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This article is about political apportionment. For the legal term, see apportionment.

Apportionment is the process of allocating political power among a set of principles (or defined constituencies). In most governments, political power is apportioned among constituencies based on population. The United States Constitution, however, apportions political power, within the legislature, among the states of the union as opposed to political parties or the people directly. Each state is apportioned two seats in the US Senate regardless of the state's size, location, or population. 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 partition their geography into equally populous single member electoral districts where representatives will be elected to serve in the US House of Representatives. States can lose or gain seats at each decentennial census. Districts must be redrawn within each state after each census.

Apportionment is also applied in party-list proportional representation elections to distribute seats between different parties once they've won a particular percentage of the vote, much like how different U.S. states obtain different shares of the population from the census. In a perfectly apportionmented system, every person's vote carries the same weight.

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. 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, 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 where the overall country has a very low degree of malapportionment. 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)/Q-m > P(B)/Q-n, 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]:

• f(x)=x (the Adams method or method of smallest divisors)
• f(x) set to the harmonic mean of x and x+1 (the Dean method)
• f(x) set to the geometric mean of x and x+1 (the Huntington-Hill method or method of equal proportions)
• f(x) set to the arithmetic mean of x and x+1 (the Webster method or method of major fractions)
• f(x)=x+1 (the Jefferson method or method of greatest divisors)

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.

It is a tendency for the size of constituencies to vary according to some factor such as geographic location. Well-known examples include the differences between urban and rural constituency sizes in many Australian states (Western Australia, Queensland and South Australia in the past afforded far more notorious examples), and the recently abolished smaller United Kingdom parliamentary constituencies in Scotland (with the notable exception of Orkney and Shetland. The UK retains a substantial malapportionment in favour of urban voters mainly because districting process has not caught up with the residential shift to suburb.^{[citation needed]} , which currently benefits the British Labour Party^{[citation needed]}. The effects of malapportionment vary with time: deliberate over-representation of rural Queensland changed from favouring Labor to favouring the National Party^{[citation needed]}.

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The United States Congress

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 the 17th Amendment this made perfect sense because the state legislatures appointed the Senators. As such the people of each state, as they elected their state legislators also indirectly elected the Senators. This caused a certain political "awareness" and a familiarity among the electorate, but more importantly it formed a check on the abuse of power by the Federal government and most especially the executive branch. The proximity of the state legislators to their constituents and the relative isolation of the state legislators from the infamous "lobby" as well as the national party apparatus located in Washington D.C. may have provided a somewhat better representation for the common people at the expense of the Washington establishment. At present, due to the huge size of Senatorial constituencies, the cost of candidacy is approximately $12M. This cost of candidacy virtually assures that only the rich and the well connected can hope to be seated in the US Senate. A malapportionment caused by an amendment to the Constitution.

However, due to the small membership of the US House of Representatives (435), for a population of what is now roughly 300 million, the political power of the House of Representatives and the several states is malapportioned because that power was defined by the US Constitution to be based on population. The malapportionment occurs due to the huge discrepancies created with round-off, and the only possible cure within the confines of the Constitution is to dramatically increase the number of members/seats. At present the per capita power of the state of Wyoming is almost twice that of Montana. (See Article The First.) In Late 2007 the US Constitution method, a new formula was created to fairly represent each state in the House respectively in accordance with the constitutional mandated "one for every thirty thousand" as written article 1, section 2, clause 3.

Many states suffered through periods of malapportionment which were created by failures to reapportion after significant population shifts within established districts. The State's legislature is historically the body which draws districts lines and apportions. Being a political body, and one which is elected, there were many legislatures who would not reapportion for fear of changing the make up of populations in districts in such a way that would threaten their reelection, or weaken their party's or caucus' political power.

In many states throughout the US, malapportionment had political and racial overtones. For example, during much of the 20th century in Southern States the Democratic rural areas dominated urban Republican strongholds by allowing the representation for such areas to remain constant even as their populations began to rise considerably. 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 legal battles were brought in the early 1960s which challenged numerous state apportionment systems, Baker v. Carr and Reynolds v. Sims being the most important of these. The plaintiffs claimed that malapportionment was discriminatory and illegal under the Fourteenth Amendment. The US Supreme Court agreed with the doctrine of "One Man, One Vote"^{[citation needed]}.

One example of “One person, One vote” has helped to minimize malapportionment is it requires congressional redistricting every ten years. 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, it does allow for the use of Gerrymandering. [2] During congressional redistricting, districts may all have an equal population, but the use of gerrymandering may lead to malapportionment along a political party.

Some more recent incidents are that following the 1990 census the state house of Tennessee's first attempt being thrown out for systematically overrepresenting (then predominantly Democratic) rural West Tennessee at the expense of (then predominantly Republican) rural East Tennessee^{[citation needed]}. Also following the 2000 census, Georgia's first attempt at drawing the state senate was thrown out for systematically underpopulating then Democratic-held seats and systematically overpopulating then Republican-held seats 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 450,000 people electing the same number of Senators as New South Wales, which has a population of six million. The senate is designed to ensure that the smaller states are not neglected. [3]

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. 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.

Since every province is allotted at least one representative in the House of Representatives of the Philippines regardless of population, this results in seats that represent populations that do not meet the 250,000 to 500,000 apportionment criteria. Based on 2000 census figures, there are 15 single district provinces that have under 250,000 inhabitants: Abra, Apayao, Aurora, Batanes, Biliran, Camiguin, Catanduanes, Dinagat Islands, Guimaras, Ifugao, Kalinga, Marinduque, Mountain Province, Quirino, and Siquijor.

In addition, upon becoming a highly-urbanized city in 1995, Mandaluyong was granted its own seat in Congress, leaving the municipality (now city) of San Juan with its own seat despite not meeting the population requirement — mainly because in order to meet the threshold and keep the district contiguous, San Juan would have to be redistricted with a part of either Manila or Quezon City because no adjacent city or municipality other than Mandaluyong can be wholly combined with San Juan to form a justifiable single district. To date, the population of San Juan City is still under the 250,000 threshold.

The apportionment of congressional districts is not done regularly by a specially-mandated independent agency, but rather through Republic Acts which are drawn up by members of congress. Apportionment, therefore, is often influenced by political motivations. Incumbent representatives who are not permitted to hold their seats by law after three consecutive terms sometimes resort to dividing their district, or even creating a new province which will be guaranteed a seat, just so that they will be able to run and serve terms in a technically different district.

Currently the district with the lowest population is the lone district of Batanes, with only 16,467 inhabitants in 2000 (with only 8,872 voters). The most populated congressional district, the 2nd District of Quezon City, has seventy times more inhabitants, with a total population of 1,163,537. The most under-represented jurisdiction is the province of Cavite, with only 3 seats out of a possible 8.

Provinces that can gain more representation using the 250,000-per-district minimum threshold to calculate the maximum number of seats and the 500,000-per-district maximum to get the minimum number of seats:
Provincial figures exclude populations of highly-urbanized cities that meet the population requirement as of 2000, but count component cities and municipalities even if they themselves meet the population requirement

Highly urbanized cities that have met the population requirement (as of 2000) but are still represented in congress as part of a province:

Highly urbanized cities that can gain more representation using the 250,000-per-district minimum threshold to calculate the maximum number of seats and the 500,000-per-district maximum to get the minimum number of seats:

Component cities and municipalities that have over 250,000 inhabitants and can potentially be given their own representation in Congress:

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. ^[2] 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 ^[3]. However the number of voters per deputy varied from 129,269 in Barcelona ^[4] and 127,377 in Madrid ^[5] to 38,714 and 26,177 respectively in the smallest provinces of Teruel ^[6] and Soria. ^[7]

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 communites 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 in 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.

• United States Congressional apportionment
• Apportionment in the European Parliament.
• Rotten borough
• Gerrymandering
• History of 19th Century Congressional Apportionment In Ohio

• P.A. Madison's excellent historical review of the 14th amendment's apportionment clause.
• Reapportionment and Redistricting in the US an article from the ACE Project
• Index of articles relating to Boundary Delimitation from the ACE Project
• Explanation of the 1991 and 1992 US Supreme Court cases challenging the use of the method of equal proportions
• A guide to the various formulae for apportionment, and statistical differences between them
• The House of Representatives Apportionment Formula: An Analysis of Proposals for Change and Their Impact on States