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Representation in the Electoral College: How do states compare?

The 2020 election will be the last of the decade before electoral votes are reallocated based on Census results. See how the current distribution of the nation’s 538 electoral votes compares to the number of people living in all 50 states and Washington, DC.

Published on Thu, August 13, 2020 2:49PM PDT | Updated Tue, February 6, 2024 12:54PM PST

How does the Electoral College work?

Every four years, 538 electors hailing from all 50 states plus Washington, DC cast their votes for president and vice president of the United States. A candidate needs a majority of 270 electoral votes to win each race. In this system, known as the Electoral College , each state gets the same number of electors as it has members of Congress — one for each member in the House of Representatives and one for each of the state’s two senators. This means that each state is guaranteed a minimum of three electors, regardless of population size. It also means that there is always a total of 538 electors, or equivalently, 538 electoral votes — that’s the sum of 435 voting members of the House, 100 senators, and three electors assigned to Washington, DC.

So, when voters cast ballots for president and vice president on Election Day, they’re actually voting for a slate of electors who have pledged to vote for their favored candidates. Most states (with the exceptions of Maine and Nebraska) use a “winner-take-all” system of choosing electors, meaning that — assuming electors vote according to their pledges — all of the state’s electoral votes are cast for the candidate that wins the majority of the state’s popular vote.

Electoral votes and population: Why one electoral vote accounts for 193,000 people in Wyoming and over 700,000 people in Texas or California.

Generally, states that are home to more people control more electoral votes. California — the largest state by population — has 55 electoral votes, while Wyoming — the smallest — has the minimum allocation of three. But because electoral votes are allocated according to seats in Congress, where each state holds two Senate seats regardless of population size, electoral representation varies quite a bit across states.

One way to think about electoral representation is to consider how many people each electoral vote represents, based on a state’s population. According to 2018 population estimates, one electoral vote in Wyoming accounts for around 193,000 people, while a vote in Texas or California accounts for over 700,000. For context, if all 538 electoral votes were distributed evenly among the US population, each vote would represent about 607,000 people.

Another way of thinking about electoral representation is to consider the difference between a state’s share of the nation’s total population and its share of all electoral votes. For example, Wyoming makes up about 0.18% of the US population but controls 0.56% of all electoral votes. This difference may seem minuscule, but it translates to approximately two additional electoral votes for Wyoming, relative to its population share. If Wyoming’s electoral share aligned with its share of the US population, it would have 0.18% of all 538 votes, which is about one electoral vote — but because votes are allocated based on seats in Congress, the state has the minimum of three votes in the Electoral College.

On the other end of the spectrum, California represents 12.1% of the US population and has 10.2% of all electoral votes. This means California controls roughly 10 fewer votes in the Electoral College than it would if votes were allocated based on population alone (because 12.1% of the total 538 votes is about 65 electoral votes, but California currently controls 55). For context, 10 votes is equivalent to the entire electoral share assigned to states like Maryland, Minnesota, and Missouri. It’s also the same as the combined vote shares of Iowa and Maine, or of all three states of Montana, Delaware, and Idaho.

Total population helps determine how electoral votes are allocated, but eligible voters determine how the votes are cast.

These examples demonstrate electoral representation based on each state’s share of the national population, and that’s because states receive representation in both the House of Representatives and the Electoral College according to the total resident population , not just according to how many voters live in the state. The resident population is all who live in the state at the time of the Census count, including both citizen and noncitizen residents, and both adults and children. Still, another way to view electoral representation is to see how the distribution of electoral votes compares to the distribution of eligible voters among states.

When determined according to the voting-eligible population nationwide, electoral representation looks a bit more equal across states. In particular, the two most populous states — California and Texas — are underrepresented by fewer votes when looking at representation among the voting-eligible population instead of the total resident population. These large states have higher proportions of non-citizen adults and a lower median age than many other states, so their shares of the voting-eligible population are smaller than their shares of the total US population. For example, California makes up 12.1% of the total US population but 11% of the citizen voting-age population; so by total population share, the state is about 10 votes underrepresented in the Electoral College, but by its share of eligible voters, the difference is closer to four votes.

What if electoral vote shares were equal to population shares in every state?

It’s important to note that even if electoral votes were allocated exactly according to each state’s share of the US population or share of eligible voters, the electoral process would not resemble a national popular vote . This is because of the winner-take-all rule for choosing state electors, currently used by 48 states and Washington, DC. According to this rule, all electoral votes go toward the candidate that earns the most votes in the state’s general election; therefore, votes cast for any other candidate do not earn any of the state’s electoral votes.

In other words, according to the winner-take-all policy, a candidate may earn 49.9% of a state’s popular vote and earn 0% of the state’s electoral votes. This explains how a candidate may win the national popular vote but, by failing to earn 270 electoral votes, may still lose the presidential election in the Electoral College — a scenario which has occurred in five US presidential elections, including the most recent election in 2016.

After this November's election, electoral votes will be reallocated based on Census results.

The total of 538 electoral votes is fixed, but how these votes are distributed between states can change as a result of the decennial Census . Every 10 years, the results of the Census determine how seats in the House of Representatives are apportioned, and states may gain or lose electoral votes accordingly. This November’s election will be the last of the decade before the reallocation of electoral votes.

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How the Great Compromise and the Electoral College Affect Politics

By: Amanda Onion

Updated: August 9, 2023 | Original: April 17, 2018

The Great Compromise was forged in a heated dispute during the 1787 Constitutional Convention: States with larger populations wanted congressional representation based on population, while smaller states demanded equal representation. To keep the convention from dissolving into chaos, the founding fathers came up with the Great Compromise. The agreement, which created today’s system of congressional representation, now influences everything from “pork barrel” legislation to the way votes are counted in the electoral college during presidential elections.

The debate almost destroyed the U.S. Constitution.

At the Constitutional Convention of 1787, delegates from larger states believed each state’s representation in the newly proposed Senate should be proportionate to population.

Smaller states with lower populations argued that such an arrangement would lead to an unfair dominance of larger states in the new nation’s government, and each state should have equal representation, regardless of population.

The disagreement over representation threatened to derail the ratification of the U.S. Constitution since delegates from both sides of the dispute vowed to reject the document if they didn’t get their way. The solution came in the form of a compromise proposed by statesmen Roger Sherman and Oliver Ellsworth of Connecticut.

The Great Compromise created two legislative bodies in Congress.

Also known as the Sherman Compromise or the Connecticut Compromise, the deal combined proposals from the Virginia (large state) plan and the New Jersey (small state) plan.

According to the Great Compromise, there would be two national legislatures in a bicameral Congress. Members of the House of Representatives would be allocated according to each state’s population and elected by the people.

In the second body—the Senate —each state would have two representatives regardless of the state’s size, and state legislatures would choose Senators. (In 1913, the 17th Amendment was passed, tweaking the Senate system so that Senators would be elected directly by the people.)

The plan was at first rejected, but then approved by a slim margin on July 23, 1787.

Smaller states have disproportionately more power in the Senate.

At the time of the convention, states’ populations varied, but not by nearly as much as they do today. As a result, one of the main lingering political effects of the Great Compromise is that states with smaller populations have a disproportionately bigger voice in the nation’s Congress.

As political scientist George Edwards III of Texas A&M University points out, California hosts about 68 times more people than Wyoming, yet they have the same number of votes in the Senate.

“The founders never imagined … the great differences in the population of states that exist today,” says Edwards. “If you happen to live in a low-population state you get a disproportionately bigger say in American government.”

The imbalance of proportionate power favoring smaller states in the Senate means that interests in those states, such as mining in West Virginia or hog farming in Iowa, are more likely to get attention—and money—from federal coffers.

“In the Senate when they’re trying to get to 51 votes to pass a bill, every vote counts,” says Todd Estes, a historian at Oakland University in Rochester, Michigan. “That’s when the smaller states can demand amendments and additions to bills to look out for their own state’s interest.”

The Great Compromise also skewed the electoral college.

The principle of protecting small states through equal representation in the Senate carries over into the electoral college, which elects the president since the number of electoral votes designated to each state is based on a state’s combined number of representatives in the House and Senate.

That means, for example, even though Wyoming only has three votes in the electoral college, with the smallest population of all the states, each elector represents a far smaller group of people than each of the 55 electoral votes in the most populous state of California.

The system ensures power is distributed geographically.

Some scholars see the small-state bias in the Senate as critical. The arrangement means that power in the Senate is distributed geographically, if not by population, ensuring that interests across the entire country are represented.

Gary L. Gregg II, a political scientist at the University of Louisville in Kentucky, argues in a 2012 article in Politico that major metropolitan areas already hold power by hosting major media, donor, academic and government centers. The structure of the Senate and the corresponding representation in the electoral college, he says, ensures that the interests of rural and small-town America are preserved.

Was that the intention of the Founding Fathers? Edwards is doubtful since, as he points out, the majority of Americans at the time of Constitutional Congress came from rural areas—not urban. “No one was thinking about protecting rural interests,” Edwards says. “Rural interests were dominant at the time.”

Whatever the viewpoint on the fairness of the Great Compromise’s distribution of delegates to the Senate, it is unlikely to ever change. This is because equal-state representation in the Senate is specifically protected in the Constitution.

According to Article V of the Constitution, no state can lose its equal representation in the Senate without the state’s permission. And no state is likely to willingly give up their say in the Senate.

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Creating the United States Creating the United States Constitution

Representation.

Republican purists and residents of large (geographic and population) states wanted representation to be based on population within states or some other contrived district. Those from smaller (geographic and population) states or who on principle wanted to restrict the power of the people wanted representation to be based solely on the state as an individual entity. The creative compromise of the delegates was to devise a bicameral (two-house) national legislature with one house (Senate) having equal representation from each state with the members chosen by the state legislatures and a second house (House of Representatives) having membership based on a proportional population formula and elected by the voters in the states. Where did this idea come from? »

Sect. 1. ALL legislative powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives. Sect. 2. The House of Representatives shall be composed of members chosen every second year by the people of the several states, . . . Representatives and direct taxes shall be apportioned among the several states which may be included within this Union, according to their respective numbers, which shall be determined by adding to the whole number of free persons, including those bound to servitude service for a term of years, and excluding Indians not taxed, three-fifths of all other persons.

Sect. 3. The Senate of the United States shall be composed of two senators from each state, chosen by the legislature thereof, for six years: and each senator shall have one vote.

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Article I, Section 3, Clause 1:

The Senate of the United States shall be composed of two Senators from each State, chosen by the Legislature thereof, for six Years; and each Senator shall have one Vote.

Ratified in 1913, the Seventeenth Amendment superseded Article I, Section 3, Clause 1, providing for Senators to be popularly elected rather than selected by state legislatures. 1 Footnote U.S. Const. amend. XVII . The Seventeenth Amendment , however, incorporated other provisions of Article I, Section 3, Clause 1: equal suffrage among states, each state accorded two Senators, each of whom would have one vote and serve a six-year term. 2 Footnote Id. ( “The Senate of the United States shall be composed of two Senators from each State, elected by the people thereof, for six years; and each Senator shall have one vote.” ).

Adopted by the Constitutional Convention and incorporated in the Seventeenth Amendment , the text set forth in Article I, Section 3, clause 1, providing that “[t]he Senate of the United States shall be composed of two Senators from each State . . . and each Senator shall have one vote” 3 Footnote U.S. Const. art. I, § 3, cl. 1 ; U.S. Const. amend. XVII . is foundational to the federal nature of the U.S. Government. By providing for each state to be represented in the Senate by two Senators, each with a single vote, the Constitution ensures that all states are equal in the Senate regardless of their relative population, wealth, power, or size. 4 Footnote See, e.g. , Joseph Story , Commentaries on the Constitution of the United States § 691 (1833) ( “[E]ach state in its political capacity is represented upon a footing of perfect equality, like a congress of sovereigns, or ambassadors, or like an assembly of peers.” ). By allocating power in the Senate equally among the states, the Framers counterbalanced allocating power in the House based on a state’s share of the national population. 5 Footnote Compare U.S. Const. art. I, § 3, cl. 1 with U.S. Const. art. I, § 2, cl. 3 .

The different compositions of the House of Representatives and Senate reflect the Framers’ conception of the U.S. Government as both national and federal. 6 Footnote Joseph Story , Commentaries on the Constitution of the United States § 696 (1833) ( “[T]he very structure of the general government contemplated one partly federal, and partly national.” ). Consistent with a National Government, the Constitution provides for the American people to be equally represented in the House. 7 Footnote U.S. Const. art. I, § 2, cl. 3 . Consistent with a federation of states, the Constitution provides for equal representation of states in the Senate. 8 Footnote U.S. Const. art. I, § 3, cl. 1 . Stressing that equal suffrage is critical to state sovereignty in his Commentaries on the Constitution of the United States , Justice Joseph Story stated: “The equal vote allowed in the senate is . . . at once a constitutional recognition of the sovereignty remaining in the states, and an instrument for the preservation of it. It guards them against (what they meant to resist as improper) a consolidation of the states into one simple republic.” 9 Footnote Joseph Story , Commentaries on the Constitution of the United States § 696 (1833) . See also The Federalist No. 62 (James Madison) ( “[T]he equal vote allowed to each State is at once a constitutional recognition of that portion of sovereignty remaining in the individual States, and an instrument for preserving that residuary sovereignty. So far the equality ought to be no less acceptable to the large than to the small States; since they are not less solicitous to guard, by every possible expedient, against an improper consolidation of the States into one simple republic.” ). By arranging for the House and Senate to exercise legislative power jointly, the Framers required U.S. law to have both national and federal approval—a majority vote in the House of Representatives demonstrates national approval while a majority vote in the Senate expresses federal approval. 10 Footnote The Federalist No. 62 (James Madison) ( “No law or resolution can now be passed without the concurrence, first, of a majority of the people, and then, of a majority of the States.” ). The Framers also saw the division of power between the House and Senate as ensuring that they would check abuses of power by the other. Id. ( “[A] senate, as a second branch of the legislative assembly, distinct from, and dividing the power with, a first, must be in all cases a salutary check on the government. It doubles the security to the people, by requiring the concurrence of two distinct bodies in schemes of usurpation or perfidy, where the ambition or corruption of one would otherwise be sufficient.” ).

How does America apportion congressional seats?

Through census results, which this year shifted power south and west.

AMERICA’S CONSTITUTION requires the government to perform a complete count of each person living in the country every ten years. The results of this census are used for many purposes, among the most important of which is allocating congressional representatives proportionally to the population in each state. Because Congress fixed the number of seats in the House of Representatives at 435 in 1929, the Census Bureau has to shuffle seats between states as their populations grow and shrink.

On April 26th the Bureau released its estimates for the next decade. They show a shifting of political power as southern and western states have grown at higher rates than northern ones. According to the new tallies, which took over a year to complete and were delayed because of the covid-19 pandemic, California, Illinois, Michigan, New York, Ohio, Pennsylvania, and West Virginia will each lose one House member for the next Congress. (California’s loss is its first ever; its population has grown more slowly than that of other states.) Colorado, Florida, Montana, North Carolina and Oregon will each gain one, while Texas will gain two (see map).

It will take months more before states redraw their individual Congressional plans to determine which areas will gain or lose districts. That is because the fine-grained data that enumerate populations at the neighbourhood level, which redistricting committees need to run their incredibly precise districting software, will not be released by the Census Bureau until the autumn. Those counts take much longer to finalise than the aggregated state-level estimates.

Once the Census Bureau sends states their data, the race to redraw districts begins. Many states face legal requirements to finish the redistricting in a matter of months. Idaho, for example, gives the independent redistricting commission only 90 days to draw and agree on new maps. It is one of seven states that use a non-partisan commission of citizens, usually chosen by courts, the state auditor or the legislature, to draw district borders. As of 2021 Arizona, California, Colorado, Idaho, Michigan, Montana and Oregon are the only states that let citizens, with inputs from experts and their legislatures, decide how maps get drawn. Ten others delegate the redistricting process to citizen commissions with a partisan imbalance, commissions made up of elected officials, independent boards that only get a say if the legislature can’t pick a map, or other appointed staff. The rest leave the process up to the state legislatures, which are much more likely to draw districts that are biased towards one party or against a minority racial group—known as “gerrymandering”—despite some having constitutional standards against partisan bias.

Until 2013, Section 5 of the 1965 Voting Rights Act required jurisdictions with a history of racial discrimination or segregation to receive approval for proposed districting plans from the Department of Justice before implementing them, a process known as preclearance. In 2011, that requirement applied to nine whole states—all but one were Southern—and smaller portions of six others. But in 2013 the Supreme Court said the formula that had identified states plagued by racial bias was based on old data. In Shelby County v Holder , the court invalidated the coverage formula, putting Section 5 out of service unless Congress creates a new one, which it has not yet done.

Because census results were delayed, most states will have to rush their redistricting processes to meet deadlines for the 2022 elections. The lack of preclearance will give states greater leeway in drawing maps, though racially biased ones can still be challenged in court and subsequently adjusted. But however districts are ultimately apportioned within states, the next Congress will reflect America’s continuing population shift southward and westward.

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Connecticut Compromise

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Connecticut Compromise , in United States history, the compromise offered by Connecticut delegates Roger Sherman and Oliver Ellsworth during the drafting of the Constitution of the United States at the 1787 convention to solve the dispute between small and large states over representation in the new federal government. The compromise provided for a bicameral federal legislature that used a dual system of representation: the upper house would have equal representation from each state, while the lower house would have proportional representation based on a state’s population.

(Read John Kennedy’s Britannica entry on Oliver Ellsworth.)

In 1787 the convention met in the Pennsylvania State House in Philadelphia , ostensibly to amend the Articles of Confederation (the first U.S. constitution, 1781–89). The idea of amending the Articles was discarded, though, and the assembly set about drawing up a new scheme of government. One area of disagreement between delegates from small states and those from large states was the apportionment of representation in the federal government. Edmund Randolph offered a plan known as the Virginia, or large state, plan , which provided for a bicameral legislature with representation of each state based on its population or wealth. William Paterson proposed the New Jersey, or small state, plan , which provided for equal representation in Congress. Neither the large nor the small states would yield. Ellsworth and Sherman, among others, proposed a bicameral legislature with proportional representation in the lower house (the House of Representatives ) and equal representation of the states in the upper house (the Senate ). All revenue measures would originate in the lower house. That compromise was approved July 16, 1787.

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Here's How The 1st 2020 Census Results Changed Electoral College, House Seats

Hansi Lo Wang

Connie Hanzhang Jin

Zach Levitt

Texas has gained two more votes in Congress and the Electoral College for the next decade, while Colorado, Florida, Montana, North Carolina and Oregon each gained one seat, based on the first set of results from the 2020 census, released Monday. The seven states losing one vote each are California, Illinois, Michigan, New York, Ohio, Pennsylvania and West Virginia.

The U.S. Census Bureau's acting director, Ron Jarmin, reported the new state population counts at a virtual news conference . The long-awaited announcement has reset the balance of power for the next decade in the House of Representatives and the Electoral College, where each state's share of votes is tied to its census numbers .

The scramble for the last of the 435 seats for voting members in the House was remarkably close.

"If New York had had 89 more people, they would have received one more seat," said Kristin Koslap during the press conference. Koslap, senior technical expert on 2020 census congressional apportionment in the Census Bureau's Population Division, said instead that last seat went to Minnesota.

The results had been held up for months due to delays caused by the coronavirus pandemic and the Trump administration's interference last year. Under current federal law , these state population numbers were due by the end of 2020. But the bureau had been warning since April 2020 that census results would be delivered later than originally planned. A bipartisan group of lawmakers recently renewed a push in Congress to extend legal reporting deadlines formally for the 2020 count.

COMIC: How Your State Wins Or Loses Political Power Through The Census

Census Estimates U.S. Population As High As 336 Million Ahead Of Actual Count

Last year's tally was the country's 24th census — a once-a-decade tradition required by the Constitution since 1790 — and it is the ninth count for which the U.S. government has attempted to include every person living in the country in the numbers used for reapportioning seats in Congress. Before the 1940 census, the phrase "excluding Indians not taxed" in the Constitution excluded some American Indians from the apportionment counts.

Here's what else you need to know:

Why did it take so long to get these census results?

COVID-19 forced the agency to postpone in-person counting for months, and the bureau's door knockers also had to contend with hurricanes and wildfires in some parts of the country. As NPR first reported , the census was further disrupted last July when the Trump administration decided to cut short the schedule for gathering census responses and running quality checks on the collected data. Extra time was needed, the bureau argued, to sort through a high volume of duplicate and incomplete responses .

Were people who died from COVID-19 last year counted in the census?

After A Disrupted Census, Congress Tries Again To Extend Deadlines For Results

The census was intended to be a snapshot of the country's population as of Census Day (April 1, 2020), so it was not supposed to count U.S. residents who died before that date, according to the bureau's residence criteria . People who died on or after April 1 last year should have been counted.

Is there information about race, ethnicity, age and sex, as well as population numbers for counties, cities, towns and other smaller areas, in these census results?

No, this information will be released with the second set of 2020 census results. This more detailed demographic information is needed for the redrawing of voting districts. It's also used to guide the distribution of an estimated $1.5 trillion a year in federal money for Medicare, Medicaid, education and other public services for local communities.

When will that demographic data be released?

Stuck At 435 Representatives? Why The U.S. House Hasn't Grown With Census Counts

The bureau plans to start releasing this information by Aug. 16 . New redistricting data was due to the states by the end of March. But the bureau said it is behind schedule on running quality checks after the Trump administration pressured it to prioritize the new state numbers that former President Donald Trump wanted to alter before leaving office.

The timing may change, however, depending on how two lawsuits turn out. Alabama and Ohio are asking the federal courts to force the bureau to put out this data by the end of July so they can meet their state redistricting deadlines. Alabama's lawsuit is also trying to stop the bureau from adopting a new technique, known as differential privacy, for keeping personal information in anonymized census data confidential. If Alabama wins, the data's release would be delayed by "multiple months" past August, the agency's chief scientist said in a recent court filing .

How accurate are these census numbers?

Can President-Elect Biden Redo The 2020 Census? It's Complicated

It will be difficult to say for certain immediately. The bureau's career officials have said the agency has not found anything in the data suggesting the census is not "fit for its constitutional and statutory purposes."

But no U.S. census has been perfect. The pandemic and Trump officials' last-minute changes to the schedule have heightened concerns about how well certain groups were counted , especially historically undercounted groups who are less likely to participate in the census unless they receive in-person visits from door knockers. The Trump administration's failed push for a citizenship question may also have further discouraged households with immigrants and people of color from getting counted.

For the first time, the bureau is releasing quality metrics at the national and state levels on the same day it puts out the first numbers. But census experts say metrics at a more detailed level are needed because the quality of the count can vary greatly from neighborhood to neighborhood.

Immigration Hard-Liner Files Reveal 40-Year Bid Behind Trump's Census Obsession

Researchers with the American Statistical Association are conducting an independent audit of the count's quality, and they are set to release their first report in June . The Census Bureau is conducting its Post-Enumeration Survey to estimate how many people may have been missed as well as rates of overcounting and undercounting among racial and ethnic groups. Those results are not expected to start rolling out until December .

Can we redo the census?

It's not clear if state population numbers from a do-over can be used to redistribute seats in the House of Representatives — the count's main purpose as outlined by the Constitution. Federal law does allow for a "mid-decade census" in 2025, but the results can't be used for reapportioning the House. There's also a question about money: Would Congress be willing to fund another head count shortly after what's estimated to be the most costly census in U.S. history at $15.6 billion?

What happens next to the first census results?

Why Deployed Troop Counts Are A 'Wildcard' In 2020 Census Results

These state population counts and the new assignment of House seats are part of a handoff process involving the commerce secretary overseeing the bureau, the president and Congress. Ultimately, the numbers are certified by the clerk of the House , who is then charged with officially reporting them to the states.

Some states that have lost seats may sue the Biden administration to challenge how the House was reapportioned, and that may change some states' new number of congressional districts before next year's midterm elections. The new Electoral College map, with votes based on each state's latest share of seats in Congress, goes into effect beginning with the 2024 presidential race.

Correction April 26, 2021

An earlier web and radio version of this story misattributed a quote from Kristin Koslap, senior technical expert on 2020 census congressional apportionment in the Census Bureau's Population Division, to Karen Battle, chief of the bureau's Population Division.

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Module 6: Creating a Government (1776-1789)

The constitutional convention, learning objectives.

• Identify the central issues of the 1787 Constitutional Convention and their solutions
• Explain the differences between the Virginia Plan, the New Jersey Plan, and the Connecticut Compromise

There had been earlier efforts to address the Confederation’s perilous state. In early 1786, Virginia’s James Madison advocated a meeting of states to address the widespread economic problems that plagued the new nation. Heeding Madison’s call, the legislature in Virginia invited all thirteen states to meet in Annapolis, Maryland, to work on solutions for the issue of commerce between the states. Eight states responded to the invitation. But the resulting 1786 Annapolis Convention failed to provide any solutions because only five states sent delegates. These delegates did, however, agree to a plan put forward by Alexander Hamilton for a second convention to meet in May 1787 in Philadelphia. Shays’ Rebellion gave greater urgency to the planned convention. In February 1787, in the wake of the uprising in western Massachusetts, the Confederation Congress authorized the Philadelphia convention. This time, all the states except Rhode Island sent delegates to Philadelphia to confront the problems of the day.

The stated purpose of the Philadelphia Convention in 1787 was to amend the Articles of Confederation. Very quickly, however, the attendees decided to create a new framework for a national government. That framework became the United States Constitution, and the Philadelphia convention became known as the Constitutional Convention of 1787. Fifty-five men met in Philadelphia in secret; historians know of the proceedings only because James Madison kept careful notes of what transpired. The delegates knew that what they were doing would be controversial; Rhode Island refused to send delegates, and New Hampshire’s delegates arrived late. Two delegates from New York, Robert Yates and John Lansing, left the convention when it became clear that the Articles were being put aside and a new plan of national government was being drafted. They did not believe the delegates had the authority to create a strong national government.

Link to Learning

Read “Reasons for Dissent from the Proposed Constitution” in order to understand why Robert Yates and John Lansing, New York’s delegates to the 1787 Philadelphia Convention, didn’t believe the convention should draft a new plan of national government.

The Question of Representation

Figure 1 . James Madison’s Virginia Plan, shown here, proposed a strong national government with proportional state representation.

One issue that the delegates in Philadelphia addressed was the way in which representatives to the new national government would be chosen. Would individual citizens be able to elect representatives? Would representatives be chosen by state legislatures? How much representation was appropriate for each state?

James Madison put forward a proposition known as the Virginia Plan , which called for a strong national government that could overturn state laws. The plan featured a bicameral or two-house legislature, with an upper and a lower house. The people of the states would elect the members of the lower house, whose numbers would be determined by the population of the state. State legislatures would send delegates to the upper house. The number of representatives in the upper chamber would also be based on the state’s population. This proportional representation gave the more populous states, like Virginia, more political power. The Virginia Plan also called for an executive branch and a judicial branch, both of which were absent under the Articles of Confederation. The lower and upper house together were to appoint members to the executive and judicial branches. Under this plan, Virginia, the most populous state, would dominate national political power and ensure its interests, including slavery, would be safe.

The Virginia Plan’s call for proportional representation alarmed the representatives of the smaller states. William Paterson introduced a New Jersey Plan to counter Madison’s scheme, proposing that all states have equal votes in a unicameral national legislature. He also addressed the economic problems of the day by calling for the Congress to have the power to regulate commerce, to raise revenue through taxes on imports and through postage, and to enforce Congressional requisitions from the states.

Roger Sherman from Connecticut offered a compromise to break the deadlock over the thorny question of representation. His Connecticut Compromise , also known as the Great Compromise, outlined a different bicameral legislature in which the upper house, the Senate, would have equal representation for all states; each state would be represented by two senators chosen by the state legislatures. Only the lower house, the House of Representatives, would have proportional representation.

This video explains how the Connecticut Compromise ultimately solved the contest between the nationalists, who wanted a strong national government and proportional representation, and those who emphasized state rights and wanted equal state representation.

You can view the  transcript for “The Great Compromise” here (opens in new window) .

The Question of Slavery

The question of slavery stood as a major issue at the Constitutional Convention because slaveholders wanted enslaved people to be counted along with Whites, termed “free inhabitants,” when determining a state’s total population. This, in turn, would increase the number of representatives accorded to those states in the lower house. Some northerners, however, such as New York’s Gouverneur Morris, hated slavery and did not even want the term included in the new national plan of government. Slaveholders argued that slavery imposed great burdens upon them and that, because they carried this liability, they deserved special consideration; enslaved people needed to be counted for purposes of representation.

The issue of counting or not counting enslaved people for purposes of representation connected directly to the question of taxation. Beginning in 1775, the Second Continental Congress asked states to pay for war by collecting taxes and sending the tax money to the Congress. The amount each state had to deliver in tax revenue was determined by a state’s total population, including both free and enslaved individuals. States routinely fell far short of delivering the money requested by Congress under the plan. In April 1783, the Confederation Congress amended the earlier system of requisition by having enslaved people count as three-fifths of the White population. In this way, slaveholders gained a significant tax break. The delegates in Philadelphia adopted this same three-fifths formula in the summer of 1787.

Under the three-fifths compromise in the 1787 Constitution, each enslaved person would be counted as three-fifths of a White person. Article 1, Section 2 stipulated that “Representatives and direct Taxes shall be apportioned among the several states . . . according to their respective Number, which shall be determined by adding to the whole number of free Persons, including those bound for service for a Term of Years [White servants], and excluding Indians not taxed, three fifths of all other persons.” Since representation in the House of Representatives was based on the population of a state, the three-fifths compromise gave extra political power to states with an enslaved population, although not as much as if the total population, both free and slave, had been used. Significantly, no direct federal income tax was immediately imposed. (The Sixteenth Amendment, ratified in 1913, put in place a federal income tax.) Northerners agreed to the three-fifths compromise because the Northwest Ordinance of 1787, passed by the Confederation Congress, banned slavery in the future states of the northwest. Northern delegates felt this ban balanced political power between states with slaves and those without. The three-fifths compromise gave an advantage to slaveholders; they added three-fifths of their human property to their state’s population, allowing them to send representatives based in part on the number of enslaved people they held, even though those people were not allowed to speak for themselves or vote.

The Question of Democracy

Many of the delegates to the Constitutional Convention had serious reservations about democracy, which they believed promoted anarchy. To allay these fears, the Constitution blunted democratic tendencies that appeared to undermine the republic. Thus, to avoid giving the people too much direct power, the delegates made certain that senators were chosen by the state legislatures, not elected directly by the people (direct elections of senators came with the Seventeenth Amendment to the Constitution, ratified in 1913). As an additional safeguard, the delegates created the Electoral College, the mechanism for choosing the president. Under this plan, each state has a certain number of electors, which is its number of senators (two) plus its number of representatives in the House of Representatives. Critics, then as now, argue that this process prevents the direct election of the president.

This video reviews the historical context surrounding the creation of the Constitution and some of the compromises that were made during the Constitutional Convention.

You can view the  transcript for “The Constitution, the Articles, and Federalism” here (opens in new window) .

Review Question

Explain the argument that led to the three-fifths rule and the consequences of that rule.

anti-federalists:  those who opposed the 1787 Constitution and favored stronger individual states

bicameral:  having two legislative houses, an upper and a lower house

Connecticut Compromise:  also known as the Great Compromise, Roger Sherman’s proposal at the Constitutional Convention for a bicameral legislature, with the upper house having equal representation for all states and the lower house having proportional representation

electoral college:  the mechanism by which electors, based on the number of representatives from each state, choose the president

federalists:  those who supported the 1787 Constitution and a strong central government; these advocates of the new national government formed the ruling political party in the 1790s

proportional representation:  representation that gives more populous states greater political power by allowing them more representatives

three-fifths compromise:  the agreement at the Constitutional Convention that each enslaved person would count as three-fifths of a White person for purposes of representation

• The Constitutional Convention and Federal Constitution. Provided by : OpenStax College. Located at : https://openstax.org/books/us-history/pages/7-4-the-constitutional-convention-and-federal-constitution . License : CC BY: Attribution . License Terms : Access for free at https://openstax.org/books/us-history/pages/1-introduction
• Constitution of the United States. Provided by : Wikipedia. Located at : https://en.wikipedia.org/wiki/Constitution_of_the_United_States . License : CC BY-SA: Attribution-ShareAlike
• The Constitution, the Articles, and Federalism: Crash Course US History #8. Provided by : CrashCourse. Located at : https://youtu.be/bO7FQsCcbD8?t=1s . License : All Rights Reserved . License Terms : Standard YouTube License
• The Great Compromise. Provided by : NBC News Learn. Located at : https://www.youtube.com/watch?v=pgEj6QCX63I . License : Other . License Terms : Standard YouTube License

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Why do all states have equal representation in the U.S. Senate, regardless of population?

For example, while California (population: 39,144,818) has two senators to represent them, Wyoming (population: 586,107) also has two senators to represent them. The population of California is more than 66 times the population of Wyoming, but California and Wyoming still have equal representation in the Senate.

The Senate has a great amount of power when it comes to passing legislation and approving Supreme Court nominees. Though, a Wyomingite's vote counts significantly more than a Californian's vote.

• united-states

• 25 It's not a defect, it's a feature. –  user1530 Commented Apr 30, 2016 at 18:35
• 3 @user1530 Asking why something is does not imply that one thinks it's a defect. –  phoog Commented Aug 13, 2021 at 14:04

Because it was a compromise struck at the Constitutional Convention between the large colonies like Virginia and New York, and the smaller colonies like Connecticut and Rhode Island that all states would get an equal say in the Senate to prevent the large states from forcing their policies on the Smaller states.

It was known as the Connecticut Compromise . This was done because the states have rights too, and each state will have an equal say in matters before the senate.

The other side of the compromise was that the House of Representatives does have proportional representation. Roughly speaking, the idea was for the House to represent the people and the Senate to represent the states.

• 25 +1 Note that the other side of the compromise was proportional representation in the House. Roughly speaking, the idea was for the House to represent the people and the Senate to represent the states. –  Era Commented Apr 29, 2016 at 23:05
• 5 @KDog - While I tend to agree that these principles when applied as intended do, they can also be used to oppress as was done throughout the US south in the 50's and 60s. –  SoylentGray Commented Oct 28, 2016 at 15:26
• 1 @DeplorableNumber9035768 - The Constitution was groundbreaking. Confederations were already well known in the 18th century; you can pick up histories like Thucydides' and find confederations of city-states easily. –  indigochild Commented Oct 28, 2016 at 15:46
• 1 @indigochild - You should create your own answer then. –  SoylentGray Commented Oct 28, 2016 at 16:20
• 3 It should also be noted that the members of the senate used to be picked by the state legislators and not the people in the state. –  Joe W Commented Aug 13, 2021 at 13:21

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What’s Going On in This Graph? | Senate Representation by State

Two senators represent each state in Congress. How does that affect political representation across the United States?

By The Learning Network

Note: We are featuring this graph for two weeks at the top of the “What’s Going On in This Graph” column. On Wednesday, Nov. 9, there will be a live-moderated discussion of this graph.

According to the 17th Amendment to the U.S. Constitution, “The Senate of the United States shall be composed of two Senators from each State, elected by the people thereof, for six years; and each Senator shall have one vote.” All states, regardless of population size, have two senators.

This infographic, which appeared elsewhere on NYTimes.com, shows the number of voters — citizens 18 years and older, per senator for a sample of six states. Comparable infographics can be constructed for all states.

On Wednesday, Nov. 9, we will moderate your responses live online. By Friday morning, Nov. 11, we will provide the “Reveal” — the infographic’s free online link, additional questions, shout outs for student headlines and Stat Nuggets.

1. After looking closely at the graph above (or at this full-size image ), answer these four questions:

What do you notice?

What do you wonder?

How does this relate to you and your community?

What’s going on in this graph? Create a catchy headline that captures the graph’s main idea.

The questions are intended to build on one another, so try to answer them in order.

2. Next, join the conversation online by clicking on the comment button and posting in the box. (Teachers of students younger than 13 are welcome to post their students’ responses.)

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What Is a Bicameral Legislature and Why Does the U.S. Have One?

About half of the world’s governments have bicameral legislatures

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How Common are Bicameral Legislatures?

Why does the us have a bicameral congress, just like the founding fathers saw it, why are the house and senate so different, why are the differences important, bicameral versus unicameral legislatures, representatives always seem to be running for election, does older mean wiser, cooling the lawmaking coffee.

• B.S., Texas A&M University

The term “bicameral legislature” refers to any lawmaking body of government that consists of two separate houses or chambers, such as the House of Representatives and the Senate that make up the United States Congress .

Key Takeaways: Bicameral Systems

• Bicameral systems separate the legislative branch of government into two separate and distinct divisions or “chambers,” as opposed to unicameral systems which employ no such division.
• The U.S. bicameral system—the Congress—is composed of the House of Representatives and the Senate.
• The number of members of the House of Representatives is based on each state’s population, while the Senate is composed of two members from each state.
• Each chamber of a bicameral legislature has different powers in order to ensure fairness through checks and balances within the system.

Indeed, the word “bicameral” comes from the Latin word “camera,” which translates to “chamber” in English.

Bicameral legislatures are intended to provide representation at the central or federal level of government for both the individual citizens of the country, as well as the legislative bodies of country’s states or other political subdivisions. About half of the world’s governments have bicameral legislatures.

In the United States, the bicameral concept of shared representation is exemplified by the House of Representatives, whose 435 members look after the interests of all residents of the states they represent, and the Senate, whose 100 members (two from each state) represent the interests of their state governments. A similar example of a bicameral legislature can be found in the English Parliament’s House of Commons and House of Lords.

There have always been two differing opinions on the effectiveness and purpose of bicameral legislatures:

Bicameral legislatures enforce an effective system of checks and balances preventing the enactment of laws unfairly impacting or favoring certain factions of the government or the people.

The procedures of bicameral legislatures in which both chambers must approve legislation often result in complications slowing or blocking the passage of important laws.

Currently, about 41% of governments worldwide have bicameral legislatures and about 59% employ various forms of unicameral legislatures. Some countries with bicameral legislatures include Australia, Brazil, Canada, the Czech Republic, Germany, India, the United Kingdom, Ireland, the Netherlands, Russia, and Spain. In countries with bicameral legislatures, the size, length of term in office, and manner of election or appointment for each chamber will vary. Growing somewhat in popularity during the 20th century, unicameral legislatures have more recently been adopted in countries like Greece, New Zealand, and Peru.

The bicameral legislature in the United Kingdom—the Parliament—originally formed in 1707, consists of the House of Lords and the House of Commons. The upper House of Lords represents a smaller, more elite social class, while the lower House of Commons represents a larger, less-exclusive class. While the U.S. Senate and House were modeled after the British House of Lords and House of Commons, America’s bicameral legislature was designed to represent residents in different geographic locations rather than different socio-economic classes.

In the bicameral U.S. Congress, those complications and blocking of the legislative process can happen at any time but are far more likely during periods when the House and Senate are controlled by different political parties.

So why do we have a bicameral Congress? Since members of both chambers are elected by and represent the American people, wouldn't the lawmaking process be more efficient if bills were considered by only one “unicameral” body?

While it is at times truly clumsy and overly time-consuming, the bicameral U.S. Congress works today exactly the way a majority of the framers of the Constitution envisioned in 1787. Clearly expressed in the Constitution is their belief that power should be shared among all units of government. Dividing Congress into two chambers, with the positive vote of both required to approve legislation, is a natural extension of the framers' concept of separation of powers to prevent tyranny.

The provision of a bicameral Congress didn't come without debate. Indeed, the question almost derailed the entire Constitutional Convention. Delegates from the small states demanded that all states be equally represented in Congress. The large states argued that since they had more voters, representation should be based on population. After months of great debate, delegates arrived at the “ Great Compromise ,” under which the small states got equal representation (two Senators from each state) in the Senate, and the large states got proportional representation based on population in the House.

But is the Great Compromise really all that fair? Consider that the largest state–California—with a population about 73 times larger than that of the smallest state—Wyoming—both get two seats in the Senate. Thus, it can be argued that an individual voter in Wyoming wields about 73 times more power in the Senate than an individual voter in California. Is that “​one man—one vote?”

Have you ever noticed that major bills are often debated and voted on by the House in a single day, while the Senate's deliberations on the same bill take weeks? Again, this reflects the Founding Fathers' intent that the House and Senate were not carbon-copies of each other. By designing differences into the House and Senate, the Founders assured that all legislation would be carefully considered, taking both the short and long-term effects into account.

The Founders intended that the House be seen as more closely representing the will of the people than the Senate.

To this end, they provided that members of the House— U.S. Representatives —be elected by and represent limited groups of citizens living in small geographically defined districts within each state. Senators, on the other hand, are elected by and represent all voters of their state. When the House considers a bill, individual members tend to base their votes primarily on how the bill might impact the people of their local district, while Senators tend to consider how the bill would impact the nation as a whole. This is just as the Founders intended.

In contrast to bicameral legislatures, with two chambers, unicameral legislatures consist of only one house or assembly that legislates and votes as one. 

Bicameral legislatures, like the United States Congress, are typically justified as an extension of the larger principle of checks and balances . In theory, bicameral legislatures are desirable because they avoid hasty and extreme legislation by ensuring more thoughtful deliberation. Because of their requirement for mutual agreement of both chambers, bicameral legislatures are considered to be more likely than unicameral legislatures to result in a measured compromise between different political and social ideals.

Despite occasional opposition to them, bicameral national government legislatures remained prevalent throughout the 20th century. Following patterns established in the 19th century, unicameral councils or commissions came to predominate in American cities and counties. During the early 1900s, dissatisfaction with the sluggishness of bicameral American state legislatures led to numerous proposals for single-chamber systems. Today, however, Nebraska remains the only U.S. state with a unicameral legislature.

Following World War II, constitutional trends reflected a growing preference for unicameral systems among non-federal countries in which the national governments maintain exclusive power over all geographic areas. Many European countries and several Latin American countries established unicameral legislatures. Some modern countries with unicameral legislatures include Cuba, Honduras, Guatemala, Bulgaria, Denmark, Hungary, Monaco, Ukraine, Serbia, Turkey, and Sweden.

In Britain, where the Parliament’s House of Commons has become far more powerful than the House of Lords, and in France where the Senate, under the 1958 foundation of the Fifth Republic, remains virtually impotent, the governments effectively operate, on the unicameral principle. A unitary system of government does not imply a unicameral legislature. Modern constitutional countries often retain two-chamber legislatures even though true bicameralism has declined overall.

All members of the House are up for election every two years. In effect, they are always running for election. This ensures that members will maintain close personal contact with their local constituents, thus remaining constantly aware of their opinions and needs, and better able to act as their advocates in Washington. Elected for six-year terms, Senators remain somewhat more insulated from the people, thus less likely to be tempted to vote according to the short-term passions of public opinion.

By setting the constitutionally-required minimum age for Senators at 30 , as opposed to 25 for members of the House, the Founders hoped Senators would be more likely to consider the long-term effects of legislation and practice a more mature, thoughtful, and deeply deliberative approach in their arguments. Setting aside the validity of this "maturity" factor, the Senate undeniably does take longer to consider bills, often brings up points not considered by the House, and just as often votes down bills passed easily by the House.

A famous (though perhaps fictional) quip often quoted to point out the differences between the House and Senate involves an argument between George Washington, who favored having two chambers of Congress, and Thomas Jefferson, who believed a second legislative chamber unnecessary. The story goes that the two Founding Fathers were arguing the issue while drinking coffee. Suddenly, Washington asked Jefferson, "Why did you pour that coffee into your saucer?" "To cool it," replied Jefferson. "Even so," said Washington, "we pour legislation into the senatorial saucer to cool it."

• Republic vs. Democracy: What Is the Difference?
• Representative Democracy: Definition, Pros, and Cons
• About the Legislative Branch of U.S. Government
• The Great Compromise of 1787
• About the United States Senate
• The Powers of Congress
• Where, When, and Why Does the US Congress Meet?
• What Was the Virginia Plan?
• The U.S. House of Representatives
• Supermajority Vote in US Congress
• The House of Commons in Canada's Parliament
• The Three Branches of US Government
• How Bills Become Laws According to the U.S. Legislative Process
• Major Parliamentary Governments and How They Work
• Requirements to be a US Senator
• The U.S. Constitution

Chapter 11: Congress

Congressional Representation

Learning outcomes.

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

• Explain the basics of representation
• Describe the extent to which Congress as a body represents the U.S. population
• Explain the concept of collective representation
• Describe the forces that influence congressional approval ratings

The tension between local and national politics described in the previous section is essentially a struggle between interpretations of representation. Representation is a complex concept. It can mean paying careful attention to the concerns of constituents, understanding that representatives must act as they see fit based on what they feel best for the constituency, or relying on the particular ethnic, racial, or gender diversity of those in office. In this section, we will explore three different models of representation and the concept of descriptive representation. We will look at the way members of Congress navigate the challenging terrain of representation as they serve, and all the many predictable and unpredictable consequences of the decisions they make.

TYPES OF REPRESENTATION: LOOKING OUT FOR CONSTITUENTS

By definition and title, senators and House members are representatives. This means they are intended to be drawn from local populations around the country so they can speak for and make decisions for those local populations, their constituents, while serving in their respective legislative houses. That is, representation refers to an elected leader’s looking out for his or her constituents while carrying out the duties of the office. [1]

Theoretically, the process of constituents voting regularly and reaching out to their representatives helps these congresspersons better represent them. It is considered a given by some in representative democracies that representatives will seldom ignore the wishes of constituents, especially on salient issues that directly affect the district or state. In reality, the job of representing in Congress is often quite complicated, and elected leaders do not always know where their constituents stand. Nor do constituents always agree on everything. Navigating their sometimes contradictory demands and balancing them with the demands of the party, powerful interest groups, ideological concerns, the legislative body, their own personal beliefs, and the country as a whole can be a complicated and frustrating process for representatives.

Traditionally, representatives have seen their role as that of a delegate, a trustee, or someone attempting to balance the two. A representative who sees him- or herself as a delegate believes he or she is empowered merely to enact the wishes of constituents. Delegates must employ some means to identify the views of their constituents and then vote accordingly. They are not permitted the liberty of employing their own reason and judgment while acting as representatives in Congress. This is the delegate model of representation .

In contrast, a representative who understands their role to be that of a trustee believes he or she is entrusted by the constituents with the power to use good judgment to make decisions on the constituents’ behalf. In the words of the eighteenth-century British philosopher Edmund Burke, who championed the trustee model of representation , “Parliament is not a congress of ambassadors from different and hostile interests . . . [it is rather] a deliberative assembly of one nation, with one interest, that of the whole.” [2] In the modern setting, trustee representatives will look to party consensus, party leadership, powerful interests, the member’s own personal views, and national trends to better identify the voting choices they should make.

Understandably, few if any representatives adhere strictly to one model or the other. Instead, most find themselves attempting to balance the important principles embedded in each. Political scientists call this the politico model of representation . In it, members of Congress act as either trustee or delegate based on rational political calculations about who is best served, the constituency or the nation.

For example, every representative, regardless of party or conservative versus liberal leanings, must remain firm in support of some ideologies and resistant to others. On the political right, an issue that demands support might be gun rights; on the left, it might be a woman’s right to an abortion. For votes related to such issues, representatives will likely pursue a delegate approach. For other issues, especially complex questions the public at large has little patience for, such as subtle economic reforms, representatives will tend to follow a trustee approach. This is not to say their decisions on these issues run contrary to public opinion. Rather, it merely means they are not acutely aware of or cannot adequately measure the extent to which their constituents support or reject the proposals at hand. It could also mean that the issue is not salient to their constituents. Congress works on hundreds of different issues each year, and constituents are likely not aware of the particulars of most of them.

DESCRIPTIVE REPRESENTATION IN CONGRESS

In some cases, representation can seem to have very little to do with the substantive issues representatives in Congress tend to debate. Instead, proper representation for some is rooted in the racial, ethnic, socioeconomic, gender, and sexual identity of the representatives themselves. This form of representation is called descriptive representation .

At one time, there was relatively little concern about descriptive representation in Congress. A major reason is that until well into the twentieth century, white men of European background constituted an overwhelming majority of the voting population. African Americans were routinely deprived of the opportunity to participate in democracy, and Hispanics and other minority groups were fairly insignificant in number and excluded by the states. While women in many western states could vote sooner, all women were not able to exercise their right to vote nationwide until passage of the Nineteenth Amendment in 1920, and they began to make up more than 5 percent of either chamber only in the 1990s.

Many advances in women’s rights have been the result of women’s greater engagement in politics and representation in the halls of government, especially since the founding of the National Organization for Women in 1966 and the National Women’s Political Caucus (NWPC) in 1971. The NWPC was formed by Bella Abzug, Gloria Steinem, Shirley Chisholm, and other leading feminists to encourage women’s participation in political parties, elect women to office, and raise money for their campaigns. For example, Patsy Mink (D-HI), the first Asian American woman elected to Congress, was the coauthor of the Education Amendments Act of 1972, Title IX of which prohibits sex discrimination in education. Mink had been interested in fighting discrimination in education since her youth, when she opposed racial segregation in campus housing while a student at the University of Nebraska. She went to law school after being denied admission to medical school because of her gender. Like Mink, many other women sought and won political office, many with the help of the NWPC. Today, EMILY’s List, a PAC founded in 1985 to help elect pro-choice Democratic women to office, plays a major role in fundraising for female candidates. In the 2012 general election, 80 percent of the candidates endorsed by EMILY’s List won a seat. [3]

In the wake of the Civil Rights Movement, African American representatives also began to enter Congress in increasing numbers. In 1971, to better represent their interests, these representatives founded the Congressional Black Caucus (CBC), an organization that grew out of a Democratic select committee formed in 1969. Founding members of the CBC include Ralph Metcalfe (D-IL), a former sprinter from Chicago who had medaled at both the Los Angeles (1932) and Berlin (1936) Olympic Games, and Shirley Chisholm, a founder of the NWPC and the first African American woman to be elected to the House of Representatives.

In recent decades, Congress has become much more descriptively representative of the United States. The 116th Congress, which began in January 2019, had a historically large percentage of racial and ethnic minorities. African Americans made up the largest percentage, with fifty-seven members, while Latinos accounted for forty-six members, up from thirty just a decade before. [4] Yet, demographically speaking, Congress as a whole is still a long way from where the country is and remains largely white, male, and wealthy. For example, although more than half the U.S. population is female, only 25 percent of Congress is. Congress is also overwhelmingly Christian.

REPRESENTING CONSTITUENTS

Ethnic, racial, gender, or ideological identity aside, it is a representative’s actions in Congress that ultimately reflect his or her understanding of representation. Congress members’ most important function as lawmakers is writing, supporting, and passing bills. And as representatives of their constituents, they are charged with addressing those constituents’ interests. Historically, this job has included what some have affectionately called “bringing home the bacon” but what many (usually those outside the district in question) call pork-barrel politics . As a term and a practice, pork-barrel politics—federal spending on projects designed to benefit a particular district or set of constituents—has been around since the nineteenth century, when barrels of salt pork were both a sign of wealth and a system of reward. While pork-barrel politics are often deplored during election campaigns, and earmarks—funds appropriated for specific projects—are no longer permitted in Congress (see feature box below), legislative control of local appropriations nevertheless still exists. In more formal language, allocation , or the influencing of the national budget in ways that help the district or state, can mean securing funds for a specific district’s project like an airport, or getting tax breaks for certain types of agriculture or manufacturing.

GET CONNECTED!

Language and Metaphor

The language and metaphors of war and violence are common in politics. Candidates routinely “smell blood in the water,” “battle for delegates,” go “head-to-head,” “cripple” their opponent, and “make heads roll.” But references to actual violence aren’t the only metaphorical devices commonly used in politics. Another is mentions of food. Powerful speakers frequently “throw red meat to the crowds;” careful politicians prefer to stick to “meat-and-potato issues;” and representatives are frequently encouraged by their constituents to “bring home the bacon.” And the way members of Congress typically “bring home the bacon” is often described with another agricultural metaphor, the “earmark.”

In ranching, an earmark is a small cut on the ear of a cow or other animal to denote ownership. Similarly, in Congress, an earmark is a mark in a bill that directs some of the bill’s funds to be spent on specific projects or for specific tax exemptions. Since the 1980s, the earmark has become a common vehicle for sending money to various projects around the country. Many a road, hospital, and airport can trace its origins back to a few skillfully drafted earmarks.

Relatively few people outside Congress had ever heard of the term before the 2008 presidential election, when Republican nominee Senator John McCain touted his career-long refusal to use the earmark as a testament to his commitment to reforming spending habits in Washington. [5] McCain’s criticism of the earmark as a form of corruption cast a shadow over a previously common legislative practice. As the country sank into recession and Congress tried to use spending bills to stimulate the economy, the public grew more acutely aware of its earmarking habits. Congresspersons then were eager to distance themselves from the practice. In fact, the use of earmarks to encourage Republicans to help pass health care reform actually made the bill less popular with the public.

In 2011, after Republicans took over the House, they outlawed earmarks. But with deadlocks and stalemates becoming more common, some quiet voices have begun asking for a return to the practice. They argue that Congress works because representatives can satisfy their responsibilities to their constituents by making deals. The earmarks are those deals. By taking them away, Congress has hampered its own ability to “bring home the bacon.”

Are earmarks a vital part of legislating or a corrupt practice that was rightly jettisoned? Pick a cause or industry, and investigate whether any earmarks ever favored it, or research the way earmarks have hurt or helped your state or district, and decide for yourself.

Follow-up activity: Find out where your congressional representative stands on the ban on earmarks and write to support or dissuade him or her.

Such budgetary allocations aren’t always looked upon favorably by constituents. Consider, for example, the passage of the ACA in 2010. The desire for comprehensive universal health care had been a driving position of the Democrats since at least the 1960s. During the 2008 campaign, that desire was so great among both Democrats and Republicans that both parties put forth plans. When the Democrats took control of Congress and the presidency in 2009, they quickly began putting together their plan. Soon, however, the politics grew complex, and the proposed plan became very contentious for the Republican Party.

Nevertheless, the desire to make good on a decades-old political promise compelled Democrats to do everything in their power to pass something. They offered sympathetic members of the Republican Party valuable budgetary concessions; they attempted to include allocations they hoped the opposition might feel compelled to support; and they drafted the bill in a purposely complex manner to avoid future challenges. These efforts, however, had the opposite effect. The Republican Party’s constituency interpreted the allocations as bribery and the bill as inherently flawed, and felt it should be scrapped entirely. The more Democrats dug in, the more frustrated the Republicans became.

The Republican opposition, which took control of the House during the 2010 midterm elections, promised constituents they would repeal the law. Their attempts were complicated, however, by the fact that Democrats still held the Senate and the presidency. Yet, the desire to represent the interests of their constituents compelled Republicans to use another tool at their disposal, the symbolic vote. During the 112th and 113th Congresses, Republicans voted more than sixty times to either repeal or severely limit the reach of the law. They understood these efforts had little to no chance of ever making it to the president’s desk. And if they did, he would certainly have vetoed them. But it was important for these representatives to demonstrate to their constituents that they understood their wishes and were willing to act on them.

Historically, representatives have been able to balance their role as members of a national legislative body with their role as representatives of a smaller community. The Obamacare fight, however, gave a boost to the growing concern that the power structure in Washington divides representatives from the needs of their constituency. [6] This has exerted pressure on representatives to the extent that some now pursue a more straightforward delegate approach to representation. Indeed, following the 2010 election, a handful of Republicans began living in their offices in Washington, convinced that by not establishing a residence in Washington, they would appear closer to their constituents at home. [7]

COLLECTIVE REPRESENTATION AND CONGRESSIONAL APPROVAL

The concept of collective representation describes the relationship between Congress and the United States as a whole. That is, it considers whether the institution itself represents the American people, not just whether a particular member of Congress represents his or her district. Predictably, it is far more difficult for Congress to maintain a level of collective representation than it is for individual members of Congress to represent their own constituents. Not only is Congress a mixture of different ideologies, interests, and party affiliations, but the collective constituency of the United States has an even-greater level of diversity. Nor is it a solution to attempt to match the diversity of opinions and interests in the United States with those in Congress. Indeed, such an attempt would likely make it more difficult for Congress to maintain collective representation. Its rules and procedures require Congress to use flexibility, bargaining, and concessions. Yet, it is this flexibility and these concessions, which many now interpret as corruption, that tend to engender the high public disapproval ratings experienced by Congress.

After many years of deadlocks and bickering on Capitol Hill, the national perception of Congress is near an all-time low. According to Gallup polls, Congress has a stunningly poor approval rating of about 16 percent. This is unusual even for a body that has rarely enjoyed a high approval rating. For example, for nearly two decades following the Watergate scandal in the early 1970s, the national approval rating of Congress hovered between 30 and 40 percent. [8]

Yet, incumbent reelections have remained largely unaffected. The reason has to do with the remarkable ability of many in the United States to separate their distaste for Congress from their appreciation for their own representative. Paradoxically, this tendency to hate the group but love one’s own representative actually perpetuates the problem of poor congressional approval ratings. The reason is that it blunts voters’ natural desire to replace those in power who are earning such low approval ratings.

As decades of polling indicate, few events push congressional approval ratings above 50 percent. Indeed, when the ratings are graphed, the two noticeable peaks are at 57 percent in 1998 and 84 percent in 2001. In 1998, according to Gallup polling, the rise in approval accompanied a similar rise in other mood measures, including President Bill Clinton’s approval ratings and general satisfaction with the state of the country and the economy. In 2001, approval spiked after the September 11 terrorist attacks and the Bush administration launched the “War on Terror,” sending troops first to Afghanistan and later to Iraq. War has the power to bring majorities of voters to view their Congress and president in an overwhelmingly positive way. [9]

Nevertheless, all things being equal, citizens tend to rate Congress more highly when things get done and more poorly when things do not get done. For example, during the first half of President Obama’s first term, Congress’s approval rating reached a relative high of about 40 percent. Both houses were dominated by members of the president’s own party, and many people were eager for Congress to take action to end the deep recession and begin to repair the economy. Millions were suffering economically, out of work, or losing their jobs, and the idea that Congress was busy passing large stimulus packages, working on finance reform, and grilling unpopular bank CEOs and financial titans appealed to many. Approval began to fade as the Republican Party slowed the wheels of Congress during the tumultuous debates over Obamacare and reached a low of 9 percent following the federal government shutdown in October 2013.

One of the events that began the approval rating’s downward trend was Congress’s divisive debate over national deficits. A deficit is what results when Congress spends more than it has available. It then conducts additional deficit spending by increasing the national debt. Many modern economists contend that during periods of economic decline, the nation should run deficits, because additional government spending has a stimulative effect that can help restart a sluggish economy. Despite this benefit, voters rarely appreciate deficits. They see Congress as spending wastefully during a time when they themselves are cutting costs to get by.

The disconnect between the common public perception of running a deficit and its legitimate policy goals is frequently exploited for political advantage. For example, while running for the presidency in 2008, Barack Obama slammed the deficit spending of the George W. Bush presidency, saying it was “unpatriotic.” This sentiment echoed complaints Democrats had been issuing for years as a weapon against President Bush’s policies. Following the election of President Obama and the Democratic takeover of the Senate, the concern over deficit spending shifted parties, with Republicans championing a spendthrift policy as a way of resisting Democratic policies.

LINK TO LEARNING

Find your representative at the U.S. House website and then explore his or her website and social media accounts to see whether the issues on which your representative spends time are the ones you think are most appropriate.

CHAPTER REVIEW

See the Chapter 11.3 Review for a summary of this section, the key vocabulary , and some review questions to check your knowledge.

• Steven S. Smith. 1999. The American Congress. Boston, MA: Houghton Mifflin. ↵
• Edmund Burke, "Speech to the Electors of Bristol," 3 November 1774, http://press-pubs.uchicago.edu/founders/documents/v1ch13s7.html (May 1, 2016). ↵
• "Claire McCaskill, Emily’s List Celebrate Women’s Wins in 2012," 14 November 2012, http://abcnews.go.com/blogs/politics/2012/11/claire-mccaskill-emilys-list-celebrate-womens-wins-in-2012/ (May 1, 2016). ↵
• Grace Panetta and Samantha Lee. 12 January 2019. "This Graphic Shows How Much More Diverse the House of Representatives Is Getting." Business Insider. https://www.businessinsider.com/changes-in-gender-racial-diversity-between-the-115th-and-116th-house-2018-12 . ↵
• "Statement by John McCain on Banning Earmarks," 13 March 2008, http://www.presidency.ucsb.edu/ws/?pid=90739 (May 15, 2016); "Press Release - John McCain’s Economic Plan," 15 April 2008, http://www.presidency.ucsb.edu/ws/?pid=94082 (May 15, 2016). ↵
• Kathleen Parker, "Health-Care Reform’s Sickeningly Sweet Deals," The Washington Post, 10 March 2010, http://www.washingtonpost.com/wp-dyn/content/article/2010/03/09/AR2010030903068.html (May 1, 2016); Dana Milbank, "Sweeteners for the South," The Washington Post, 22 November 2009, http://www.washingtonpost.com/wp-dyn/content/article/2009/11/21/AR2009112102272.html (May 1, 2016); Jeffry H. Anderson, "Nebraska’s Dark-Horse Candidate and the Cornhusker Kickback," The Weekly Standard, 4 May 2014. ↵
• Phil Hirschkorn and Wyatt Andrews, "One-Fifth of House Freshmen Sleep in Offices," CBS News, 22 January 2011, http://www.cbsnews.com/news/one-fifth-of-house-freshmen-sleep-in-offices/ (May 1, 2016). ↵
• "Congress and the Public," http://www.gallup.com/poll/1600/congress-public.aspx (May 15, 2016). ↵

an elected leader’s looking out for his or her constituents while carrying out the duties of the office

a model of representation in which representatives feel compelled to act on the specific stated wishes of their constituents

a model of representation in which representatives feel at liberty to act in the way they believe is best for their constituents

a model of representation in which members of Congress act as either trustee or delegate, based on rational political calculations about who is best served, the constituency or the nation

the extent to which a body of representatives represents the descriptive characteristics of their constituencies, such as class, race, ethnicity, and gender

federal spending intended to benefit a particular district or set of constituents

the relationship between Congress and the United States as a whole, and whether the institution itself represents the American people

American Government (2e - Second Edition) Copyright © 2019 by OpenStax and Lumen Learning is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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May 21, 2024 ABA Task Force for American Democracy

Proportional representation, ruth greenwood, drew penrose, and deborah apau.

Modern politics in the United States is so rife with disturbing trends that the phrase “politics is broken” has become cliche. There exists near consensus that our political system must change, but no such consensus has emerged for what of the available reforms would have the greatest impact. This Working Paper argues that many of our most serious democratic shortcomings stem from one policy choice: The near-exclusive use of winner-take-all elections. To remedy these shortcomings, the United States should join the majority of other modern democracies in adopting proportional representation for Congress, as well as state and local legislative elections.

Proportional representation is a way of conducting elections that follows the simple principle that parties should earn seats in proportion to the number of votes cast for them. For example, if a party secures one-third of the vote, it should expect to win roughly one-third of legislative seats. Today, proportional representation is the most common electoral system among the world’s democracies.

Most elections in the United States instead use a winner-take-all system: Instead of multiple parties earning seats in proportion to their support, each election is won by a single party, usually in a single-member district. Scholarship finds that winner-take-all elections contribute to several concerning problems. Elections can be overwhelmingly uncompetitive, partisan and racial minorities are systematically underrepresented, and polarization and anti-democratic extremism tend to be more severe.

Various scholars, lawmakers, and civil society groups have therefore begun advocating that U.S. elections adopt proportional systems in lieu of winner-take-all. While proportional systems vary considerably in their designs, research consistently finds that they produce more competitive elections, more equal representation for all voters, and less pernicious polarization and associated extremism. No one model of electoral system is a panacea, but proportional systems appear to contribute to more representative and resilient democracies.

Problem Statement

How can we address the ways that winner-take-all elections harm our politics, prevent meaningful representation for certain communities, and threaten our democracy?

Background: The impact of winner-take-all elections

Legislative elections in the United States almost uniformly follow a winner-take-all rule. For the House of Representatives, each congressional district elects a single member, who “takes all” by virtue of being the only one elected. This is in contrast to proportional systems, where each district elects several members, with each party earning seats in proportion to its share of the vote. The Constitution does not require winner-take-all elections; the exclusive use of single-member districts for the House of Representatives is a policy choice mandated by federal law since 1967. That policy choice has produced a number of concerning consequences.

First, congressional elections are overwhelmingly uncompetitive. Most districts are easily identifiable as “red” or “blue,” before any votes are cast, turning the general election into a mere formality where the dominant party nominee wins by a commanding margin. As of writing, the 2024 general election is over six months away, yet Republicans have, in a sense, already won 192 seats (44 percent of the House), and Democrats have already won 173 (40 percent of the House). In these safe districts, voters will only have the opportunity to cast a powerless vote in an election that was decided years ago by cartographers. Meanwhile, control of the House will be decided by the small minority of voters (as few as 10% by some measures) who happen to live in swing districts.

In theory, congressional elections could be made more competitive by emphasizing competition when adopting district maps. However, people often live in communities that share political interests and partisan preferences, and so doing so would require an affirmative effort to emphasize competition over other considerations. Due to such geographic sorting, it will usually be easier to draw uncompetitive districts, and infeasible to draw every district as competitive. Meanwhile, most states still put the right to redistrict in the hands of partisan actors, who are often averse to emphasizing competition and instead prone to intentionally gerrymander districts. Though the effort towards independent redistricting has been valiant, and surprisingly successful, as long as single-member districting is used, gerrymandering will exist. Proportional, multi-member districts are extremely hard to gerrymander, while winner-take-all, single-member districts are uniquely prone to gerrymandering.

Second, single-member districts exaggerate the electoral power of majorities and underrepresent minorities. Because of their “take-all” structure, a party that wins more than 50 percent in a district (or in many cases, only a plurality) effectively wins 100 percent of representation. When patterned across a state, this dynamic can produce significantly biased results. For instance, in Massachusetts, despite commanding roughly a third of the statewide vote, Republicans regularly win zero of the state’s nine House seats. In Oklahoma, Democrats likewise win roughly a third of the statewide vote, and yet win zero of the state’s five House seats.

These electoral biases carry especially troubling implications for racial minorities, who tend to likewise be underrepresented in winner-take-all elections. Where racially polarized voting exists, the only way a minority group can elect a candidate of choice is by being the largest group of voters in a district. The result is that racial minorities, even if a substantial voting bloc, can be systematically underrepresented. In Alabama, Louisiana, and South Carolina, for example, Black voters constitute over 25 percent of voters overall, yet candidates of choice of the Black community win roughly 15 percent of their House seats.

To partially correct for these outcomes, states may deliberately design “majority-minority” or “minority opportunity” districts. Absent a minority opportunity district, Black voters would likely elect no representatives of their choice in South Carolina, for example. At its best, this approach is limited: it relies on patterns of residential segregation that may not (and arguably should not) exist for groups in the near-future, and does not exist for some racial groups now. Even where districts can be effective, the approach of achieving minority representation through redistricting relies on a legal requirement for such districts to be drawn, given that the map-making authority is often majority-controlled. That legal requirement is found today in the Voting Rights Act, but its dictates have been significantly weakened by judicial decisionmaking.

Third, winner-take-all elections are associated with higher levels of affective polarization. When elections are winner-take-all, politics drives toward a binary: Either “we” win and “they” lose, or “they” win and “we” lose. This creates a zero-sum dynamic where partisans can gain just as much by denigrating and alienating their opposition as by making a positive case for themselves. Internationally, this kind of negative, “affective” polarization is most severe in countries with winner-take-all elections. In countries with deep and severe division, such as the United States, winner-take-all elections tend to exacerbate divisions, whereas proportional systems create mechanisms that facilitate greater management of partisan conflict.

All of the above dynamics combine to make our system vulnerable to authoritarianism. Distorted partisan representation can result in one party winning majority control without majority support among the electorate. Such a distortion creates strong incentives for it to further frustrate majority rule and entrench its advantage. That includes eroding the legal protections for enfranchisement of minority voters: both in terms of blocking access to voting (voter suppression) and offering only a meaningless ballot to people of color (vote dilution). With few competitive districts, the ability of voters to push back against an increasingly authoritarian party (by voting for its opposition) is severely diminished. As partisan polarization becomes more and more severe, authoritarians can gain support from otherwise pro-democracy voters, because the only available alternative is voting for a party that feels not only opposed on policy but alien in identity. This all combines to create a “doom loop” that threatens democracy itself.

Proposed Solution: Proportional representation

To address the problems attributable to winner-take-all elections, the U.S. should join the majority of other modern democracies in adopting a system of proportional representation.

Proportional representation is a class of electoral system that aims to ensure seats reflect votes : that is, a political party’s share of seats in a delegation and a legislature is commensurate with its share of its vote: If a party wins 30 percent of votes, it should earn 30 percent of seats, and likewise for any other share. Proportionality is achieved by using multi-member districts instead of single-member districts, in which multiple seats are allocated according to parties’ vote shares. For example, a state like Louisiana that elects six members to the House of Representatives could elect all six statewide on a proportional basis, or it could divide into two equal-population districts that each elect three members on a proportional basis.

Proportional representation does not guarantee any particular outcome for any groups. Rather, it makes it possible for a share of voters to elect an equal share of seats. The parties and candidates must still make the case to voters and earn their votes. But any party that earns those votes will also win its fair share of seats.

While all proportional systems aim to ensure proportionality in outcomes, no two systems around the world are exactly alike. When countries adopt proportional systems, they do so within the context of their political histories and with a mind to their specific challenges. While there are certain common models of proportional representation, details vary considerably. For example, multi-member districts could elect as few as three winners or as many as 10 or more ( “district magnitude”). Within a multi-member district, voters could vote for a single candidate as they do today (as in “open list” proportional representation), or they could vote only for a political party (“closed list”), or they could rank candidates (“proportional ranked choice voting”). This Working Paper does not advocate for any specific system, and indeed given the federal nature of the United States, different states could adopt different systems, allowing for local variation and experimentation.

Electoral competition

With proportional representation, there are no “red” or “blue” districts. The greater the district magnitude, the easier it is for a party to win a seat, and the smaller a percent of the vote is needed to change the outcome. In other words, proportional multi-member districts will be nearly universally competitive: No district would be totally safe for one party.

Proportional systems are less vulnerable to both geographic sorting and intentional gerrymandering. Republicans in cities and Democrats in rural areas would be expected to win a share of seats commensurate with their support, rather than being completely shut out. In Massachusetts, Democrats would still win a majority of seats, but Republicans would win their fair share as well. Likewise, in Oklahoma, Republicans would still win most of the seats, but Democrats would earn representation too.

A higher district magnitude makes attempts to gerrymander districts for partisan advantage increasingly difficult and less effective. Internationally, we see far less susceptibility to gerrymandering in countries with proportional systems. Even a modest increase in district magnitude can significantly blunt attempts to gerrymander, and gerrymandering becomes functionally impossible where districts each elect at least five members.

Minority voting power

Minority groups, including women and communities of color, have battled disenfranchisement and attempts at voter suppression throughout much of American history. Proportional representation is one way to further the U.S.’s progress in representing historically marginalized communities.

Studies show that winner-take-all systems tend to systematically underrepresent racial minorities, and that proportional systems are more likely to provide for both greater descriptive and substantive minority representation. Under winner-take-all, the dominant voter-group “takes all” in a district; and so unless a racial group can garner support from a majority (either by being the majority themselves or by convincing enough non-minority voters to support their preferred candidates), they remain barred from representation. Such is the case for many Black, Latino, Asian, and Native voters, particularly those who are geographically dispersed outside of minority opportunity districts. In Nevada, for example, Latino voters comprise nearly 20 percent of the electorate, but there are no Latino representatives in the House delegation.

A majority of Black voters in southern states with a history of racially polarized voting live in majority-white (often safe Republican) districts. Modeling exercises find that if these states were to utilize proportional multi-member districts in the place of the single-member districts, the share of Black voters able to elect at least one candidate of their choice increases to 98 percent. Comparative research consistently finds better representation for ethnic minorities in countries that use proportional representation.

More people of color would be able to elect a candidate of their choice because proportional representation would translate votes to seats proportionally, liberating the power of any given group of votes from the need for a favorable district map to secure representation. For example, in a proportional multi-member district with three seats in which Black voters constitute one third of the population, they can be expected to elect their preferred candidate to at least one seat if they vote cohesively (and more seats if they garner support from non-Black voters for additional candidates of choice).

If this same region is divided into three single-member districts, however, the ability of Black voters to elect their preferred candidate becomes dependent on their geographic distribution and on the choice of district map. To meet the needs of its diverse population, the United States should consider an electoral design which utilizes district magnitudes of five or more to minimize the potential for racial vote dilution and to enable representation of those members of the electorate who do not constitute a majority in their district. Such a design would make the Voting Rights Act’s guarantee of an equal opportunity to elect harder to violate through vote dilution.

Proportional representation may have particular significance for women’s representation as well. In 2023, women were 50.4 percent of the overall population, yet women representatives comprised only 28 percent of the U.S. House. While there is rarely parity between rates of female and male representation in democracies, the U.S. performs particularly poorly when compared to countries that elect proportionally, such as Germany (35%), Denmark (40%), or New Zealand (50%). Overall, countries that elect proportionally elect more women. Female candidates also tend to be more successful when running in multiparty elections and in multi-member districts.

Fairness of partisan results

Proportional representation can also almost guarantee partisan fairness in electoral results. With single-member districts, the choice of district boundaries can profoundly change who wins and loses with any given group of voters, whereas with proportional representation, a share of votes elects a roughly equal share of seats. Taking Oklahoma as an example: In 2022, Democrats won between 22 and 37 percent of the vote in each of its five congressional districts (for 31 percent of the vote statewide), winning zero seats. This large proportion of wasted votes in single-member districts can create severe distortions in aggregate. For example, in 2012, Republicans were able to win a majority of seats in the House of Representatives despite Democrats earning significantly more votes in aggregate.

Proportional representation would essentially eliminate these disparities, both within states and in aggregate. Returning to Oklahoma, a proportional formula would ensure that the Democratic minority within the state would have the votes to elect one or two of the five representatives. In fact, simulations suggest that even with modest district magnitudes, no multi-member district in any state would be likely to exclusively elect a single party slate; Democrats would win in places like Oklahoma and Republicans would win in places like Massachusetts. When aggregated across all districts, proportional representation results in a much closer fit between votes and seats.

Correcting for the severe partisan imbalances of single-member districts is often the most straightforward case for proportional representation. For example, when New Zealand elected its national legislature in single-member districts, it suffered two consecutive elections in which one party won a majority of seats despite its opposition earning more votes. This immediately led to a push for proportional representation that ultimately succeeded in 1993, leading to the country’s use of a proportional electoral system ever since (with no such electoral inversions occurring since its adoption).

Polarization and extremism

Proportional representation, by ending the all-or-nothing, binary choice associated with winner-take-all, would help reduce partisan polarization. In general, countries with more proportional systems tend to have less affective polarization, tend to be more effective at managing political conflict, and tend to have lower levels of ethnic-based political violence.

In a single-member district, demonizing the opposition is often an effective way to win elections. In districts that are safe for one party, the election is effectively decided at the primary election stage, where a smaller, more partisan, and less representative group of voters decides the winner. In competitive districts, hostile negative campaigning can drive down turnout for an opponent. These incentives are reversed under proportional representation, where there are no safe districts, and where the greater number of choices means that campaigning is less zero-sum - attacking an opponent does not necessarily help when the voter has other choices available.

More broadly, proportional representation can facilitate multiparty politics, which tends to result in shifting coalitions, “where few political enemies are ever permanent.” In countries with proportional representation, voters tend to view opposition parties less negatively. Likewise, opposition parties themselves are more likely to accept the results of elections under proportional representation, in part because rather than being shut out, they will have earned their fair share of political power and influence. In this environment, politics may still be quite partisan, but will not develop patterns of affective polarization that can lead to extremism and democratic decline.

The way that proportional representation addresses these issues is particularly important. Historically, conventional wisdom held that the two-party system prevented extremism by suppressing extremist parties. However, that very dynamic created a vulnerability: if extremists could capture one of the two major parties, they could significantly expand their influence. Under proportional representation, on the other hand, extremists can win some seats, but never more than the share of votes they are able to earn. For example, Poland’s 2023 elections show how an otherwise-unlikely coalition of pro-democracy parties can overcome a rise in authoritarianism under a more proportional system.

Next Steps: How we can move toward proportional representation

Winner-take-all elections are not inevitable. They are a policy choice. Already, reformers and voting rights activists have made progress in moving towards more proportional systems.

There is a history of advocacy for proportional representation at the state and local levels. From 1870 to 1980, Illinois elected its state house of representatives in three-member districts using cumulative voting, a semi-proportional system. Because cumulative voting is only semi-proportional, and because districts only elected three winners, the system was modest in its impact - the state house still had many uncompetitive contests and a two-party system. However, even such a modest system had a significant impact. Both Republicans and Democrats won seats in all parts of the state, resulting in a less polarized and more effective state legislature during its use, and Black members won election to the House throughout the Jim Crow era when we saw very few Black state legislators elected in southern legislatures.

From 1915 through the 1940s, some 24 cities, including Cincinnati and New York City, experimented with proportional ranked choice voting (Cambridge, Massachusetts retains the system from this era). These uses have a record of improving representation. For example Cincinnati elected its first Black councilmembers under the system at a time when the city was about 10 percent Black. The one city that used the system in partisan elections, New York City, went from a two party system to a multiparty system (then back to a two party system after returning to winner-take-all).

In the 1990s, some of the first tentative steps toward greater use of proportional representation came as the result of litigation brought under the Voting Rights Act. Vote dilution lawsuits brought under Section 2 of the Voting Rights Act usually seek to replace winner-take-all at-large elections with districts, including some number of majority-minority or opportunity districts. However, some of these cases have instead ended with the parties agreeing to a “modified at-large,” which retains at-large elections but replaces the winner-take-all voting rule with something more proportional.

To date, more than 100 local jurisdictions have adopted a semi-proportional method, limited voting or cumulative voting, to remedy a vote dilution claim. Although these methods are far from proportional, they do make it possible for a minority bloc of voters to elect a candidate without the use of districts. A few recent cases have even adopted proportional ranked choice voting, a more truly proportional system. The use of proportional representation can sometimes be a more effective remedy than districts, and it can also allow the jurisdiction to retain the at-large nature of the election, which it may prefer in some contexts.

In the wake of the Voting Rights Act being successively weakened by federal courts (see above), some states have passed state-level Voting Rights Acts, and these often explicitly name semi-proportional and proportional voting methods as available remedies in vote dilution lawsuits.

Outside of the litigation contexts, advocates have begun a new wave of momentum for proportional representation at the state and local levels. The diversity of places considering the reform speaks to its many benefits: For example (deep blue) Portland, Oregon became the first new city to adopt proportional representation for its city council in 2022 and will use it for the first time in November, 2024. While, the Rainey Center’s Andy Craig recently published a report arguing for proportional representation for the (ruby red) state legislature of Wyoming.

For Congress, proportional representation, while certainly a big change, may not be quite as big a lift as some may assume. The exclusive use of single-member districts to elect the House of Representatives is nowhere to be found in the Constitution. Rather, it comes from the Uniform Congressional District Act, a law passed in 1967. States could start using proportional representation to elect their congressional delegations if that law were simply amended to make that possible. Amending the UCDA would cost nothing and would not require any changes to take place that states did not want to adopt voluntarily.

Most elections in the United States follow a winner-take-all rule, but this is a choice that we can and should revisit. Adopting proportional representation would carry benefits that speak directly to many of our most pressing political problems. Consideration of proportional representation should be a high priority for those interested in improving our politics.

This document has been submitted to the Task Force for American Democracy for consideration and has been posted and/or circulated for information purposes only. The views expressed herein represent the opinions of the author(s) and not those of the Task Force or the ABA. They have not been reviewed or approved by the House of Delegates or the Board of Governors of the American Bar Association and, accordingly, should not be construed as representing the position of the Association or any of its entities. This publication is freely available to download, copy and distribute provided there is attribution to the ABA Task Force for American Democracy, and provided this notice is reproduced on all copies.

Deborah Apau

Protect democracy.

Deborah Apau   is a research specialist at Protect Democracy. Before joining Protect Democracy, Deborah worked as policy analyst with a focus on policies impacting vulnerable children. She has also worked as an Immigration Services Officer and Special Emphasis Program Manager in the U.S. Department of Homeland Security (USCIS). Deborah received her B.A from New York University and Master’s from the London School of Economics and Political Science where she was a research officer for the 89 Initiative.

Ruth Greenwood

Harvard law school.

Ruth Greenwood is an Assistant Clinical Professor and the Director of the Election Law Clinic at Harvard Law School. She engages in litigation and advocacy on a variety of election law cases, while training the next generation of election lawyers. Ruth litigated two partisan gerrymandering cases from the trial level to the Supreme Court of the United States,  Gill v. Whitford  and  Rucho v. Common Cause . She has also litigated minority vote dilution claims under state and federal voting rights acts, racial gerrymandering claims, and cases alleging a burden on the fundamental right to vote. In addition, Ruth has advised dozens of state advocates on drafting and implementing independent redistricting commissions, state voting rights acts, and adopting ranked choice voting. Ruth’s publications include  Voting Rights Federalism  (coauthored with Nicholas O. Stephanopoulos, Emory L.J. vol. 73(2) 2024) and  Fair Representation in Local Government  (Ind. J. L. & Soc. Equality vol 5(1) 2017).

Drew Penrose

Drew Penrose is a policy strategist at Protect Democracy, a non-partisan, non-profit organization working to prevent U.S. democracy from declining into a more authoritarian form of government. He brings over a decade of experience in the electoral reform space, including a prior leadership role at FairVote, and as lead author of  Our Shared Republic: The Case for Proportional Representation in the House of Representatives . Drew is a graduate of the James E. Rogers College of Law at the University of Arizona.

AP Decision Notes: What to expect in Colorado's state primaries

Colorado’s congressional delegation faces a reshuffling in new week's state primaries after a retirement, resignation and one relocation have ensured that at least a third of the state’s population will have new representation in Washington next year

WASHINGTON -- Colorado’s congressional delegation faces a reshuffling in Tuesday’s state primaries after a retirement, a resignation and a relocation have ensured that at least a third of the state’s population will have new representation in Washington next year.

Tuesday’s primaries will also lay the groundwork for a general election in which two competitive Colorado districts could help determine control of the narrowly divided U.S. House in November.

In the 3rd Congressional District, two-term Republican U.S. Rep. Lauren Boebert faced a tough rematch with Democrat Adam Frisch , who came within 546 votes of toppling the congresswoman in 2022. However, when fellow Republican Ken Buck decided in 2023 not to seek a sixth term in the neighboring 4th Congressional District, Boebert opted instead to head east and run for Buck’s open seat , where Republicans enjoy a bigger electoral advantage.

She now faces a crowded Republican primary field that includes state Reps. Mike Lynch and Richard Holtorf, conservative activist and talk radio host Deborah Flora, Logan County Commissioner and former state Senate President Pro Tempore Jerry Sonnenberg and banking executive Peter Yu. Running for the Democratic nomination are speechwriter Trisha Calvarese, Marine Corps veteran Ike McCorkle and engineer John Padora.

Buck resigned from his seat in March, triggering a special general election to serve out the remaining six months of his term. The race appears on the ballot alongside the regularly scheduled primaries for the full term.

Several of the candidates vying for the full-term seat also sought the Republican nomination to fill Buck’s vacancy, but a state Republican Party committee nominated former Parker Mayor Greg Lopez , who is not running for a full term. He will face Democrat Calvarese and two third-party candidates.

Since her election in 2020, Boebert has become a polarizing figure for her combative style and penchant for controversy . The past year has been particularly chaotic for Boebert’s personal life, with a messy divorce , the arrest of her son in a series of break-ins and thefts, a health scare requiring surgery for a blood clot and her highly publicized ejection from a Denver theater for causing a disturbance.

Despite the controversies, Boebert likely improved her chances at reelection with the move to a district that former President Donald Trump carried twice with almost 60% of the vote. She leads the field in fundraising and has the backing of Trump, House Speaker Mike Johnson and the state party.

Back in Boebert’s former district, Frisch is unopposed for the Democratic nomination. He will face the winner of a crowded Republican primary field, which includes former state Rep. Ron Hanks, the state party’s preferred candidate. Although Frisch came close to beating Boebert in 2022, the district still leans Republican. Voters there gave Trump 53% of the vote in 2016 and 2020.

Colorado’s most competitive U.S. House race this fall will likely be in the 8th Congressional District, where first-term U.S. Rep. Yadira Caraveo is unopposed in the Democratic primary. Her Republican opponent will be either state Rep. Gabe Evans or former state Rep. Janak Joshi. Evans is an Army veteran and former police officer, while Joshi is a retired physician and has the state party’s endorsement.

Caraveo won her seat in 2022 with just 48% of the vote in this new district near Denver, Boulder and Fort Collins. Trump received 46% of the vote in the area in the last two presidential elections, enough to outperform Hillary Clinton in 2016 but about 4 percentage points shy of Joe Biden in 2020.

In the 5th Congressional District, Republican U.S. Rep. Doug Lamborn’s upcoming retirement after nine terms has created an opening for this Republican-friendly seat anchored by Colorado Springs. Political consultant and talk radio host Jeff Crank and state party chairman Dave Williams are running for the Republican nomination. Williams has Trump’s endorsement as well as that of the state party he runs.

Some Republicans including Crank have criticized Williams for using the state party apparatus to promote his own congressional aspirations. The Democratic nominee will be either River Gassen or Joe Reagan. Trump received 53% of the District’s vote in 2020 and 56% in 2016. Lamborn received 56% in his 2022 reelection.

Farther down the ballot are contested primaries for state Senate and state House. About half of the state’s 35 state Senate seats and all 65 state House seats are up for election this year. Democrats enjoy about a 2-to-1 majority in both chambers.

Here’s a look at what to expect on Tuesday:

The Colorado state primary will be held Tuesday. Polls close at 9 p.m. ET.

The Associated Press will provide vote results and declare winners in 35 contests, including six contested primaries for the U.S. House, seven for the state Senate, 18 for the state House, two state boards of education, one for the University of Colorado Board of Regents and one special general election for the 4th Congressional District.

Registered party members may vote only in their own party’s primary. In other words, Democrats can’t vote in the Republican primary or vice versa. Independent or unaffiliated voters may participate in any party’s primary.

By running for a different seat, Boebert exchanged Colorado’s sprawling westernmost district for its sprawling easternmost district. In the 3rd District, the most influential counties in elections are Republican-friendly Mesa to the west, which includes Grand Junction, and Democratic-friendly Pueblo to the east. The candidate who carries both counties, as Boebert did in the 2020 primary when she unseated incumbent GOP Rep. Scott Tipton , would be difficult to defeat.

In Boebert’s new 4th District, the key county to win is Douglas, nestled between Denver and Colorado Springs. Douglas has by far the largest population in the district, casting more than half of the votes in Buck’s 2022 reelection. A candidate trailing in Douglas would need overwhelming margins in the rest of the District to eke out a win. Douglas votes less Republican than the rest of the District, giving Trump about 52% of its vote in 2020, compared to about 60% to nearly 90% in other counties.

The AP does not make projections and will declare a winner only when it’s determined there is no scenario that would allow the trailing candidates to close the gap. If a race has not been called, the AP will continue to cover any newsworthy developments, such as candidate concessions or declarations of victory. In doing so, the AP will make clear that it has not yet declared a winner and explain why.

Colorado allows for automatic recounts in races where the vote margin is 0.5% or less of the leader’s vote total. The AP may declare a winner in a race that is eligible for a recount if it can determine the lead is too large for a recount or legal challenge to change the outcome.

As of June 1, there were nearly 4.5 million registered voters in Colorado. Of those, 26% were Democrats, 23% were Republicans and about half were unaffiliated or independent.

In the 2022 primaries, turnout was 12% of registered voters in the Democratic primaries and 15% in the Republican primaries. Colorado conducts its elections predominantly by mail.

As of Tuesday, a total of 449,721 ballots had already been cast, about 42% in the Democratic primary and 41% in the Republican primary. A total of 75,516 votes have already been cast in the 4th Congressional District special election.

In the 2022 primaries, the AP first reported results at 9:04 p.m. ET, or four minutes after polls closed. The election night tabulation ended at 4:05 a.m. ET with about 90% of total votes counted.

As of Tuesday, there will be 133 days until the November general election.

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• Published: 21 June 2024

Mathematical biases in the calculation of the Living Planet Index lead to overestimation of vertebrate population decline

• Anna Toszogyova   ORCID: orcid.org/0000-0001-6084-625X 1 ,
• Jan Smyčka   ORCID: orcid.org/0000-0001-6142-5510 1 &
• David Storch   ORCID: orcid.org/0000-0001-5967-1544 1 , 2  

Nature Communications volume  15 , Article number:  5295 ( 2024 ) Cite this article

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• Biodiversity
• Conservation biology
• Population dynamics

The Living Planet Index (LPI) measures the average change in population size of vertebrate species over recent decades and has been repeatedly used to assess the changing state of nature. The LPI indicates that vertebrate populations have decreased by almost 70% over the last 50 years. This is in striking contrast with current studies based on the same population time series data that show that increasing and decreasing populations are balanced on average. Here, we examine the methodological pipeline of calculating the LPI to search for the source of this discrepancy. We find that the calculation of the LPI is biased by several mathematical issues which impose an imbalance between detected increasing and decreasing trends and overestimate population declines. Rather than indicating that vertebrate populations do not substantially change, our findings imply that we need better measures for providing a balanced picture of current biodiversity changes. We also show some modifications to improve the reliability of the LPI.

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Rare and common vertebrates span a wide spectrum of population trends

Clustered versus catastrophic global vertebrate declines

Random population fluctuations bias the Living Planet Index

Introduction.

The indicators of biodiversity change are of paramount importance for monitoring and understanding current biodiversity crisis. An influential methodology has been provided by the World Wildlife Fund (WWF) in collaboration with the World Conservation Monitoring Centre in 1997, and is commonly known as the Living Planet Index (LPI) 1 . The LPI uses available population time series to calculate the average trend in populations of vertebrate species from terrestrial, freshwater, and marine ecosystems 1 , 2 , 3 . It was first published in the WWF’s Living Planet Report 1998 4 , and in a collaborative partnership with the Zoological Society of London has been reported every two years. In 2006 it was adopted by the Convention on Biological Diversity (CBD) as one of the headline indicators of progress towards its Strategic Plan for Biodiversity 2011-2020 5 with its Aichi targets. Now it is a component indicator of the Kunming-Montreal Global Biodiversity Framework 6 . The LPI has also been adopted by the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES). The LPI message is often reported in media and has become a key tool for convincing the public that the changing state of nature is serious and requires solutions. The most recently published Living Planet Report 2022 7 shows an average 69% decrease in almost 32,000 monitored populations of mammals, birds, amphibians, reptiles, and fish between 1970 and 2018, although there is variation among biogeographical regions and ecosystem types 7 .

The worrying overall decline of vertebrate populations indicated by the LPI contrasts with several current studies based on the same type of data that show that population increases and decreases are surprisingly well balanced 8 , 9 . Moreover, the removal of less than 3% of the most declining vertebrate populations completely reverses the overall population trend as expressed by the LPI towards an overall increase, revealing a strong sensitivity of the LPI to extreme population trends 10 . These findings have raised the question whether there is not a bias in the calculation of the LPI. One such bias may stem from the weighted averaging procedure, when the taxa and regions are weighted by the estimated species richness of respective groups. The weighted form of the global LPI shows a decline which is 38% greater than the unweighted form 3 (see also Fig.  1 , Supplementary Table  1 and Methods ‘Calculating the Living Planet Index’). The weighting is not necessarily a problem per se, but weighting by the species richness of a given taxon and region means that the poorly represented species-rich regions (typically tropical ones) may be driving the global LPI trajectory (see also ref. 11 ). Another potential issue is that the data used for the LPI calculation include many extremely short time series, which are prone to high measurement errors due to interannual variability and sampling issues 12 , 13 , 14 .

The calculation of the global LPI and the LPI for each ecosystem adjusted (i) by increasing the number of records in individual populations included (time series with at least 5 records), (ii) by increasing the length of the population series included (time series at least 5 years long), (iii) by removing zeros from the population time series, (iv) by removing zeros from the population time series and including those with at least 5 records, (v) by removing zeros from the population time series and including those at least 5 years long, (vi) by not using the weights (compensating different species richness) for taxa and realms, (vii) and the unweighted LPI of the time series with at least 5 records, or (viii) at least 5 years long. (ix) The unweighted LPI without zeros in the population time series, (x) and unweighted without zeros in the population time series included with at least 5 records, or (xi) at least 5 years long. The values represent the final LPI values (the value of 1 was set for 1970). The green gradient shows the rate of decrease in the index decline (a positive difference between the adjusted and original value—the adjusted index declines less than the original). The red gradient shows the rate of increase in the index decline (a negative difference between the adjusted and original value—the adjusted index declines more than the original). For an extended version of the table, see Supplementary Table  1 .

Recently, Buschke et al. 15 pointed out several other potential sources of bias in the LPI calculation. One problem can be due to using the GAM method for smoothing the time series and the fact that LPI values are affected by the values of the previous period (see Fig.  2 ). A general feature of GAM models is that they misestimate the marginal values of the population time series, even more so the more the population fluctuates. This effect causes the LPI to spuriously decline by about 9.6% 15 . Buschke et al. 15 have also used a simple simulation model to argue that there is a fundamental asymmetry in the calculation of the LPI (see also ref. 16 ), as populations that fluctuate randomly and symmetrically from the same initial point reveal the decreasing LPI. Potentially, there may be multiple issues in the way the LPI is calculated, as well as in the data which are used for this calculation, that may lead to various biases and misunderstandings. It is thus worth exploring the LPI calculation in more depth.

(1) Addition of a constant of 1% of the population mean to all values of the time series, if the time series contains zero in any year. (2) Estimation of the new population values by two methods; GAM method (time series >5 records) or chain method (time series <=5 records or if the GAM does not fit well). (3) Logarithmic transformation (using base 10) of the population values. (4) Calculation of the population growth rate ( λ ) as the difference between (logarithmized) population values between every two consecutive years = the logarithm of the ratio of population values \(\lambda={log }_{10}\left({N}_{{year}+1}/{N}_{{year}}\right)\) . (5 − 9) Sequence of hierarchical averaging of population growth across populations, species, taxa, realms and ecosystems for a single year. (10) Calculation of the LPI as \(I={I}_{{year}-1}\times {10}^{\lambda }\) . The index of the initial year 1970 is set to 1. (11) The bootstrap calculation of the confidence intervals of the index. For a detailed description of individual steps of the calculation, see Methods ‘Calculating the Living Planet Index’.

Here we provide a detailed inspection of the methodological pipeline and computer codes used for calculating the LPI. We identify the sensitivity of the LPI to particular subjective decisions as well as potential methodological flaws in the calculation, some of them previously reported in the literature 10 , 11 , 14 , 15 , 17 , but most of them unnoticed before. A thorough analysis suggests that accounting for these issues has the potential to weaken or even revert the trends of the LPI, altering the conclusions given by the Living Planet Reports 7 , 18 . We also point out that the major issues related to the LPI are not only caused by the calculation itself, but are deeply related to the quality and representativeness of the underlying data.

The LPI properly reflects the stationarity of the system

A recently published criticism of the LPI by Buschke et al. 15 has been based on the finding that the index declined even if the population trends were stable on average. Buschke et al. 15 derived the index value for simulated randomly fluctuating populations, where population changes adhered to a Poisson distribution with equal probability of being either positive or negative on arithmetic scale. Such populations diffusely diverged from one initial point (see Fig. 1 in ref. 15 ) and the whole set of all populations revealed the declining LPI. We found that the problem with this simulation strategy is that it leads to unrealistic non-stationary population size distributions. Even though the mean community abundance remains stable in the initial part of the simulation (50 years in Buschke et al. 15 ), the population sizes steadily diverge, and community equitability thus decreases with time, the community being characterized by increasing difference between abundant and rare species. Moreover, such a process has an absorption boundary at zero, so all populations would eventually go extinct after a finite number of steps. The declining LPI in this case thus appropriately reflects the non-stationarity of the system when many species become rare, and those with increasing populations do not increase that much. In contrast, the LPI is stable whenever the distribution of population abundances is stationary and/or when population fluctuations are symmetric on logarithmic scale (Fig.  3 ). The symmetry on logarithmic scale makes a good sense, as population increase and decrease are essentially multiplicative processes, while symmetric changes in the arithmetic scale imply that the multiplicative increase of populations is lower than the multiplicative decrease (see also refs. 19 , 20 ). The LPI thus properly reflects symmetric multiplicative population changes, the decreasing LPI indicating asymmetry in this multiplicative population growth towards higher multiplicative decreases than increases.

Simulations (right column) of 500 populations (thin blue lines) all started with 50 individuals and were run for the period of 50 years. Random fluctuations can be either stationary ( a – d ) or non-stationary ( e – h ), and can be symmetric on either arithmetic ( a , b , e , f ) or logarithmic scale ( c , d , g , h ). In stationary systems ( a – d ), where populations fluctuate on arithmetic ( a , b ) or logarithmic scale ( c , d ), mean community abundance (central blue line), equitability, as well as the LPI (red line) remain stable. Note that the first scenario ( a , b ) can correspond to sampling errors of otherwise stable populations (it is modeled as gaussian deviations from a stable mean). Populations fluctuating randomly from the previous value based on Poisson distributions with lambda of 3 ( e , f ) (derived from Buschke et al. 15 ) have a stable mean community abundance, but the decreasing LPI. The reason is that in such a case the population increases cannot compensate for population decreases on logarithmic scale. This system has an absorption boundary at zero, meaning that all populations would eventually go extinct. In contrast, a non-stationary system with symmetric fluctuations on logarithmic scale ( g , h ) reveals a changing mean community abundance, but the stable LPI, since the LPI expresses mean multiplicative population changes that correspond to symmetric fluctuations on logarithmic scale. The LPI is thus stable when populations do not go extinct and their sizes have a stationary distribution ( a – d ) or when their distribution is non-stationary, but population fluctuations have a multiplicative nature ( g , h ), corresponding to a random walk in the logarithmic scale. In contrast, the LPI systematically decreases in the case when population sizes diverge (the distribution is not stationary) and population fluctuations are symmetric in the arithmetic scale ( e , f ).

A related criticism of the LPI by Puurtinem et al. 16 also highlighted the issue that population increases and decreases of the same magnitude on arithmetic scale lead to a decline in the index. The problem arises, according to the authors, from the LPI reliance on geometric averaging. According to the criticism, geometric averaging is appropriate only when population changes are averaged over a time series of interdependent values within a single population, but the LPI calculation instead averages trends across multiple populations for a certain year. But using geometric averaging for statistically independent measurements is not inherently flawed, given the multiplicative nature of population changes mentioned above. For example, populations that experience a doubling in size may be compensated in a stable system by populations that undergo a halving in size, ensuring that the LPI remains unchanged on average while total abundance may or may not increase for that particular year (see Fig. 1a in ref. 16 ). The criticism of geometric averaging is usually based only on a one-step change from year to year. However, in stable systems, where populations do not go extinct and do not experience systematic changes over time, both the LPI and mean abundance may show fluctuations, but may ultimately maintain stationarity (Fig.  3 ). Therefore, the LPI methodology can still offer a valid representation of the mean populations’ stability.

The effect of the number of records in the time series

According to the Living Planet Report 21 , the duration of time series included in the calculation does not influence the LPI. However, while the length of time series (in years) and the number of time series used in the calculation indeed do not systematically affect the LPI, the number of records in time series does have an effect (Methods ‘The effect of the duration and the number of records in the time series’, Fig.  1 , Supplementary Table  1 , Supplementary Fig.  1 , 2 ). The time series with fewer records tend to be declining on average (see also ref. 17 ), which could be one of the reasons why some studies 8 , 9 , 22 that did not include these time series (less than 5, 6, or 10 recorded time points) did not show the prevalence of decreasing populations. Note that the existing LPI method also uses data of only two records per population, the exclusion of which reduces the decline in the index by 14.3% (Methods ‘The effect of the duration and the number of records in the time series’).

Including time series with the low number of records certainly has its merit, as they may be informative by themselves. However, one methodological factor may cause these time series to bias the LPI towards overall decrease. Population dynamics are affected by variability arising from demographic, environmental, and sampling stochasticity, which introduces uncertainty into the LPI 15 , 20 . To mitigate this uncertainty, a smoothing procedure based on the GAM method is applied during the index calculation. However, this smoothing model is applied only to time series longer than five records and only when it fits well (see Methods ‘Calculating the Living Planet Index’). In contrast, short time series are processed by a method that does not employ data smoothing and thus retains the uncertainty, which has been shown to negatively bias the LPI 14 . Sampling errors act symmetrically on arithmetic scale and if populations are stable, the sample population sizes represent a stationary distribution and the index does not decrease. But short time series with sampling error typically increase or decrease overall, so they appear as involving non-stationary fluctuations on arithmetic scale. This leads, after averaging across multiple populations, to a decreasing index (Figs.  3 ,  4 ). This bias is particularly striking when populations values are low and discrete (Fig.  4 ).

Assume there is a stable population of three individuals (light blue circles). If such a population was surveyed in two separate time windows, it results in two population time series (dark blue circles) which may reveal increase and decrease, respectively, due to sampling error. Since sampling errors act symmetrically on arithmetic scale, the overall population growth is negative even if the increases and decreases are balanced—the LPI in the depicted case decreases from 1 to 0.75 (the change from 3 to 5 represents a multiplication by 5/3 = 1.66, while the arithmetically equivalent negative change from 3 to 1 represent a division by 3). The sampling-based increases and decreases of populations with a few records thus appear as non-stationary fluctuations even if the population is actually stable (see Fig.  3e, f ). This bias is particularly pronounced when population values are low and discrete. The two-record populations represent a substantial portion of the data (see Supplementary Fig.  3 ) that may cause the LPI to decrease even if the sampling-based increases are balanced by sampling-based decreases. Note that it does not matter whether the two records occur in subsequent years or they are more distant in time.

Although the population series with the low number of records, and especially those with just two records, represent a non-negligible portion of the data and their removal would exacerbate geographical bias and reduce taxonomic and geographical representativeness (Supplementary Fig.  3 , Supplementary Table  2 ), the problem of representativeness is accounted by weighting and thus is not as serious. In contrast, the bias produced by the sparse population time series in which the sampling error causes non-symmetric multiplicative population changes is substantial, and is responsible for a significant portion of the LPI decrease, as shown by removing these population time series (Supplementary Fig.  1 , 2 ).

Extreme sensitivity of the LPI to the initial decline of a few populations

The LPI is extremely sensitive to the availability of population time series at the beginning of the study period. It follows from the step-by-step calculation of the LPI, where the population change ( N year+1 / N year ) is calculated between every two consecutive years and the index values are based on the multiplication of the previous value of the index by the geometric mean of population change (Fig.  2 , Methods ‘Calculating the Living Planet Index’). It means that the population increases/declines at the beginning of the time series transcribe through all the subsequent years. Since the population data from 1970s are sparse (Supplementary Fig.  4 , 5 ), the low values of the LPI may easily result from few declining populations at the beginning of the study period. The LPI is presented in the arithmetic scale and in this respect it is asymmetric—since its value is calculated as the product of the previous year’s value and the geometric mean of population change, the index does not fluctuate much if the previous value is way below one even if the population growth rate is relatively high, while it may fluctuate considerably if the previous index value is high. An initial decrease of the LPI thus typically does not permit its later increase.

This effect is strengthened by the hierarchical averaging procedure—if some taxa are represented by only a few populations, these populations have the potential to disproportionately affect the global index. An extreme case comprises the herptiles in the Palearctic region, represented by only one (declining) population of viper Vipera berus for the period 1974-1977. Hierarchical averaging across taxa and biogeographical regions leads to the situation in which these four records of the viper population cause an 89.5% greater decrease (the index changes from the original value of 0.826 to 1.721 after removing these four records) in the final state of the LPI for the Palearctic realm (Fig.  5 ) and a 3.3% greater decrease in the LPI for the whole terrestrial system in comparison to the LPI without these four records (weighted in both cases). This viper population is the only single-population representative of the terrestrial system; for all the cases of single-population representatives of freshwater and marine ecosystems and their effects on the LPI, see  Supplementary Notes . All the single-population representatives of population trends are situated at the beginning of the measurement period for a particular taxon and biogeographical realm. Although the end of the whole study period is also characterized by a lower number of population time series, this does not seem to have a substantial effect on the trend in the LPI, as restricting the population data to a particular end year does not change the final shape of the index. Although the latest version of the Living Planet Database (LPD) includes information which populations are no longer used for the global LPI calculation (including the abovementioned viper population), this does not solve the problem, as there are still cases in which a single population represents the entire taxon (e.g. again in Palearctic herptiles). Additionally, particular subsets of the data used for the calculation of the LPI for different taxa and/or regions will contain different single-population representatives. Moreover, the single representatives are the extreme case—if the beginning of the study period is represented by just two or three populations, it can have a similarly disproportionate effect on the LPI as a single-population representative. This situation will persist with updated versions of the LPD, as the newly added population time series will most likely not overlap the beginning of the study period.

The original LPI for the whole Palearctic realm is blue and the LPI calculated without the 4 records (1974-1977) of one population of viper Vipera berus is yellow. The Palearctic LPI consists of the averaged population growth rate of three taxa (mammals, birds, herptiles), one of which (herptiles) was represented in 1974–1977 by only one declining population, causing the entire index to decline, subsequently affecting the remaining trajectory. Note that removing the effect of the four values of the viper, marked with arrows, changes not only the overall level of the LPI, but also its relative fluctuation, as low index values fluctuate less in the arithmetic scale by the very definition of the LPI. The colored area shows the confidence intervals and the lines show the LPI values.

Note that the effect of the hierarchical averaging and underrepresentation of some taxa/realms depends on the grouping. If one (relatively smaller) group shows a significantly negative/positive population trend, this will strongly affect the resulting average of all groups. However, if this group is merged with another group, its negative/positive values are dissolved among all the values of both groups, and only then this merged group is averaged with other groups. For example, if we consider 5 realms and 3 taxa (in the unweighted form, as we compare it with the unweighted form of the next grouping) it decreases the decline in the terrestrial LPI by 6.3% (leading to the less decreasing LPI) compared to the situation when 6 realms and 4 taxa are distinguished (again in the unweighted form, as the weights are not available for this grouping) (Methods ‘The number of biogeographical realms and vertebrate taxa’).

The problem with the low number of population time series at the beginning of the study period cannot be easily solved. If we want to have the index for the whole period, we need to include all available time series, even if they are not particularly representative. In such a case, however, it is desirable to test the index for the sensitivity of their inclusion or removal, as well as for different ways of the grouping of taxa and realms.

The problem of zeros in population time series

A conceptually more important issue is the way zeros are treated when calculating the index. The LPI is based on averaging the interannual growth rate log 10 ( N year+1 / N year ), which cannot be calculated if the population size is zero in one of the compared years. This problem is solved in the LPI calculation by the replacement of zeros by a small value. In particular, a constant of 1% of the population mean is added to all values in the time series if any year contains zero (Fig.  2 , Methods ‘Calculating the Living Planet Index’). This is in fact, equivalent to a drop (in the case zero is at the end of time series) or an increase (if it is at the beginning) of the population size by two orders of magnitude, which is considerably larger than typical population fluctuations. Such population change is entirely arbitrary, and using a different proportion than 1% of the population mean would lead to very different interannual growth rate of a given population, and consequently a different LPI. If zeros were randomly distributed across population time series, this effect would cause just an increasing error, and not necessarily a bias towards the declining LPI. However, it is reasonable to assume that zeros occur with a higher frequency at the end of the time series, since populations are rarely studied when there are no individuals at the beginning. Such an asymmetry could cause the bias towards apparently declining populations. Indeed, the time series with zeros at the end outnumber those that begin with zero values in the Living Planet Database (Supplementary Table  3 ). Although the middle zeros or the middle sequences of zeros predominate overall, they cannot cause any bias.

To explore the extent of this effect, we recalculated the LPI with the removed zeros from all population time series (if zeros were in the middle of the time series, the series were split into multiple independent series; note that a significant number of population time series included sequences of several zeros; Supplementary Table  3 ). The change was substantial (Fig.  6 , Fig.  1 , Supplementary Table  1 )—the decline of the global LPI was reduced by 19.2%, from the original drop to 32.7% (assuming 100% in 1970) to 51.9%—but differed among ecosystems. The reduction of the LPI decline was 33.8% in the case of the terrestrial ecosystem (from the original decrease to 36.8% to the decrease to only 70.6%), 19.3% for the freshwater ecosystem (from 18% to 37.3%), and less than 1% for the marine ecosystem (from 52.6% to 53.2%) (Supplementary Fig.  6 , Fig.  1 , Supplementary Table  1 ). The differences between ecosystems appear to be due to the different prevalence of zero-valued ends of the time series (Supplementary Table  3 ). Importantly, removing zeros sometimes led to considerable broadening of confidence intervals, so that they overlapped the value of one, implying that it is often impossible to say with certainty whether there was any significant population decrease (Fig.  6 , Supplementary Fig.  6 ).

The original global LPI is blue and the LPI calculated without zeros in the population time series is yellow. The colored area shows the confidence intervals and the lines show the LPI values. For the effect of removing zeros for individual ecosystems, see Supplementary Fig.  6 .

Although the removal of zeros from population time series may look contentious, we argue that it is more appropriate than leaving the zeros in. Population fluctuations represent a process which is well characterized by the ratio of population sizes in consecutive time steps, corresponding to per-capita population vital rates that link population sizes in consecutive years. In contrast, colonization and extinction represent different processes which break this inter-annual link and thus cannot be mixed with population fluctuations even if the fluctuations sometimes do result in extinction. If a population is non-existent in one of the two years, population growth does not have any meaning. Replacing zeros with any value then arbitrarily modifies the link (or its absence) between population states in consecutive years and seriously distorts statistical properties of population fluctuations. Importantly, there is no justification for the claim that zeros should not be removed on the ground that this would change species composition across the time series (see refs. 23 , 24 ). As long as each population series is not bounded by a sequence of zeros throughout the whole study period, species composition changes regardless of whether zeros are excluded or included.

The zeros in the LPD certainly have various information values, some representing real extinctions, some emigration, and others just reflect sampling errors due to low population density or detectability. However, even if we could distinguish these situations, the methodology of the LPI calculation is unable to properly treat them. When the data undergo any transformation that involves division or logarithmization, the zeros can be only (1) replaced by a non-zero value or (2) removed. Even if the zeros are genuine and have a real basis, their replacement by any other value introduces a bias and statistical distortion due to the LPI algorithm (see refs. 23 , 24 ). The exclusion of zero values is thus essential for maintaining the integrity and accuracy of the population trends analysis. We do not dispute that ecologically meaningful zeros provide important insights into population dynamics, but they should be evaluated by an alternative analytical method alongside the LPI method (see refs. 8 , 24 ), e.g. by treating the colonization and extinction dynamics separately from population fluctuations. Note that this problem of the presence of zeros in population time series goes far beyond the methodology of the LPI and concerns all studies that focus on population dynamics and need to deal with both population fluctuations (the realm of classical population biology) and colonization-extinction dynamics (the realm of metapopulation biology).

After we have accounted for the issues with the low number of records in some population time series and with the presence of zeros, we found that the adjusted Living Planet Index indicates considerably lower population declines than the original index (Fig.  7 , Fig.  1 , Supplementary Table  1 ; note the positive effects, depicted by green color in the tables, of the adjustments of the LPI).

The original LPI is blue and the adjusted LPI is yellow, calculated without zeros in the time series of populations with at least 5 records globally ( a ) and separately for the terrestrial ( b ), freshwater ( c ) and marine ( d ) ecosystem. The colored area shows the confidence intervals and the lines show the LPI values.

We have shown that the LPI exhibits substantial variability depending on calculation settings. While these settings must necessarily at least partially depend on subjective choices, some of these decisions may compromise the robustness of the index. This problem is aggravated by the specificities of the data, namely the presence of population time series that have very few records, single-population representatives for some periods, taxa and regions, and presence of zeros. Due to the sensitivity of the LPI to subjective decisions and to specific problems with the LPI calculation, the LPI does not seem to accurately represent biodiversity trends. An indicator of the global state of nature should not be sensitive to the fact that 50 years ago one population of viper did not thrive well, and should not be affected by the particular way population sizes were measured and how population absence was treated in the end or the beginning of the time series (see ref. 25 ). Similarly, a universal index of population change should not be sensitive to particular grouping to taxa and biogeographical realms if its aim is to provide a rigorous, repeatable indicator with a straightforward interpretation. These issues deserve particular attention if the LPI is calculated for individual regions or countries (see ref. 26 ), in which the effect of these biases may be even stronger than in the case of the global data.

Some of the issues mentioned above can be addressed in a relatively straightforward way. If an index that integrates population changes across regions and taxa into one number is desirable, it is necessary to find ways to make the index more robust and reliable. Since the calculation of the index inherently involves subjective settings, it is essential to thoroughly evaluate its sensitivity to these subjective decisions. The index calculation should thus encompass the full spectrum of reliable alternative decisions concerning grouping and weighting taxa and regions. Similarly, due to the fact that the geometric mean is strongly influenced by outliers, especially if the number of values entering the calculation is low, the index should use all variants of the removal of the single-population-representatives, i.e. sort of sensitivity analysis; see ref. 26 . Other possibilities include shifting the reference year to limit the small number of populations at the beginning of the study period, reshuffling population time series within the study period (see also refs. 11 , 12 , 13 , 25 , 27 ). or weighting the data by the number of population records. It is also worth considering whether it is appropriate to use time series shorter than 1-10 years or with less than 3-10 recorded time points (see refs. 12 , 13 ) as they may not be able to adequately capture population trends 11 , 28 , are subject to large sampling stochasticity and introduce uncertainty causing a downward bias 14 . Although removing sparse time series reduces taxonomic and geographical representativeness in terms of the number of utilized populations, it is less problematic than leaving them in the calculation, as they introduce a significant downward bias. Due to the way the index is calculated (i.e. by addition of the value of population change to the index value of the previous year), all process and measurement biases are accumulated at each step of the index calculation, increasing the inaccuracy of the LPI 14 . Additionally, the procedure of the LPI calculation based on averaging the interannual population growth rates is not compatible with the presence of zeros in the population time series, even if all zeros were ecologically meaningful. The more appropriate solution is thus not to include zeros. We are aware that the presence of zeros can be understood as an indication of population colonization or extinction, but these are essentially different processes from population fluctuations and should be thus treated separately alongside the LPI calculation (see refs. 8 , 24 for an example of how to do it, although these approaches also have their own limits and would also require a proper sensitivity analysis).

The LPI corrected for the biases explained above does not indicate as strong global population declines as the original LPI, published in the Living Planet Reports 7 , 18 . However, this does not necessarily mean that the situation is in reality better. Population time series in the Living Planet Database do not represent the results of a standardized systematic survey, but simply comprise all populations sampled for very different reasons (see refs. 29 , 30 ). It is possible that the data do not include many populations that actually rapidly declined without even being documented, and ultimately disappeared—many habitats which were entirely converted to intensive agriculture, plantations or human settlements were not explored before the transformation, and are typically not studied after the transformation to document population disappearance. Many populations have been studied in pristine and/or protected areas, so the overall sample may be biased towards stable or increasing populations 31 , 32 . On the other hand, there may be some bias also in the opposite direction, stemming from the fact that ecologists typically begin to study populations which are already established and not those recently emerging 27 , or directly focus on species at higher risk of extinction 33 . As the relative weight of these biases is hard to compare, the LPI corrected for all the calculation biases may still underestimate or overestimate real population changes.

The potential importance of these biases can be shown by the effect of weighting by taxon- and region-specific species richness. Although weighting was justified in order to reduce bias due to heavily oversampled regions, it introduces another bias as the weighted index is driven mainly by tropical populations (species-rich regions) 11 . These regions might be sampled for specific reasons and at specific locations. The declared advantage of the Living Planet Database, namely the high number of time series collected, cannot overcome the fact that the database is a heterogeneous set of spatially and temporally biased data collected for different purposes. A solution to this problem would be to use only population time series from standardized systematic surveys (see ref. 25 ) where all populations have been sampled regardless of their size, trends, and environmental changes, but such studies are rare and (again) strongly geographically biased 34 , 35 , 36 .

Even at the regional or national level where more balanced sampling may be ensured, the data should not be sensitive to weaknesses in the LPI methodology (including errors in the code; see Methods ‘Calculating the Living Planet Index’ and Supplementary Notes ), otherwise this method may produce even greater inaccuracies in population trend estimates than in the case of a larger dataset, as we show for specific taxa and regions. The LPI methodology and datasets are already used to evaluate biodiversity changes and to monitor compliance with various international agreements and targets tailored to specific regions and groups (e.g. the LPI for Belgium, Netherlands, China, Austria, Mediterranean wetlands, migratory species, freshwater megafauna, reptiles, specific biomes; see ref. 26 ), and it is questionable to what extent the resulting indices are distorted by the abovementioned shortcomings.

In summary, we have shown that there are issues with the calculation of the Living Planet Index that lead to an overestimation of vertebrate population declines. Some of the biases can be corrected in a straightforward way—for instance, there have been small errors in the code which can cause serious bias in smaller datasets, and we provide the corrected code ( Supplementary Software ). The zeros need to be removed from the population time series and the LPI method needs to be accompanied by an analysis of extinction/colonization (see ref. 8 ) or a method capable of processing zero values should be used (see ref. 24 ). It is also necessary to account for the uncertainty introduced by the data by including time series of a reasonable number of population records to avoid downward bias. Additionally, a rigorous approach should include the exploration of the consequences of changing biogeographical/taxonomic groupings and the exclusion of sparsely populated taxa, to assess the sensitivity of these alternatives on the resultant index. Even after accounting for all abovementioned issues, the reliability of the LPI may be compromised by the heterogeneity and unequal geographical cover of the data (see ref. 11 ), suggesting the need for standardized survey data collected independently of specific purposes or locations.

Calculating the Living Planet Index

We have explored the code used for the calculation of the LPI. Although Loh et al. 1 , Collen et al. 2 and McRae et al. 3 provide the basic principle of calculating the LPI, the exact methodological procedure is clear only from the code of the package rlpi (v.0.1.0) in R 37 . This package was created and made available by the Zoological Society of London in 2017 and presented in McRae et al. 3 , who also introduced the diversity-weighted form of the LPI. In fact, without the precise procedure it is not possible to replicate the calculation to obtain the LPI identical to the one presented in the Living Planet Reports 7 , 18 . We are aware of the possibility that an updated version of the code exists, but we have been confined only to the material that is publicly presented and recommended for use.

The procedure consists of several steps; addition of a constant to the whole time series if it contains zeros, estimation of new population values by the GAM or chain method, calculating mean population growth of each population for each year, and hierarchical averaging of population growth from populations to species, taxa, biogeographical realms and ecosystems (Fig.  2 ; see below for the detailed description and Methods ‘The Living Planet Database’ for a description of the database used). In a detailed R-code inspection we found errors in the original calculation of the LPI; see  Supplementary Notes for their complete list and R-scripts with marked errors ( Supplementary Software ). All calculation errors in the code have a negligible effect on the final shape of the global LPI trajectory, but are evident in some cases where the LPI is calculated for a smaller subset of data—a certain taxon or biogeographical realm (Supplementary Fig.  7 ). We provide the R-code with all errors corrected ( Supplementary Software ).

The methodological procedure for calculating the LPI consists of these steps:

Addition of a constant of 1% of the population mean (the mean from all non-zero values) to all values of the time series if the time series contains zero in any year. If a population series contains only zeros, the added constant is 10 −17 (we removed these cases).

Estimation of the new population values by two methods (also the way to estimate missing values, i.e. values for years without population records):

GAM method is used if the length of the time series is equal to or longer than 6 records and only if the GAM fits well. The GAM smoothing parameter is set to 1/2 of the length of the time series. The GAM method is implemented on logarithmic (base e) values and the values estimated by the model are subsequently delogarithmized.

Chain method is used if the length of the time series is less than 6 records or if the GAM does not fit well (or if all population values are the same). It is a log-linear interpolation for missing values in the population series (see Equation 2 in Collen et al. 2 ).

Logarithmic transformation (base 10) of the population values.

Calculating the difference between the (logarithmized) population values between every two consecutive years = the logarithm of the ratio of population values = population growth = lambda:

Calculating the arithmetic mean of lambdas (the logarithm of the geometric mean) of all populations of one species within one biogeographical realm (for an individual year). There are 5 (for the terrestrial and freshwater ecosystem) or 6 (for the marine ecosystem) biogeographical realms distinguished (see below).

Calculating the arithmetic mean of species-specific lambdas across all species of one taxon within one realm (for an individual year). There are 3 (for the terrestrial ecosystem) or 4 (for the freshwater and marine ecosystem) taxa distinguished (see below).

Calculating the weighted arithmetic mean of taxon-specific lambdas across all taxa within one realm (for an individual year). The taxon-specific lambdas are weighted by the ratio of the species richness of a given taxon and the species richness of all the taxa together (the weighted method was implemented by McRae et al. 3 ).

Calculating the weighted arithmetic mean of realm-specific lambdas across all realms (for an individual year). The realm-specific lambdas are weighted by the ratio of the species richness of a given realm and the species richness of all the realms together (the weighted method was implemented by McRae et al. 3 ). The result is one lambda for a certain year.

Calculating the arithmetic mean of ecosystem-specific lambdas across all ecosystems (for an individual year) is obtained by dividing the realm-specific weights by the number of ecosystems (only in the case when the global LPI is calculated), i.e. all the realm-specific weights are multiplied by 1/3 (this procedure is not implemented in the code).

The calculation of the LPI as \(I={I}_{p}\times {10}^{\lambda }\) , where Ip is the index of the previous year and the index of the starting year 1970 was set to 1.

The bootstrap calculation of the confidence intervals of the index. The method involves 100 resamplings of species from each taxon with replacement.

The last 7 steps run in a loop for each year.

More formally, the global LPI is calculated as a hierarchical sequence of five geometric means:

\({s}_{x}={({\prod }_{i=1}^{n}{p}_{i})}^{1/n}\) , i.e. a geometric mean of n ratios ( p ) of population values ( N ) of two consecutive years ( \({p}_{i}={N}_{{year}+1}/{N}_{{year}}\) ) of the x th species,

\({t}_{q}={({\prod }_{x=1}^{d}{s}_{x})}^{1/d}\) , i.e. a geometric mean of d species-specific s x of the q th taxon,

\({r}_{b}={({\prod }_{q=1}^{c}{t}_{q})}^{1/c}\) , i.e. a geometric mean of c taxon-specific t q of the b th realm,

\({e}_{y}={({\prod }_{b=1}^{f}{r}_{b})}^{1/f}\) , i.e. a geometric mean of f realm-specific r b ,

\(g={({\prod }_{y=1}^{h}{e}_{y})} \, ^{1/h}\) , i.e. a geometric mean of h ecosystem-specific e y .

The global LPI is then calculated as \(I={I}_{p}\times g\) ,

therefore it is the product of the previous year’s index ( I p ) and g . It holds that the logarithm of g is the final lambda ( λ )—the mean population growth rate of all populations. The index can be thus expressed as \(I={I}_{p}\times {10}^{\lambda }\) .

In practice, the calculation is performed as a hierarchical sequence of arithmetic means, where in the first step the logarithm of the ratio of population values is averaged arithmetically. The arithmetic mean of logarithms is equivalent to the logarithm of the geometric mean, thus \(\lambda={\log }_{10}\left(g\right)\) .

The R-function from the package rlpi ( https://github.com/Zoological-Society-of-London/rlpi ) allows various calculation settings of the LPI. It is possible to change the minimum length of the time series (the number of records, but not the number of years) included in the calculation, the constant replacing zeros, the length of the time series for which the GAM or chain method is used, the GAM smoothing parameter, the limit value for outlying lambda and whether to replace the outlying lambdas, and the use of weighting. The weights of particular taxa and realms were obtained from McRae et al. 3 .

The shape of the LPI curve is mostly influenced by two parameters; the number of records in the time series (fullness) and the use of weights (see ref. 3 ). The difference between the weighted and unweighted form of the global LPI is 44.5% (much greater decline in the weighted than unweighted form). The effect of weighting for the terrestrial, freshwater and marine LPI causes a 14.8%, 47.3% and 83.5% greater decline, respectively, in the weighted than unweighted form (Supplementary Table  1 ).

The effect of the duration and the number of records in the time series

The original method of calculating the index takes into consideration all time series longer than one record (2 or more). If the global LPI is calculated only with the time series with at least 3, 5, 10 records, the decline in the index is reduced by 14.3%, 14.7%, and 26.4%, respectively (Supplementary Table  1 , Supplementary Fig.  1 ). In the case of the terrestrial LPI, the inclusion of only time series with at least 5 records causes a 5.5% reduction in the decline. If the freshwater LPI is calculated with time series equal to or longer than 5 records, the decline in the index is reduced by 14.2%. Similarly, for the marine LPI, the decline in the index is reduced by 25.6% (Supplementary Table  1 for all 3/5/10-records options, Supplementary Fig.  2 ). However, the length of the time series of estimated values may not correspond to the number of population records in the time series. If the individual records are not consecutive in each year, the missing values are calculated (by the GAM or chain method). Therefore, it can happen that a time series having five records can enter the index calculation as a time series of more than five estimated population values, i.e. longer than four years. In any case, the number of the records in the time series (adjustable parameter in the R-code) limits the minimum length of the time series, i.e. its duration in years (which is not an adjustable parameter in the original code). On the other hand, the length of the time series (the duration) does not affect the minimum number of records, as it can be always as few as two records. A relatively smaller decline in the index after removing time series with fewer records would suggest that time series with lower fullness (as defined here) are on average those comprising decreasing populations, but this may be an effect of sampling errors (Fig.  4 ). In contrast, the length of the time series (the interval between the first and last observation) has very little effect on the overall trend (Supplementary Table  1 , Supplementary Fig.  1 and 2 ; see also ref. 38 ). We tested a simple removal of population time series based on a selected number of records/years, because such an extremely heterogeneous dataset of taxa/species and abundance proxies does not allow the establishment of unequivocal criteria for the minimum number of records needed to detect a population trend.

The index calculation includes a smaller number of populations when limited by the duration of the time series (19,205/16,555/12,660 populations considered for at least 3/5/10-year-long time series). Even fewer populations are included when the limitation is based on the number of records in the time series (17,753/13,868/9,528 populations considered for at least 3/5/10-record-long time series) (see also Supplementary Fig.  3 , Supplementary Table  2 ). However, the resulting index is affected only by the limit on the number of records in the time series. This suggests that the LPI does not demonstrate a systematic trend based on the number of population series utilized and duration of time series, but it does reveal a trend influenced by the number of records within the time series.

The Living Planet Database

The data for the LPI calculation was obtained from the Living Planet Database (LPD) ( https://livingplanetindex.org ), which currently includes freely available time series data since 1970 to the present (the data on many realms and taxa are there only until 2014) for 22,175 populations of 4,777 mammal, bird, reptile, amphibian and fish species from terrestrial, freshwater and marine ecosystems (data downloaded at 5/2021 and 1/2022; all data were updated to 1/2022) (Supplementary Table  4 ). The LPD is repeatedly updated with new population time series throughout the considered time frame; as a result, each new round of the LPI calculation works with a different data collection. The basic data units (records) are population sizes or various proxies of abundances (e.g. the number of individuals, breeding pairs, eggs, the number of burrows) or population densities or biomass (based on pitfall or camera traps, weight of net catch, various records per area or time) for different years. The population time series begin and end in different years and the records were sampled with different frequencies and often irregularly. The original LPI calculation considers 5 biogeographical realms and 3 taxa for the terrestrial ecosystem, 5 realms and 4 taxa for the freshwater ecosystem, and 6 realms and 4 taxa for the marine ecosystem (see SI in McRae et al. 3 ).

The number of biogeographical realms and vertebrate taxa

In the LPD, there are 6 biogeographical realms distinguished for the terrestrial/freshwater ecosystem; Afrotropical, Palearctic, Nearctic, Neotropical, Australasia and Indo-Malayan. The alternative is that Australasia and Indo-Malayan realms are merged into the Indo-Pacific. For vertebrate taxa, 5 groups are distinguished; birds, mammals, fish, reptiles and amphibians. Reptiles and amphibians can be merged into one group of herptiles. For the marine ecosystem there are 6 realms; Arctic, Atlantic North Temperate, Atlantic Tropical and Subtropical, Pacific North Temperate, Tropical and Subtropical Indo-Pacific, South Temperate and Antarctic. As there were weights for only 5 terrestrial/freshwater realms (Australasia and Indo-Malayan as one Indo-Pacific realm) and 3 and 4 taxa, respectively (reptiles and amphibians as herptiles), it was necessary to use the merged alternatives.

Reporting summary

Further information on research design is available in the  Nature Portfolio Reporting Summary linked to this article.

Data availability

Data of population time series stored within the Living Planet Database are managed and maintained by the Indicators & Assessments Unit at the Zoological Society of London (ZSL) and WWF International (WWF) and available on their website ( https://livingplanetindex.org/data_portal ). The downloaded data (1/2022) included the entire publicly available collection of population time series of vertebrate species from around the world. The terms of use for data from the Living Planet Database are set out in the Data Use Policy ( https://livingplanetindex.org/documents/data_agreement.pdf ).

The values for weighting individual groups are available in Supplementary Tables  S10 - S13 from McRae et al. (2017).

Code availability

The open-source code used to calculate the Living Planet Index from LPD data is contained in the R-package ‘rlpi’ (v 0.1.0), developed and maintained by the Zoological Society of London (ZSL) and available from the GitHub repository: https://github.com/Zoological-Society-of-London/rlpi . R-code and outputs (R-scripts and RData files) for all analyses used for this study are available in  Supplementary Software .

Loh, J. et al. The Living Planet Index: using species population time series to track trends in biodiversity. Philos. Trans. R. Soc. B: Biol. Sci. 360 , 289–295 (2005).

Article   Google Scholar  

Collen, B. et al. Monitoring change in vertebrate abundance: the Living Planet Index. Conserv. Biol. 23 , 317–327 (2009).

Article   PubMed   Google Scholar  

McRae, L., Deinet, S. & Freeman, R. The diversity-weighted Living Planet Index: controlling for taxonomic bias in a global biodiversity indicator. PLoS ONE 12 , e0169156 (2017).

Article   PubMed   PubMed Central   Google Scholar  

Loh, J. et al. Living Planet Report 1998 (1998).

UNEP (United Nations Environment Programme). UNEP/CBD/COP/DEC/X/2 Strategic Plan for Biodiversity 2011-2020 and the Aichi Biodiversity Targets . Decision adopted by the Conference of the Parties to the Convention on Biological Diversity . (2010).

UNEP (United Nations Environment Programme). CBD/COP/DEC/15/5 Monitoring framework for the Kunming-Montreal Global Biodiversity Framework . Decision adopted by the Conference of the Parties to the Convention on Biological Diversity . (2022).

Almond, R. E. A., Grooten, M., Juffe Bignoli, D. & Petersen, T. (eds). Living Planet Report 2022—Building a Nature-Positive Society (WWF, 2022).

Dornelas, M. et al. A balance of winners and losers in the Anthropocene. Ecol. Lett. 22 , 847–854 (2019).

Daskalova, G. N., Myers-Smith, I. H. & Godlee, J. L. Rare and common vertebrates span a wide spectrum of population trends. Nat. Commun. 11 , 4394 (2020).

Article   ADS   CAS   PubMed   PubMed Central   Google Scholar  

Leung, B. et al. Clustered versus catastrophic global vertebrate declines. Nature 588 , 267–271 (2020).

Article   ADS   CAS   PubMed   Google Scholar  

Dove, S., Böhm, M., Freeman, R., McRae, L. & Murrell, D. J. Quantifying reliability and data deficiency in global vertebrate population trends using the Living Planet Index. Glob. Change Biol. 29 , 4966–4982 (2023).

Article   CAS   Google Scholar  

Wauchope, H. S., Amano, T., Sutherland, W. J. & Johnston, A. When can we trust population trends? A method for quantifying the effects of sampling interval and duration. Methods Ecol. Evol. 10 , 2067–2078 (2019).

Daskalova, G. N., Phillimore, A. B. & Myers-Smith, I. H. Accounting for year effects and sampling error in temporal analyses of invertebrate population and biodiversity change: a comment on Seibold et al. 2019. Insect Conserv. Diversity 14 , 149–154 (2021).

Hébert, K. & Gravel, D. The Living Planet Index’s ability to capture biodiversity change from uncertain data. Ecology 104 , e4044 (2023).

Buschke, F. T., Hagan, J. G., Santini, L. & Coetzee, B. W. T. Random population fluctuations bias the Living Planet Index. Nat. Ecol. Evol. 5 , 1145–1152 (2021).

Puurtinen, M., Elo, M. & Kotiaho, J. S. The Living Planet Index does not measure abundance. Nature 601 , E14–E15 (2022).

Leung, B. et al. Reply to: do not downplay biodiversity loss. Nature 601 , E29–E31 (2022).

Article   CAS   PubMed   Google Scholar  

Almond, R. E. A., Grooten, M. & Petersen, T. (eds). Living Planet Report 2020—Bending the Curve of Biodiversity Loss (WWF, 2020).

Talis, E. J. & Lynch, H. J. Capturing stochasticity properly is key to understanding the nuances of the Living Planet Index. Nat. Ecol. Evol. 7 , 1194–1195 (2023).

Buschke, F. T., Hagan, J. G., Santini, L. & Coetzee, B. W. T. Reply to: Capturing stochasticity properly is key to understanding the nuances of the Living Planet Index. Nat. Ecol. Evol. 7 , 1196–1198 (2023).

Marconi, V., McRae, L., Deinet, S., Ledger, S. & Freeman, R. Living Planet Report 2020. Bending the curve of biodiversity loss: a deep dive into the Living Planet Index https://doi.org/10.13140/RG.2.2.22981.78568 . (2020).

Leung, B., Greenberg, D. A. & Green, D. M. Trends in mean growth and stability in temperate vertebrate populations. Diversity Distrib. 23 , 1372–1380 (2017).

Buckland, S. T., Studeny, A. C., Magurran, A. E., Illian, J. B. & Newson, S. E. The geometric mean of relative abundance indices: a biodiversity measure with a difference. Ecosphere 2 , art100 (2011).

Korner-Nievergelt, F. et al. Multi-species population indices for sets of species including rare, disappearing or newly occurring species. Ecol. Indic. 140 , 109005 (2022).

Buckland, S. T. & Johnston, A. Monitoring the biodiversity of regions: key principles and possible pitfalls. Biol. Conserv. 214 , 23–34 (2017).

Ledger, S. E. H. et al. Past, present, and future of the Living Planet Index. npj Biodivers. 2 , 1–13 (2023).

Article   MathSciNet   Google Scholar  

Fournier, A. M. V., White, E. R. & Heard, S. B. Site-selection bias and apparent population declines in long-term studies. Conserv. Biol. 33 , 1370–1379 (2019).

Humbert, J.-Y., Scott Mills, L., Horne, J. S. & Dennis, B. A better way to estimate population trends. Oikos 118 , 1940–1946 (2009).

Article   ADS   Google Scholar  

Cardinale, B. J., Gonzalez, A., Allington, G. R. H. & Loreau, M. Is local biodiversity declining or not? A summary of the debate over analysis of species richness time trends. Biol. Conserv. 219 , 175–183 (2018).

Gonzalez, A. et al. Estimating local biodiversity change: a critique of papers claiming no net loss of local diversity. Ecology 97 , 1949–1960 (2016).

Murali, G., de Oliveira Caetano, G. H., Barki, G., Meiri, S. & Roll, U. Emphasizing declining populations in the Living Planet Report. Nature 601 , E20–E24 (2022).

Loreau, M. et al. Do not downplay biodiversity loss. Nature 601 , E27–E28 (2022).

Scheele, B. C. et al. Continental-scale assessment reveals inadequate monitoring for threatened vertebrates in a megadiverse country. Biol. Conserv. 235 , 273–278 (2019).

Mahony, N. A., Dale, B. C. & Miller, D. A. W. Grassland bird population declines at three Breeding Bird Survey spatial scales in contrast to a large native prairie. Ecosphere 13 , e4309 (2022).

Storch, D. et al. Decomposing trends in bird populations: Climate, life histories and habitat affect different aspects of population change. Diversity Distrib. 29 , 572–585 (2023).

Schipper, A. M. et al. Contrasting changes in the abundance and diversity of North American bird assemblages from 1971 to 2010. Glob. Change Biol. 22 , 3948–3959 (2016).

R Core Team (2022). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/ .

Westveer, J. et al. A Deep Dive into the Living Planet Index: A Technical Report (2022).

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The research was funded by the Czech Science Foundation (GAČR 20-29554X).

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Anna Toszogyova, Jan Smyčka & David Storch

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Toszogyova, A., Smyčka, J. & Storch, D. Mathematical biases in the calculation of the Living Planet Index lead to overestimation of vertebrate population decline. Nat Commun 15 , 5295 (2024). https://doi.org/10.1038/s41467-024-49070-x

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Sparse representation-based motor imagery EEG classification towards asynchronous BCI systems

Department of Applied Mechanics and Biomedical Engineering, Indian Institute of Technology Madras, Chennai-600036, India

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International Journal of Bioinformatics Research and Applications

Most of the existing motor imagery (MI)-based brain-computer interface (BCI) systems operate in synchronous to the system-generated time slots. But in real-world applications, users want to control the interface asynchronously at their own convenience. The main challenge in such asynchronous BCIs lies in the detection of relax period. In this study, sparse representation-based classification (SRC) scheme is proposed for asynchronous BCI systems. The dictionary needed for the SRC scheme is learned from the extracted EEG features using the K-SVD algorithm. The proposed framework is evaluated on two benchmark datasets from BCI competitions III and IV. The results showed the SRC's detection ability to relax states and to MI states, which is better than the detection ability of the well-known linear discriminant analysis classification method. The betterment of the proposed scheme is also shown in terms of accuracy while classifying the left-hand MI, right-hand MI, and the relaxed state.

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