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Reapportionment

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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 to 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've 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 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 although 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.

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