Apportionment (politics)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 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 voter's intentions equal weight.
Largest remainder methodThe largest remainder method (also known as Hare–Niemeyer method, Hamilton method or as Vinton's method) is one way of allocating seats proportionally for representative assemblies with party list voting systems. It contrasts with various highest averages methods (also known as divisor methods). The largest remainder method requires the numbers of votes for each party to be divided by a quota representing the number of votes required for a seat (i.e. usually the total number of votes cast divided by the number of seats, or some similar formula).
Hare quotaThe Hare quota (also known as the simple quota) is a formula used under some forms of proportional representation. In these voting systems the quota is the number of votes that guarantees a candidate, or a party in some cases, captures a seat. The Hare quota is the total number of votes divided by the number of seats to be filled. This is the simplest quota, but the Droop quota is mostly used currently. The Hare quota can be used in the single transferable vote (STV-Hare) system and the largest remainder method (LR-Hare) and other quota rule compatible methods of party-list proportional representation.
Quota ruleIn mathematics and political science, the quota rule describes a desired property of a proportional apportionment or election method. It states that the number of seats that should be allocated to a given party should be between the upper or lower roundings (called upper and lower quotas) of its fractional proportional share (called natural quota). As an example, if a party deserves 10.56 seats out of 15, the quota rule states that when the seats are allotted, the party may get 10 or 11 seats, but not lower or higher.
Electoral systemAn 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.
Imperiali quotaThe Imperiali quota is a formula used to calculate the minimum number, or quota, of votes required to capture a seat in some forms of single transferable vote or largest remainder method party-list proportional representation voting systems. It is distinct from the Imperiali method, a type of highest average method. It is named after Belgian senator Pierre Imperiali. The Czech Republic is the only country that currently uses this allocation system, while Italy and Ecuador used it in the past.
Apportionment paradoxAn apportionment paradox exists when the rules for apportionment in a political system produce results which are unexpected or seem to violate common sense. To apportion is to divide into parts according to some rule, the rule typically being one of proportion. Certain quantities, like milk, can be divided in any proportion whatsoever; others, such as horses, cannot—only whole numbers will do. In the latter case, there is an inherent tension between the desire to obey the rule of proportion as closely as possible and the constraint restricting the size of each portion to discrete values.
D'Hondt methodThe 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 method was first described in 1792 by future U.S. president Thomas Jefferson. It was re-invented independently in 1878 by Belgian mathematician Victor D'Hondt, which is the reason for its two different names.
Coherence (fairness)Coherence, also called uniformity or consistency, is a criterion for evaluating rules for fair division. Coherence requires that the outcome of a fairness rule is fair not only for the overall problem, but also for each sub-problem. Every part of a fair division should be fair. The coherence requirement was first studied in the context of apportionment. In this context, failure to satisfy coherence is called the new states paradox: when a new state enters the union, and the house size is enlarged to accommodate the number of seats allocated to this new state, some other unrelated states are affected.
Electoral thresholdThe electoral threshold, or election threshold, is the minimum share of all the votes cast that a candidate or political party requires to achieve before they become entitled to representation or additional seats in a legislature. This limit can operate in various ways, e.g. in party-list proportional representation systems where an electoral threshold requires that a party must receive a specified minimum percentage of votes (e.g. 5%), either nationally or in a particular electoral district, to obtain seats in the legislature.
