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The Droop quota is the quota most commonly used in elections held under the single transferable vote (STV) system. It is also sometimes used in elections held under the largest remainder method of party-list proportional representation (list PR). Any candidate that receives quota is declared elected. Under some STV systems, especially those of the full-preferential voting variant, often all the winners receive the quota, but in others, of the optional-preferential voting or semi-optional preferential voting variants, if is common for as many as three winners in a district to be elected with less than quota. Besides establishing winners, quota is useful to set the number of votes that are surplus and thus eligible for transfer to another candidate. Transfers can be conducted in various ways (see Counting single transferable votes). The Droop quota was devised in 1868 by the English lawyer and mathematician Henry Richmond Droop (1831–1884) as a replacement for the earlier Hare quota. Today the Droop quota is used in almost all STV elections, including the forms of STV used in India, the Republic of Ireland, Northern Ireland, Malta and Australia, among other places. It is also used to allocate seats via the largest remainder model in South Africa. The Droop quota is very similar to the simpler Hagenbach-Bischoff quota, which is also sometimes loosely referred to as the 'Droop quota'. Sources differ as to the exact formula for the Droop quota. As used in the Republic of Ireland the formula is usually written: but more precisely or where: = Total number of valid (unspoiled) votes cast in an election. = total number of seats to be filled in the election. refers to the floor or integer portion of the number, sometimes written as (The extra parentheses, while not strictly necessary from a mathematical standpoint, are often included in order to make the formula seem less ambiguous to non-mathematicians—if calculated out of sequence, an incorrect result would be arrived at, producing an incorrect quota.

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Hare quota

The 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.

Instant-runoff voting

Instant-runoff voting (IRV) is an electoral system that uses ranked voting. Its purpose is to elect the majority choice in single-member districts in which there are more than two candidates and thus help ensure majority rule. It is a single-winner version of single transferable voting. Formerly the term "instant-runoff voting" was used for what many people now call contingent voting or supplementary vote.

Electoral system

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.

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