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Removed "Hagenbach-Bischoff quota" section, since it has been copied to the Droop quota article

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Line 1: A quota is a number of votes (obtained by formula) often relevant to deciding who wins and how ballots are evaluated or modified in "[[proportional representation]]" voting methods]]. ==The two main quotas that will be described here are the "[[W:Hare quota\|]]" ~~Hare~~and the "[[Droop quota]]==". ~~The Hare quota may be given as:~~ == Hare quota == ~~:<math>\frac{\mbox{total} \; \mbox{votes}}{\mbox{total} \; \mbox{seats}}</math>~~ {{main\|Hare quota}} The "Hare quota" (also known as the "simple quota") is a formula used under some forms of the [[Single Transferable Vote]] (STV) system and the [[largest remainder method]] of [[party-list proportional representation]]. In these [[voting system]]s the quota is the minimum number of votes required for a party or candidate to capture a seat, and the Hare quota is the total number of votes divided by the number of seats. ~~Where:~~ The Hare quota is the simplest quota that can be used in elections held under the STV system. In an STV election a candidate who reaches the quota is elected while any votes a candidate receives above the quota are transferred to another candidate. <math>\text{total votes}</math> = the total valid poll; that is, the number of valid (unspoiled) votes cast in an election. <math>\text{total seats}</math> = the total number of seats to be filled in the election. The Hare quota was devised by [[Thomas Hare]], one of the earliest supporters of STV. In 1868, [[Henry Richmond Droop]] (1831–1884) invented the [[Droop quota]] as an alternative to the Hare quota, and Droop is now widely used, the Hare quota today being rarely used with STV. ==[[W: Droop quota \| 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:~~ ▲==~~[[W:~~ Droop quota ~~\| Droop quota]]~~== ~~<math >\left( \frac{\text{total valid poll}}{ \text{seats}+1 } \right) + 1</math>~~ {{main\|Droop quota}} 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). In an STV election the quota is the minimum number of votes a candidate must receive in order to be elected. Any votes a candidate receives above the quota are transferred to another candidate. 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. The Droop quota is very similar to the simpler "[[Hagenbach-Bischoff quota]]", which is also sometimes loosely referred to as the 'Droop quota'. ~~but more precisely~~ == References == ~~<math >\operatorname{Integer} \left( \frac{\text{total valid poll}}{ \text{seats}+1 } \right) + 1</math>~~ <references/> [[Category:Proportionality-related concepts]] ~~where:~~ [[Category:Quotas\|]] <math>\text{total valid poll}</math> = Total number of valid (unspoiled) votes cast in an election. * <math>\text{seats}</math> = total number of seats to be filled in the election. * <math>\operatorname{Integer}()</math> refers to the integer portion of the number, sometimes written as <math>\operatorname{floor}()</math> One reason Droop quotas are used more often than Hare Quotas for ranked [[Proportional representation\|PR]] methods is because not only do they often help reduce the amount of vote-counting necessary, but they almost entirely eliminate the possibility of a majority of voters receiving a minority of seats compared to Hare Quotas. The Droop Quota is the smallest possible quota that guarantees that there will be as many quotas as there are winners desired. ~~== Hagenbach-Bischoff Quota ==~~ The Hagenbach-Bischoff Quota (known by a few other names as well) is unambiguously (total valid poll/seats + 1) or Integer(total valid poll/seats + 1). Some sources call the HB Quota a Droop Quota instead, though nobody considers the definitions given for a Droop Quota above to be a HB Quota. It is possible to have more quotas than winners desired using the HB Quota, in which case it will usually be necessary to break at least one tie between various candidates to decide who should win.