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Droop quota: Difference between revisions
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== Droop quota ==
{{wikipedia|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:
<math >\left( \frac{\text{total valid poll}}{ \text{seats}+1 } \right) + 1</math>
but more precisely
<math >\operatorname{Integer} \left( \frac{\text{total valid poll}}{ \text{seats}+1 } \right) + 1</math>
where:
* <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.
When there are 5 seats to be filled and 100 votes cast, the Droop quota is '''17''' votes, which is calculated as: Integer((100/(5+1)) + 1) = Integer((100/6) + 1) = Integer(~16.667 + 1) = Integer(~17.667) = '''17''' votes.
In the single-winner case, a Droop quota is a majority. In general, Droop quota-based methods tend to leave at least just under a Droop quota unrepresented. See the [[utility]] article, as the debate between Hare and Droop quotas somewhat parallels and generalizes the [[utilitarianism]] vs. [[majority rule]] debate.
=== English Wikipedia description of Droop ===
Below is a description copied from [[English Wikipedia]] describing the Droop quota:<ref>The December 5, 2020 version of [[wikipedia:Droop quota]]: https://en.wikipedia.org/w/index.php?title=Droop_quota&oldid=992460095</ref>
<blockquote>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'.
</blockquote>
The article above may have changed since this writing in December 2020. See [[wikipedia:Droop quota]] for the latest version.
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