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).

Common problems

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.

Apportionment by district

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:

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.

Apportionment by party list

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:

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. [lower-alpha 1]

Unequal representation can be measured in the following ways:

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]

Examples of malapportionment

See also


  1. For instance, although the Republican candidate has won the popular vote in only one of the eight presidential elections from 1992 through 2020 (that in 2004), the Electoral College vote - and, thus, the presidency - has been won by the Republican candidate in three of those eight contests (the additional instances being in 2000 and 2016).

Related Research Articles

<span class="mw-page-title-main">Gerrymandering</span> Form of political manipulation

In representative electoral systems, gerrymandering is the political manipulation of electoral district boundaries with the intent to create undue advantage for a party, group, or socioeconomic class within the constituency. The manipulation may involve "cracking" or "packing". Gerrymandering can also be used to protect incumbents. Wayne Dawkins, a professor at Morgan State University, describes it as politicians picking their voters instead of voters picking their politicians.

<span class="mw-page-title-main">Proportional representation</span> Voting system that makes outcomes proportional to vote totals

Proportional representation (PR) refers to any type of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to political divisions among voters. The essence of such systems is that all votes cast – or almost all votes cast – contribute to the result and are effectively used to help elect someone – not just a bare plurality or (exclusively) the majority – and that the system produces mixed, balanced representation reflecting how votes are cast.

<span class="mw-page-title-main">Party-list proportional representation</span> Family of voting systems

Party-list proportional representation (list-PR) is a subset of proportional representation electoral systems in which multiple candidates are elected through their position on an electoral list. They can also be used as part of mixed-member electoral systems.

The D'Hondt method, also called the Jefferson method or the greatest divisors method, is an apportionment method for allocating seats in parliaments among federal states, or in proportional representation among political parties. It belongs to the class of highest-averages methods. The D'Hondt method reduces compared to ideal proportional representation somewhat the political fragmentation for smaller electoral district sizes, where it favors larger political parties over small parties.

The Webster method, also called the Sainte-Laguë method, is a highest averages apportionment method for allocating seats in a parliament among federal states, or among parties in a party-list proportional representation system. The Sainte-Laguë method shows a more equal seats-to-votes ratio for different sized parties among apportionment methods.

In mathematics, economics, and political science, the highest averages methods, also called divisor methods, are a class of apportionment algorithms for proportional representation. Divisor algorithms seek to fairly divide a legislature between agents. More generally, divisor methods are used to divide or round a whole number of objects being used to represent (non-whole) shares of a total.

The electoral system of Australia comprises the laws and processes used for the election of members of the Australian Parliament and is governed primarily by the Commonwealth Electoral Act 1918. The system presently has a number of distinctive features including compulsory enrolment; compulsory voting; majority-preferential instant-runoff voting in single-member seats to elect the lower house, the House of Representatives; and the use of the single transferable vote proportional representation system to elect the upper house, the Senate.

An electoral district, also known as an election district, legislative district, voting district, constituency, riding, ward, division, electorate, or (election) precinct, is a subdivision of a larger state created to provide its population with representation in the larger state's constituency. That body, or the state's constitution or a body established for that purpose, determines each district's boundaries and whether each will be represented by a single member or multiple members. Generally, only voters (constituents) who reside within the district are permitted to vote in an election held there. District representatives may be elected by a first-past-the-post system, a proportional representative system, or another voting method. They may be selected by a direct election under universal suffrage, an indirect election, or another form of suffrage.

The Bjelkemander was the term given to a system of malapportionment in the Australian state of Queensland in the 1970s and 1980s. Under the system, electorates were allocated to zones such as rural or metropolitan and electoral boundaries drawn so that rural electorates had about half as many voters each as metropolitan ones. The Country Party, a rural-based party led by Joh Bjelke-Petersen, was able to govern uninhibited during this period due to the 'Bjelkemander' and the absence of an upper house of Parliament.

<span class="mw-page-title-main">Western Australian Legislative Council</span> Upper house of the legislature of Western Australia

The Western Australian Legislative Council is the upper house of the Parliament of Western Australia, a state of Australia. It is regarded as a house of review for legislation passed by the Legislative Assembly, the lower house. The two Houses of Parliament sit in Parliament House in the state capital, Perth.

Congressional districts, also known as electoral districts in other nations, are divisions of a larger administrative region that represent the population of a region in the larger congressional body. Countries with congressional districts include the United States, the Philippines, and Japan.

The Huntington–Hill method is a method for proportional allocation of the seats in a representative assembly by minimizing the percentage differences in the number of constituents represented by each seat. Edward Huntington formulated this approach, building on the earlier work of Joseph Adna Hill, and called it the method of equal proportions. Since 1941, this method has been used to apportion the 435 seats in the United States House of Representatives following the completion of each decennial census.

A single-member district is an electoral district represented by a single officeholder. It contrasts with a multi-member district, which is represented by multiple officeholders. Single-member districts are also sometimes called single-winner voting, winner-takes-all, single-member constituencies or single-member electorates.

In Australia, a redistribution is the process of redrawing the boundaries of electoral divisions for the House of Representatives arising from changes in population and changes in the number of representatives. There is no redistribution for the Senate as each State constitutes a division, though with multiple members. The Australian Electoral Commission (AEC), an independent statutory authority, oversees the apportionment and redistribution process for federal divisions, taking into account a number of factors. Politicians, political parties and the public may make submissions to the AEC on proposed new boundaries, but any interference with their deliberations is considered a serious offence.

Redistribution is the process by which electoral districts are added, removed, or otherwise changed. Redistribution is a form of boundary delimitation that changes electoral district boundaries, usually in response to periodic census results. Redistribution is required by law or constitution at least every decade in most representative democracy systems that use first-past-the-post or similar electoral systems to prevent geographic malapportionment. The act of manipulation of electoral districts to favour a candidate or party is called gerrymandering.

Degressive proportionality is an approach to the allocation of seats in a legislature or other decision-making body. Degressive proportionality means that while the subdivisions do not each elect an equal number of members, smaller subdivisions are allocated more seats than would be allocated strictly in proportion to their population. The seats-to-votes ratio decreases for larger subdivisions.

Direct representation or proxy representation is a form of representative democracy where voters can vote for any candidate in the land, and each representative's vote is weighted in proportion to the number of citizens who have chosen that candidate to represent them.

<span class="mw-page-title-main">Electoral system</span> Method by which voters make a choice between options

An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, non-profit organisations and informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on campaign spending, and other factors that can affect the result. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices.

Apportionment in the Hellenic Parliament refers to those provisions of the Greek electoral law relating to the distribution of Greece's 300 parliamentary seats to the parliamentary constituencies, as well as to the method of seat allocation in Greek legislative elections for the various political parties. The electoral law was codified for the first time through a 2012 Presidential Decree. Articles 1, 2, and 3 deal with how the parliamentary seats are allocated to the various constituencies, while articles 99 and 100 legislate the method of parliamentary apportionment for political parties in an election. In both cases, Greece uses the largest remainder method.

Apportionment by country describes the practices used in various democratic countries around the world for partitioning seats in the parliament among districts or parties. See apportionment (politics) for the general principles and issues related to apportionment.


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  2. 1 2 Pennisi, Aline (1998). "Disproportionality indexes and robustness of proportional allocation methods". Electoral Studies. 17: 3–19. doi:10.1016/S0261-3794(97)00052-8.
  3. Balinski, Michel; H. Peyton Young (1982). Fair Representation: Meeting the Ideal of One Man, One Vote . Yale Univ Pr. ISBN   0-300-02724-9.
  4. Bochsler, Daniel (2010). "Who gains from apparentments under d'Hondt?". Electoral Studies. 29 (4): 617–627. doi:10.1016/j.electstud.2010.06.001.
  5. Liptak, Adam (March 11, 2013). "Smaller States Find Outsize Clout Growing in Senate". The New York Times. Retrieved December 10, 2016.
  6. The largest district, Thane, had a population of 1,744,592, while the smallest district, Lakeshadweep, had a population of 31,665.
  7. "Engine". Retrieved 2010-04-18.
  8. Johnston, Pattie, Dorling, Rossiter, Ron, Charles, Danny, David. "Fifty Years of Bias in the UK's Electoral System" (PDF). APSA. Retrieved 24 January 2021.{{cite web}}: CS1 maint: multiple names: authors list (link)
  9. "Fixing Japan's gerrymander". 29 April 2022.
  10. "Japan's Electoral Unfairness Goes Deeper than Malapportionment". 5 April 2013.
  11. "Japan's electoral map favours the ruling party". The Economist.
  12. "One person, one vote? In Canada, it's not even close". Toronto Star . 13 October 2019.
  13. "'The Senate is broken': system empowers white conservatives, threatening US democracy". The Guardian. March 13, 2021. Retrieved March 30, 2023.