Apportionment (politics)

Apportionment is the process of allocating political power among a set of principles (or defined constituencies). In most representative governments, political power has most recently been apportioned among constituencies based on population, but there is a long history of different approaches.

The United States Constitution, however, apportions political power differently between its upper house, the Senate, and its lower house, the House of Representatives. Within the Senate, each state is represented by two seats, the result of compromise when the constitution was written. Seats in the US House of Representatives (the House) are apportioned among the states based on the relative population of each state in the total population of the union. The states then create districts from which representatives will be elected to serve in the US House of Representatives. The ideal is that each district would have an equal amount of population. States can lose or gain seats at each decennial census. Districts must be redrawn within each state after each census to reflect population changes.

Apportionment is also applied in party-list proportional representation elections to distribute seats between different parties once they have won a particular percentage of the vote. Current philosophy is that each person's vote should carry the same weight in legislative bodies that are derived from population.

There are many different mathematical schemes for calculating apportionment, which can produce different results in terms of seats for the relevant party or sector. Additionally, all methods are subject to one or more anomalies.

With the Hamilton method, party A with vote total P(A) is entitled to its mth seat before party B with vote total P(B) is entitled to its nth seat if and only if P(A)/Qm > P(B)/Qn, where Q is a fixed amount called a quota.

A popular alternative is a family of methods where the condition can be represented as P(A)/f(m − 1) > P(B)/f(n − 1) where f(x) is a function that, for practical applications, yields a number between x and x + 1. Five choices for f(x) have received support over the years:[1]



Malapportionment, or unequal representation, is broad and systematic variance in the size of electoral constituencies resulting in disproportionate representation for a given voter. Malapportionment is only possible within electoral systems that have districted constituencies - an electoral system with only one national constituency such as those in Israel and the Netherlands cannot be malapportioned.

There is no single agreed upon way of measuring malapportionment. Using the ratio of the largest district to the smallest district may seem like an obvious way, but it does not tell us the overall degree of malapportionment.

When this ratio is low, malapportionment is absent. For example, in the US, congressional districts of the same state must be as equal in populations as possible. But even with no malapportionment, there may be gerrymandering involved.

But when the ratio is high, it only says something about the two extreme districts and nothing more. For example, in India, every district is assigned one member in the national lower chamber. The largest district, Thane, had a population of 1,744,592 in 1991. That same year the smallest district Lakeshadweep had a population of 31,665. Even though Lakeshadweep was outnumbered nearly 50:1, it received equal representation. However, this information does not tell us the overall degree of malapportionment nationwide. If the smallest and highest populated districts are outliers, they could represent extreme cases although the overall country has a very low degree of malapportionment.

An additional result of malapportionment occurs when reviewing the majority threshold of the different systems. Reaching majority in district elections occurs at a percentage-wise lower level of minimally required number of votes than in proportional elections. The exact difference is, ceteris paribus, 3/5ths the number of votes needed to reach the majority threshold in district elections to the number of votes needed to reach that threshold in proportional elections. Naturally, specific circumstances are always different, but the explanation as provided by LocalParty.Org shows that this 3/5ths level does point to the bare minimum to achieve the threshold to become the party or parties with the majority. As an example, when 60% of the eligible voters come out to vote, 30% of all eligible voters is the bare minimum to achieve the majority in proportional elections. Due to the specific nature of district elections, the bare minimum is only 18% of all eligible voters to become the majority party.[2]

This specific difference of when a party or parties achieve the majority threshold is also found when considering the heat of the elections. In district elections, a specific district can become a battlegrounds for two parties that have a 50-50 chance of winning that seat, while such kind of battleground does not occur in proportional elections. Still, what both have in common is that local strongholds can occur. Yet where political strongholds in proportional elections often still contain a few representatives of other political colors as well, the result in district elections often translates into a local political monopoly.

Because of the specific results of district elections, that party that had the most votes may still not be the majority party. In the United States, the Republican Party had fewer votes cast for its representatives in the Senate in 2004 than the Democratic representatives, yet had the majority in number of representatives nevertheless. This is only partially explained by the States electing a representative based on geography and not on number of eligible voters.

Malapportionment around the world

United Kingdom

Constituencies tend to vary according to some factor such as geographic location. In the United Kingdom constituencies in Scotland and Wales for the Westminster parliament deliberately had smaller electorates than those in England. The UK retains some malapportionment, due to rules which favour geographically 'natural' districts and which continue to give proportionally greater representation to Wales. Population movements between boundary reviews have tended to decrease the number of electors in inner-city districts, a trend that usually favours the Labour Party.[3]

United States


The US Constitution apportions political power in the Senate equally among the states of the union regardless of population or geography. Article V specifies that this cannot be changed by amendment except with the consent of all affected states. Each state was given equal power. Until passage of the 17th Amendment, this made sense because the state legislatures appointed senators.

As the people of each state elected their state legislators, they could be said to indirectly elect the Senators.

The amendment provided for direct election of senators by voters of each state. Due in part to the huge sizes of senatorial constituencies and the changes in political campaigns, the cost of candidacy is approximately $12M. This cost of candidacy has increased a candidate's need for fundraising to run a competitive campaign.[citation needed]

Due to the small number of seats in the US House of Representatives (435) Title 2 United States Code section 2 is currently repealed / omitted, opening redistricting to a greater number of US House seats relative to the nation's population of roughly 300 million. The political power of the House of Representatives for several states is malapportioned. The representation was defined by the US Constitution to be based on population, The maximum of 1 US House representative for every 30,000 people, Article I section 2 clause 3, The first census, when completed, the States used the maximum, sending 106 elected in 1792 to Represent the Thirteen States for the third Congress. The malapportionment occurs because of discrepancies created with rounding. For example, the per capita influence of the state of Wyoming is almost twice that of Montana because the states have the same number of seats, but the population of Wyoming is smaller. The only cure within the Constitution is to dramatically increase the number of members/seats in the House of Representatives. (See Article The First, Alabama paradox.)

State legislatures

Many states suffered through periods of extended malapportionment, which were created by failures of state legislators to reapportion after significant population shifts across established (often urban) districts or into the state. State legislatures were historically the bodies that drew the boundaries, and or set the rules for drawing, the districts in a state. As elected representatives, legislators have a self-interest in preserving their own power, and often did not reapportion for fear of losing political power as changes came to states.

Among the most egregious examples in malapportionment was the Alabama state legislature's refusal to reapportion either the state House or Senate from 1901 until 1972. The result was that by 1960, 25% of the population of the state controlled the majority of the seats in the white, rural-dominated legislature.[4] This rural v. urban split went beyond the related fact of racial and class disfranchisement. In 1901, like most southern states about the turn of the century, white Democratic state legislators had ratified a new constitution with provisions that effectively disfranchised African Americans and poor whites. This was a reversal of the state's having extended universal white suffrage at its establishment in 1819. By 1940, 600,000 poor whites and 520,000 African Americans had been disfranchised.[5] The disfranchised had no representation in the state legislature. The failure of the legislature to reapportion meant also that the hundreds of thousands of industrialized and urbanized populations of the state were underrepresented for most of the 20th century.

In many states in the US, malapportionment was related to racial and class issues. For example, during much of the 20th century in Southern States, the Democratic rural areas dominated urban areas by refusing to redistrict although populations changed considerably. While most African Americans were disfranchised in the South, most voters were Democrats, but the urban populations suffered from inadequate representation. The result was that, in some cases, rural districts would have drastically less population than an urban counterpart and still hold an equal or greater number of representatives or senators, thereby diluting the voice in the legislature of the latter compared to that of the former.

Several notable lawsuits brought to the Supreme Court in the early 1960s challenged state apportionment systems, with Baker v. Carr and Reynolds v. Sims among the most important of these. The plaintiffs claimed that malapportionment was discriminatory and illegal under the Fourteenth Amendment. The US Supreme Court agreed, citing the doctrine of "One Man, One Vote"[citation needed].

An example of how “One Man, One Vote” has helped to minimize malapportionment is that it requires congressional redistricting every ten years, following the census. One Pennsylvania plan was rejected by courts because the districts were nineteen voters apart, in districts of half a million people. The use of computers allows the states to virtually eliminate malapportionment every ten years with the census data. However, the ruling does allow for gerrymandering.[6] During congressional redistricting, districts may each be assigned an equal population, but the use of gerrymandering may lead to similarly unequal representation along political party lines, with the party in power trying to ensure its re-election.

Following the 1990 census, for example, the state house of Tennessee's first attempt to redistrict was rejected by the courts for systematically over-representing rural West Tennessee, then predominantly Democratic, at the expense of rural East Tennessee, then predominantly Republican.[citation needed]. Following the 2000 census, Georgia's first attempt at redistricting the state senate was thrown out for systematically under-populating then Democratic-held districts and systematically overpopulating then Republican-held districts throughout the state.[citation needed].


The Australian Senate is elected on a basis of equality among the states: all states elect 12 Senators, regardless of population. This leads to Tasmania, with a population of 502,000 people electing the same number of Senators as New South Wales, which has a population of almost 7.1 million. The senate is designed to ensure that the smaller states are not neglected.[7]

The distribution of seats in both the federal and state legislatures have been subject to malapportionment, often resulting in rural constituencies containing far fewer voters than urban ones, in turn often maintaining in power parties with rural support bases despite polling far fewer popular votes. Well-known examples include the differences between urban and rural constituency sizes in many Australian states. Past apportionments in Queensland, Western Australia and the 'Playmander' in South Australia were notorious examples. The effects of malapportionment vary with time: deliberate over-representation of rural Queensland changed from favouring Labor to favouring the National Party[citation needed]. There were well-meaning supporters of such arrangements due to Australia's unique demographics where the city population completely dominates the sparsely populated countryside. Therefore, it was argued that these practices were necessary to give country people fair representation. See: Australian electoral system#Gerrymandering and malapportionment


Another example is the systematic over-representation of voters in more rural prefectures and under-representation of voters in more urban prefectures in elections to the Japanese parliament. The conservative Liberal Democratic Party thus wins more seats in the Japanese parliament because its voters are concentrated in more rural prefectures.


The Spanish Congress of Deputies consists of 350 members. Each Spanish province is a constituency entitled to an initial minimum of two seats for a total of 100 seats, while the North African enclaves of Ceuta and Melilla are allocated one member each. The remaining 248 seats are allocated among the fifty provinces in proportion to their populations.[8] The result is that the smaller provinces are virtually guaranteed a minimum of three seats and have a disproportionate share of seats relative to their electorate. In 2004 for example, Spain had 34,571,831 voters giving an average of 98,777 voters per deputy.[9] However the number of voters per deputy varied from 129,269 in Barcelona [10] and 127,377 in Madrid [11] to 38,714 and 26,177 respectively in the smallest provinces of Teruel [12] and Soria.[13]

In the Spanish Senate each of the forty-seven mainland provinces are assigned four seats, while the three largest islands are allocated three seats each, and the seven smaller islands one each. The North African enclaves of Ceuta and Melilla are allocated two seats each. Additionally, the legislative assemblies of the seventeen autonomous communities into which the provinces of Spain are grouped are entitled to appoint at least one Senator each, as well as one Senator for every million voters. The result is a bias in favour of mainly rural areas. For example the community of Madrid with 4,458,540 voters in 2004 has 9 senators while Castilla y León with 2,179,521 voters has a total of 39 senators.


In Canada, there are 308 federal electoral districts, each represented by one member of parliament. While all districts in the 10 provinces of Canada are theoretically based on population, each territory is also given a member of parliament, and certain special clauses in the Constitution and law (the "grandfather clause" and the "senatorial clause") guarantee that provinces cannot have fewer members that they had in 1982.[14] The apportionment method is to grant 1 member to each territory, and allocate 279 other seats according to population among the 10 provinces. After doing so, the provinces with slower historical population growth since joining Confederation are granted extra seats so as not to lose MPs. After the 1991 Census, 19 such extra members across all provinces were needed for a total of 301 MPs. (All provinces except Ontario, Alberta, and British Columbia received additional MPs.) After the 2001 Census, Ontario, Alberta, and British Columbia gained 7 seats, necessitating 7 extra "grandfathered" seats for the provinces with slower population growth, for a total of 308 ridings. However, this creates huge disproportion between ridings of the different provinces but as well as between the provinces and territories. As ridings are rarely eliminated, only newly created or manipulated to attend to population shifts, this exacerberate the problem. For example; in 2006, the Alberta riding of Peace River had a population of 138,009 persons, whilst the Prince Edward Island riding of Charlottetown had a population of 32,174 respectively; both ridings receive equal representation in the House of Commons. The territory of Nunavut, along with all other Canadian territories also receives one member of parliament, while in 2006, it had a population of 29,474. Rural ridings even in populous provinces also tend to have constituents for every MP than urban ridings.

South Africa

In the South African General Election of 1948, South Africa's constituency boundaries meant that sparsely populated rural constituencies in the Afrikaner heartland had relatively few eligible voters compared to the urban constituencies in Cape Town. The rural electorates often strongly supported the Herenigde Nasionale Party, led by Daniel Malan and the urban electorates often supported Jan Christiaan Smuts' United Party (the incumbent prime minister and his party, 90% of whose seats were urban). Come the 1948 General Election, Jan Smuts' party was unpopular on account of many factors. Ultimately, Jan Smuts won the popular vote, but Daniel Malan won more seats, meaning that his party was able to form a government bilaterally with the Afrikaner Party and gain an absolute majority in parliament. Malapportionment was a key tool that allowed the National Party to implement its Apartheid program within the notionally democratic parliament.

New Zealand

Between 1881 and 1945, New Zealand applied a system of malapportionment called the country quota, which required urban districts to contain more people than rural ones but did not give them any equivalent increase in representation.

See also


  1. ^ A seemingly plausible metric can be developed for any of these methods (that is, for each of these methods, a definition of error can be given such that the method minimizes the error; this is discussed in [1].
  2. ^ "Engine". Retrieved 2010-04-18. 
  3. ^ Lewis Baston (2008-10). "The Conservatives and the electoral system because he was the one who shot lincoln". Electoral Reform Society. Retrieved 2008-07-24. 
  4. ^ Dr. Michael McDonald, "US Elections Project: Alabama Redistricting Summary", George Mason University, accessed 6 Apr 2008 Archived October 17, 2007 at the Wayback Machine
  5. ^ Glenn Feldman, The Disfranchisement Myth: Poor Whites and Suffrage Restriction in Alabama, Athens: University of Georgia Press, 2004, p.136
  6. ^ Toobin, Jeffrey (2009-01-07). "Annals of Law: The Great Election Grab". The New Yorker. Retrieved 2010-04-18. 
  7. ^ "Parliament of Australia: Senate: The Senate: a short description". 2006-03-02. Retrieved 2010-04-18. 
  8. ^ "Election Resources on the Internet: Elections to the Spanish Congress of Deputies". Retrieved 2010-04-18. 
  9. ^ "Election Resources on the Internet: Elections to the Spanish Congress of Deputies - Results Lookup". Retrieved 2010-04-18. 
  10. ^ "Election Resources on the Internet: Elections to the Spanish Congress of Deputies - Results Lookup". Retrieved 2010-04-18. 
  11. ^ "Election Resources on the Internet: Elections to the Spanish Congress of Deputies - Results Lookup". Retrieved 2010-04-18. 
  12. ^ "Election Resources on the Internet: Elections to the Spanish Congress of Deputies - Results Lookup". Retrieved 2010-04-18. 
  13. ^ "Election Resources on the Internet: Elections to the Spanish Congress of Deputies - Results Lookup". Retrieved 2010-04-18. 
  14. ^

External links

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