efficiently solve second-order IVPs of ODEs. The aim of this study is to investigate and compare the performance of two widely used numerical methods, namely the Euler method and the Runge-Kutta fourth-order method, in approximating solutions to second-order IVP of ODEs. The study of numerical methods for solving second-order IVP of ODEs with Euler's method and the Runge-Kutta fourth-order method holds significant importance in the field of numerical analysis and scientific computing. Understanding the strengths and limitations of these methods can help researchers, engineers, and scientists select the most appropriate approach for solving ODEs based on specific requirements such as accuracy, efficiency and stability. This knowledge can also aid in optimizing computational algorithms to solve ODEs and providing reliable solutions for real-world problems. In this paper we apply Eulers and fourth order Runge-Kutta method for solving initial value problem of second order ordinary differential equation. A more robust and intricate numerical technique is the Runge-Kutta fourth-order methods. The Runge-Kutta fourth-order (RK4) method generally exhibits better convergence properties compared to Euler's method when solving second-order initial value problems (IVPs) of ordinary differential equations (ODEs). We take an example of a second-order ordinary differential equation to verify our proposed formulation.

2 Problem formulation

In this section, we consider two numerical methods to find approximate solutions of the initial value problem (IVP) of the second-order ordinary differential equation having the following form [ 9 ].

Where y ′ ′ = d 2 y d x 2 , y ′ = d y d x and f ( x, y ( x ), y ′( x )) is the given function and y ( x ) is the solution of Equation (1) . To solve the second-order IVP of ODE by using the Euler and Runge-Kutta fourth-order methods, the second-order initial value problems of ODE can be transformed into a system of first-order initial value problems, which allows the use of standard numerical methods that are widely employed. This approach is commonly known as the first-order system approach and it is indeed not new. In the context of the current study focusing on Euler's method and the Runge-Kutta fourth order (RK4) method, the novelty lies in the analysis and comparison of these specific numerical methods for solving the first-order system derived from the original second-order initial value problem. Although the idea of transforming a second-order initial value problem into a system of first-order problems is not innovative, the analysis and comparison of specific numerical methods applied to the derived first-order system can provide new insights and understanding of their effectiveness, accuracy, stability, convergence properties, and computational efficiency.

We can transform Equation (1) into a system of two first-order ODEs that are grouped as

Thus, instead of solving Equation (1) , we can solve Equation (2)

We note that, with y ′ = f ( x, y, z ) = z , Equation (2) represents the second-order initial value problem.

2.1 Euler method

The Euler method is a simple numerical technique for solving ordinary second-order differential equations. It approximates the solution by taking small steps along the curve defined by the differential equation. It is a basic explicit method for the numerical integration of an ordinary differential equations. Euler proposed his method for initial value problems (IVP) in 1768 [ 5 , 9 , 11 ]. It is the first numerical method to solve IVP and serves to illustrate the concepts involved in advanced methods. It is important to study this because error analysis is easier to understand.

Now let's consider a general second-order ODE with initial value problem (IVP):

To apply Euler's method, we first transform Equation (3) in to a system of two first order ODEs. Transform Equation (3) to systems of two first order ODE, let y ′ = z and z ′ = f ( x, y, z ), then Equation (3) becomes

With initial condition, y ( d ) = α, y ′( d ) = β and z ( x ) = y ′( x ).

Now, we can apply the Euler method to this system of first-order ODEs. The Euler method updates the functions y and z at each step as follows:

This is the general formula to solve the second-order ODE with IVP using the Euler method.

2.2 Runge-Kutta fourth order method

This method was devised by two German mathematicians, Runge about 1894 and was extended by Kutta a few years later [ 6 , 11 – 13 ]. The Runge-Kutta method is the most popular because it is quite accurate, stable, and easy to programme. This method is distinguished by its order in the sense that it agrees with Taylor's series solution up to terms of h r where r is the order of the method. It does not require a prior computational analysis of higher derivatives of y ( x ) as in Taylor's series method. The Runge-Kutta fourth-order method (RK4) is widely used for solving second-order initial value problems (IVP) for an ordinary differential equation (ODE). Now let's consider a general second-order ODE with initial value problem (IVP):

To apply the Runge-Kutta method, we first transform Equation (4) into a system of two first-order ODEs. Transform equation (4) to systems of two first order ODE, let y ′ = z and z ′ = f ( x, y, z ), then Equation (4) becomes

Now, we can apply the Runge-Kutta fourth-order method to this system of first-order ODEs. The Runge-Kutta fourth order method updates the functions y and z at each step as follows:

The general formula for the Runge-Kutta approximation to solve systems of equations is given by

Where k 1 = hf ( x n , y n , z n )

3 Error analysis

Error analysis is an essential component when studying numerical methods for solving second-order Initial Value Problems (IVPs) of Ordinary Differential Equations (ODEs) using Euler's method and the Runge-Kutta fourth-order (RK4) method [ 9 ]. Error analysis allows us to quantify the accuracy of these methods and understand their convergence properties. In numerical methods, the truncation error and the global error are commonly evaluated. The truncation error in Euler's method arises from the linear approximation of the derivative [ 14 , 15 ]. It is proportional to the step size h, used in the numerical scheme. Specifically, the truncation error is of order O ( h ) 2 , meaning that by halving the step size, the error typically decreases by a factor of four. The truncation error in RK4 arises from the approximation of the derivative at various internal points within the step. It is proportional to the step size h, increased to the power of five. Therefore, the truncation error of RK4 is of order O ( h ) 5 , which is significantly smaller than Euler's method [ 16 ]. The global error in Euler's method is the cumulative effect of the truncation error at each step throughout the integration interval [ 17 ]. As the number of steps increases, the global error accumulates, resulting in a larger discrepancy between the numerical solution and the exact solution. The global error in RK4 is significantly smaller compared to Euler's method [ 15 ]. Due to its higher order of accuracy, the cumulative effect of the truncation error is reduced, resulting in a more accurate approximation of the exact solution. It is important to note that while RK4 has a smaller truncation error and is typically more accurate than Euler's method, the step size h, also plays a role. The accuracy of the solution will depend on how small we make the step size h [ 18 ]. If |y(x n)- y n | = 0, then a numerical technique is considered as convergent. Where the exact solution is denoted by y n and the approximate solution by y ( x n ).

Using a smaller step size can improve the accuracy of both methods; however, it can also increase computational cost [ 19 ]. In error analysis, it is common to compare the numerical solutions obtained using Euler's method and RK4 to an analytically available exact solution or a solution obtained using a more accurate method (such as a higher-order Runge-Kutta method). By comparing the errors, we can assess the convergence properties of the methods and determine their suitability for a specific problem. In order to verify the accuracy of the suggested methods, we examine first-order initial value problem ODE in this study. MATLAB software is used to obtain the approximate solution for the two numerical methods that are proposed, at different step sizes. The formula for calculating the maximum error is defined by e r = max 0 ≤ x ≤ s t e p s ( | y ( x n ) - y n   | ) .

3.1 Numerical example

This section examines a numerical example to verify which numerical techniques converge to an analytical solution more quickly. Errors and numerical solutions are calculated.

Example 1: We consider the initial value problem y ′′ −3 y ′+2 y = 0 , y (0) = −1 , y ′(0) = 0 on the interval 0 ≤ x ≤ 1 with h = 0.1. Then the exact solution to the given problem is given by y ( x ) = e 2 x − 2 e x .

The approximate results and maximum errors are obtained and shown in Tables 1 – 4 and the graphs of the numerical solutions are shown as follows in Figures 1 – 6 from (a)-(r).

Table 1 . Comparison between Runge–Kutta fourth order and Euler method with exact solution for step size h = 0.1.

Table 2 . Comparison between Runge–Kutta-fourth order and Euler's method with exact solution for step size h = 0.05.

Table 3 . Comparison between Runge–Kutta-fourth order and Eulers method with exact solution for step size h = 0.025.

Table 4 . Comparison between Runge–Kutta fourth order and Euler's method with exact solution for step size h = 0.0125.

Figure 1 . Exact and approximate numerical Solutions for h = 0.1, (A) graph of the approximate solution for Eulers and Runge-Kutta fourth order, (B) graph of the approximate solution of Exact and Runge-Kutta fourth order, (C) graph of the approximate solution for Eulers and Exact, and (D) graph of approximate solutions for Euler, Runge-Kutta forth order methods and exact solution.

Figure 2 . Exact and approximate numerical solutions for h = 0.05, (A) graph of the approximate solution for Eulers and Runge-Kutta fourth order, (B) graph of the approximate solution of Exact and Runge-Kutta fourth order, (C) graph of the approximate solution for Eulers and Exact, and (D) graph of approximate solutions for Euler, Runge-Kutta forth order methods and exact solution.

Figure 3 . Exact and approximate numerical solutions for h = 0.025, (A) graph of the approximate solution for Euler's and Runge-Kutta fourth order, (B) graph of the approximate solution of Exact and Runge-Kutta fourth order, (C) graph of the approximate solution for Euler's and Exact, and (D) graph of approximate solutions for Euler, Runge-Kutta forth order methods and exact solution.

4 Discussion of results

In this work the obtained results are shown in the Tables 1 – 4 and graphically representations are show in the Figures 1 – 7 . The Tables 1 – 4 shows that the comparison of the two desired methods Euler's and Runge-Kutta fourth order method with the exact solution and also the Figures 1 – 4 shows that the graph of the approximate solution for Euler and Runge-Kutta methods for each step size h. The approximated numerical solution is calculated with the step size h = 0.1, 0.05, 0.025, 0.125. The approximate solution of Euler's and Runge-Kutta fourth order methods have different values for the same step size h for each iteration for example when we compared the accuracy of the Euler and Runge-Kutta fourth order method with sizes h = 0.1 and h = 0.05, then approximated solution with the step size h = 0.1 has less accurate then the approximated solution with the step size h = 0.05 because the error of approximate values for h = 0.1 is greater than the error for h = 0.05 i n each iterations. This shows that the Euler's method with h = 0.1 and h = 0.05 does not converges to the exact solution. Similarly for the step sizes h = 0.025 and h = 0.0125, then approximate solution with the step size h = 0.025 has less accurate than the approximate the solution with the step size h = 0.0125 because of the approximate solution with the step size h = 0.0125 has less absolute error then the approximated solution for h = 0.025. This shows that the Euler's method with h = 0.1 and h = 0.05 does not converges to the exact solution but for h = 0.025 and h = 0.0125 Converges slowly to exact solution. The Runge-Kutta fourth order method with the same step size also the approximate solution obtained for h = 0.1 and h = 0.05 converges gradually to exact solution but the approximate for h = 0.025 and h = 0.0125 converges fatly to exact solution. This shows that as the step size decreases the accuracy the approximate solution also increases. The Figures 5 , 6 shows that the approximate solution of Euler and Runge-Kutta fourth order method with the same step size respectively. According to Figure 5 the graph of the approximate solution for Runge-Kutta fourth order method are approximately all are overlapped because of little difference between approximate solutions of Runge-Kutta methods with Exact solution (i.e., error) for each h values. From the Figure 6 also the graph of approximated solutions for Euler's method has the gap between two consecutives step sizes this shows that Euler's method has maximum absolute error compared to Runge-Kutta fourth order for same step size. Graph of approximated solutions for h = 0.0125 is above the graph of approximated value for h = 0.1, 0.05, 0.025 this means that the graph of approximated solution approach's to the graph of exact solution as step size decreases but the graph for approximated solution for h = 0.1 is under the graph of approximated solution for h = 0.05, 0.025, 0.0125 this means that it away from the graph of exact solution and it has maximum error for h = 0.1. In the Figure 7 the graph of maximum absolute error for Euler and Runge-Kutta fourth order for each step size are plotted. The graph of error for Euler's method in Figure 7 for h = 0.1 is above h = 0.05, 0.025, and 0.0125 this shows the approximate solution for h=0.1 has maximum error then all approximated solution for h = 0.05, 0.025, 0.0125 but for h = 0.0125 the error graph is below h = 0.05, 0.025, and 0.1 this shows that the absolute error for h = 0.0125 is less then all other approximated solution for h = 0.05, 0.025, and 0.1 for every iteration. Additionally, error analysis for Runge-Kutta method in Figure 7 the graph of error for each step size resembles overlapped to x-axis that means the error for Runge-Kutta is almost tends to zero. From the Figure 7 we observed that Runge-Kutta fourth order converges fastly then the Euler's method with the same step size. The absolute error for each step size h of Euler and Runge-Kutta fourth order methods tends to zero as the step size tends to zero. Although the fourth order Runge-Kutta method is more accurate than the Euler's approach, which only requires one-fourth the step size, it is arduous and takes four evaluations per step size. Finally, we noticed that, as the tables and figures show, the fourth order Runge-Kutta method is the most effective approach for solving second order initial value problem for ordinary differential equations, and that it is converging more quickly than the Euler method.

Figure 4 . Exact and approximate numerical Solutions for h = 0.0125, (A) graph of the approximate solution for Euler's and Runge-Kutta fourth order, (B) graph of the approximate solution of Exact and Runge-Kutta fourth order, (C) graph of the approximate solution for Eulers and Exact, and (D) graph of approximate solutions for Euler, Runge-Kutta forth order methods and exact solution.

Figure 5 . Approximate value for Runge-Kutta fourth order method for each step size.

Figure 6 . Approximate value for each step size in Euler method.

Figure 7 . The approximated error for Euler and Runge-Kutta fourth order for different step size.

5 Conclusion

In this work, we have discussed Euler's and fourth order Runge-Kutta method for solving second order initial value problems that provides efficient solutions. To achieve the desired accuracy of the numerical solution it is necessary to take step size small. From the tables and figures, we can see that accuracy of the method obtained for decreasing the step size h. The numerical solutions obtained by the two methods are in good agreement with the exact solutions. However, by comparing the results of the two methods, we state that the RK4 Method is appropriate, consistent, convergent, quite stable, and more accurate than the Euler's method and it is widely used in numerical solutions of second order initial value problems in ordinary differential equations. Our research will be helpful in many scientific areas where numerical computations are needed.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

YW: Conceptualization, Data curation, Investigation, Methodology, Resources, Software, Supervision, Validation, Visualization, Writing—original draft, Writing—review & editing, Formal analysis, Project administration. HM: Conceptualization, Data curation, Investigation, Methodology, Resources, Software, Supervision, Validation, Visualization, Writing—original draft, Writing—review & editing. BB: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing—original draft, Writing—review & editing.

The author(s) declare that no financial support was received for the research, authorship, and/or publication of this article.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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Keywords: ordinary differential equation (ODE), second order initial value problem (IVP), Euler method, fourth order Runge-Kutta method, error analysis

Citation: Workineh Y, Mekonnen H and Belew B (2024) Numerical methods for solving second-order initial value problems of ordinary differential equations with Euler and Runge-Kutta fourth-order methods. Front. Appl. Math. Stat. 10:1360628. doi: 10.3389/fams.2024.1360628

Received: 23 December 2023; Accepted: 06 February 2024; Published: 22 February 2024.

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Copyright © 2024 Workineh, Mekonnen and Belew. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Habtamu Mekonnen, habtamumekonnen2012@gmail.com

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