Apportionment (politics)

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Apportionment is the process by which seats in a legislative body are distributed among administrative divisions, such as states or parties, entitled to representation. This page presents the general principles and issues related to apportionment. The page apportionment by country describes the specific practices used around the world. The page Mathematics of apportionment describes mathematical formulations and properties of apportionment rules.

The simplest and most universal principle is that elections should give each vote an equal weight. This is both intuitive and stated in laws such as the Fourteenth Amendment to the United States Constitution (the Equal Protection Clause).

Fundamentally, the representation of a population in the thousands or millions by a reasonable size, thus accountable governing body involves arithmetic that will not be exact. Although weighing a representative's votes (on proposed laws and measures etc.) according to the number of their constituents could make representation more exact,^[1] giving each representative exactly one vote avoids complexity in governance.

Over time, populations migrate and change in number. Governing bodies, however, usually exist for a defined term of office. While parliamentary systems provide for dissolution of the body in reaction to political events, no system tries to make real-time adjustments (during one term of office) to reflect demographic changes. Instead, any redistricting takes effect at the next scheduled election or next scheduled census.

In some representative assemblies, each member represents a geographic district. Equal representation requires that districts comprise the same number of residents or voters. But this is not universal, for reasons including the following:

• In federations like the United States and Canada, the regions, states, or provinces are important as more than mere election districts. For example, residents of New York State identify as New Yorkers and not merely as members of some 415th Congressional district; the state also has institutional interests that it seeks to pursue in Congress through its representatives. Consequently, election districts do not span regions.
• Malapportionment might be deliberate, as when the governing documents guarantee outlying regions a specific number of seats. Denmark guarantees two seats each for Greenland and the Faroe Islands; Spain has a number of designated seats and Canada's apportionment benefits its territories. Remote regions might have special views to which the governing body should give dedicated weight; otherwise they might be inclined to secede.
• A lowest common denominator between adjoining voters exists, the "voting place" or "administrative quantum" (for example, a municipality, a precinct, a polling district) traditionally designed for voting convenience, tending to unite small clusters of homes and to remain little changed. ^{[clarification needed]} The government (or an independent body) does not organize the perfect number of voters into an election district, but a roughly appropriate number of voting places.
• The basis for apportionment may be out of date. For example, in the United States, apportionment follows the decennial census. The states conducted the 2010 elections with districts apportioned according to the 2000 Census. The lack of accuracy does not justify the present cost and perceived intrusion of a new census before each biennial election.

A perfectly apportioned governing body would assist but does not ensure good representation; voters who did not vote for their district's winner might have no representative who is disposed to voice their opinion in the governing body. Conversely, a representative in the governing body may voice the opinions held by a voter who is not actually their constituent, though representatives usually seek to serve their own constituents first and will only voice the interests of an outside group of voters if it pertains to their district as well or is of national importance. The representative has the power, and in many theories or jurisdictions the duty, to represent the whole cohort of people from their district.

For party-list proportional representation elections the number of seats for a political party is determined by the number of votes. Only parties crossing the electoral threshold are considered for apportionment. In this system, voters do not vote for a person to represent their geographic district, but for a political party that aligns with the voter's philosophy. Each party names a number of representatives based on the number of votes it receives nationally.

This system tallies (agglomerates) more of the voters' preferences. As in other systems parties with very few voters do not earn a representative in the governing body. Moreover, most such systems impose a threshold that a party must reach (for example, some percentage of the total vote) to qualify to obtain representatives in the body which eliminates extreme parties, to make the governing body as orderly in non-proportionate systems. With the minimum votes threshold version, if a subtype of single-issue politics based on a local issue exists, those parties or candidates distancing themselves from a broad swathe of electoral districts, such as marginal secessionists, or using a marginal minority language, may find themselves without representation.

The vast majority of voters elect representatives of their philosophies. However, unlike district systems (or the hybrid models) no one elects a representative that represents them, or their specific region, and voters might reduce personal contact with their representatives.

Apportionment methods for party-list proportional representation include:

• Sainte-Laguë method – optimal seats-to-votes ratio^[2]
• Hare quota – optimal seats-to-votes ratio^[2] and higher apportionment paradoxes^[3]
• D'Hondt method – higher seats-to-votes ratio for larger parties^[4]
• Droop quota
• Imperiali quota
• Huntington–Hill method

These apportionment methods can be categorized into largest remainder methods and highest averages methods.

Malapportionment is the creation of electoral districts with divergent ratios of voters to representatives. For example, if one single-member district has 10,000 voters and another has 100,000 voters, voters in the former district have ten times the influence, per person, over the governing body. The malapportionment can be measured by seats-to-votes ratio. Malapportionment may be deliberate, for reasons such as biasing representation toward geographic areas or a minority over equality of individuals. For example, in a federation, each member unit may have the same representation regardless of its population.

The effect might not be just a vague empowerment of some voters but a systematic bias to the nation's government. Many instances worldwide arise in which large, sparsely populated rural regions are given equal representation to densely packed urban areas.^[5] As an example, in the United States, the Republican Party benefits from institutional advantages to rural states with low populations, such that the Senate and the Presidency may reflect results counter to the total popular vote.^[a]

Unequal representation can be measured in the following ways:

• By the ratio of the most populous electoral district to the least populous. In the two figures above, the ratio is 10:1. A ratio approaching 1:1 means there are no anomalies among districts. In India in 1991, a ratio of nearly 50:1 was measured.^[6] The Reynolds v. Sims decision of the U.S. Supreme Court found ratios of up to 1081:1 in state legislatures. A higher ratio measures the severity of the worst anomalies, but does not indicate whether inequality is prevalent.
• By the standard deviation of the electorates of electoral districts.
• By the smallest percentage of voters that could win a majority in the governing body due to disparities in the populations of districts. For example, in a 61-member body, this would be half the voters in the 31 districts with the lowest populations. It is persuasive to show that far fewer than 50% of the voters could win a majority in the governing body. But it requires additional research to conclude that such an outcome is realistic: whether the malapportionment is systematic and designed to bias the body, or is the result of random factors that give extra power to voters whose interests are unlikely to coincide.^[7]

Even when electoral districts have similar populations, legislators may draw the boundaries to pursue private agendas; see Gerrymandering.

Another form of malapportionment is called reactive malapportionment, which can come about in three ways. The first is the impact of abstentions, in which a lower turnout in a constituency means fewer votes are needed to win there. This can be seen in the UK through the Labour Party's strength in inner city areas where turnout is lowest. The second is the impact of minor parties, which works in a similar way; more votes going to smaller parties means fewer votes are needed for the two larger parties. This form of malapportionment benefits the largest party in an area where minor parties excel. Finally, the instance of a minor party winning a constituency denies victory to one of the two main parties.^[8]

• 1955 System – In Japan, malapportionment benefits the Liberal Democratic Party, who have ruled for over 60 years (with two brief periods in opposition, totaling 5 years). This has been the subject of multiple Japanese Supreme Court cases.^[9][10][11]
• Population of Canadian federal ridings – in the Canadian House of Commons, in 2021, the least populous riding had 26,000 people while the most populous had 209,000 people. Several provinces are significantly overrepresented relative to their population.^[12]
• The Constitution of Australia guarantees each of the six founding states an equal number of Senators in the Australian Senate, regardless of population. But this would not necessarily apply to other states, were they admitted.
  • Bjelkemander – malapportionment in Queensland, during the 1970s and 1980s, designed to benefit the rural-based Country Party who were able to govern uninhibited during this period. The system was named after Sir Joh Bjelke-Petersen, who was leader of the Country Party and Premier of Queensland for 20 years during this period. Bjelke-Petersen's administration eventually became embroiled in corruption and lost an election to the Labor Party, who removed the malapportionment.
  • Playmander – malapportionment existed in South Australia from 1938 to 1968. It was designed to benefit the rural-based Liberal and Country League, allowing them to rule with majority of seats, even when the opposing Labor Party won the popular vote. The system was named after Sir Thomas Playford, who was leader of the LCL and Premier of South Australia for 26 years during this period. The malapportionment was mostly removed by LCL leader Steele Hall who was embarrassed at how undemocratic it was.
• The United States Constitution guarantees each state two Senators in the United States Senate regardless of population. For instance, the state of California has 70 times the population of the state of Wyoming, but each has two Senators, making those who live in California vastly underrepresented. In the 21st century, this system benefits white Americans (who are more likely to live in smaller states) and the Republican Party (there are more small red states, than small blue states), who wield political power disproportionate to their numbers. This has grown more impactful as bipartisanship has become less common, with Senators increasingly voting along party lines.^[13]
  • In the antebellum period new states were admitted in a pattern of one slave state and one free state each, creating a balance in the Senate despite the population total of the free states far exceeding that of slave states by the 1850 US Census. California being admitted as a free state under the Compromise of 1850 broke the pattern and the Thirteenth Amendment to the United States Constitution abolished slavery in all states by 1865, making the issue moot.
• Rotten and pocket boroughs in England, Great Britain, or the United Kingdom before the Reform Act 1832, which had a very small electorate and could be used by a patron to gain unrepresentative influence within the unreformed House of Commons.

• Apportionment in the European Parliament
• Apportionment in the Hellenic Parliament
• United States congressional apportionment

• Index of articles relating to Boundary Delimitation from the ACE Project
• A guide to the various formulae for apportionment, and statistical differences between them