Apportionment is the process by which seats in a legislative body are distributed among constituencies in a Redistribution operation, or among parties in a party-list proportional election; the two takes are mathematically equivalent. This page presents the general principles and issues related to apportionment. The apportionment by country page describes the specific practices used around the world. The mathematics of apportionment page 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).
One example of deliberate malapportionment is seen in bicameral legislatures: where the lower house represents constituencies in proportion to their population, the upper house represents the constituencies as such, giving them an equal number of seats despite their population variance. This is modeled after the Connecticut Compromise, which formed the basis of the United States Senate; for that reason it is particularly common in states where the regions enjoy significant political autonomy from the central government, such as federations and regionalized unitary states.
Common problems Fundamentally, the representation of a population in the thousands or millions by a reasonably sized, and 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, 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 many systems provide for dissolution of the legislature 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.
Among constituencies In many legislatures, the members represent geographical districts, which may be single-member or multi-member.
As a general rule, single-member districts are typically purpose-drawn to ensure that each district comprises the same number of residents or voters, while mutli-member districts have static borders, with only the number of seats from each district changing in a redistribution operation.Venice Commission, Code of Good Practice in Electoral Matters, Page 24 However, this is not universal, for reasons including the following:
In federations like the United States, Germany, Brazil, and Nigeria, as well as regional states such as Spain, Indonesia, and Bolivia, the regions, states, or provinces are viewed as important entities in their own right rather than mere administrative divisions, and it is not uncommon for residents of a given region identify as citizens of their region first and of the country as a whole second; the regions also have institutional interests that they seek to pursue even in matters under the jurisdiction of the federal or central government. Consequently, election districts are required to be contained in one region only. 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; Norway apportions seats between the districts under a system that considers both population and area, with each inhabitant counting as one point and each square kilometer of area counting as 1.8 points; 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. Administrative convenience: the otherwise-static borders of multi-member districts are adjusted to line up with new administrative boundaries, or with electoral districts of a higher or lower rung. For example, in Poland, local government reforms in 1998 replaced the country's 49 voivodeships with 16 large "regional" ones; the Sejm and Senate constituencies, which used the voivodeships as "building blocks", had to be completely redrawn as a consequence. In the devolved parliaments of the United Kingdom, the Scottish Parliament has multi-member regions created from combining adjacent single-member constituencies as part of its additional member system, while Wales's Senedd is elected from multi-member constituencies that are formed by pairing together adjacent constituencies for the UK House of Commons. The basis for apportionment may be out of date. For example, in India, the Forty-second Amendment of the Constitution (passed in 1976) froze the distribution of Lok Sabha seats between the states to be based on the 1971 census until the year 2000, which was later extended to 2026. This was done to ensure that government family planning programs would not cause states to "lose out" on their share of seats due to reduced population growth.
Among party lists
For party-list proportional representation elections the number of seats for a political party is determined by the number of votes. This apportionment typically takes place separately for each multi-member district; however some systems elect all of the members from a single at-large constituency, while others employ leveling seats to correct for the distortions that result from the district-level apportionments. Only parties crossing the electoral threshold are considered for apportionment.
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. 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.
Apportionment methods for party-list proportional representation include: Sainte-Laguë method – optimal seats-to-votes ratio Hare quota – optimal seats-to-votes ratio and higher apportionment paradoxes D'Hondt method – higher seats-to-votes ratio for larger parties Droop quota Imperiali quota Huntington–Hill method
These apportionment methods can be categorized into largest remainder methods and highest averages methods. These apportionment methods, also known as formulas, can be used in both list-PR and mixed-electoral systems. A third, percentage-point method can only be used in mixed-electoral systems as it requires the transfer of percentage points to one or more compensatory tiers.Ring, Robert S. (2014). Proportional-first-past-the-post: a Canadian model of proportional representation (thesis). Memorial University of Newfoundland. Ring, Robert S. (2015) Brief submitted to the Canadian House of Commons Special Committee on Electoral Reform.
Malapportionment Malapportionment is the creation of electoral districts with divergent ratios of voters to representatives. For example, if one district has 10,000 voters per seat, and another has 100,000 voters per seat, voters in the former district have ten times the influence, per person, over the governing body. 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. In some instances sparsely populated rural regions are given intentionally equal representation to densely packed urban areas with higher populations, for example the United States Senate may reflect results counter to the majority vote.
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. 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. Differences in seats-to-votes ratios. 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.
Apportioning by population instead of number of citizens results in malapportionment.
Examples of malapportionment Modern bicameral parliaments have often one house representing the population, and a second house representing regions. The regional house in most cases has the same number of deputies from every region, and prevents populous regions dominating the rest of the country, introduced with the Swiss diet, later improved and popularized by the US Senate and Connecticut compromise in the USA, a system copied by many other countries parliaments. 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. 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. 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 or created. It also does not mandate any Senators in the Northern Territory and Australian Capital Territory, and Parliament has only seen fit to provide these non-state Territories with two Senators for each Territory. In addition to the general malapportionment these requirements create between the most populous states and the least, which saw former Prime Minister Paul Keating describe the Senate as "unrepresentative swill", it also means that the Australian Capital Territory has four less Senators than Tasmania despite their populations being roughly equal. The two Senators for each territory also face re-election every election, rather than every second election, depriving the Territories of the stability that comes from long-term representation in the Senate. The Constitution of Australia mandates a minimum of five members per original state in the Australian House of Representatives. This has the effect of creating a malapportionment where Tasmania has a significantly lower number of voters per seat than the rest of the country, giving Tasmania two additional seats than they would have without this 5 seat minimum.