Editing Droop quota (section)

{{Short description|Quantity of votes in election studies}}
{{Electoral systems}}
In the study of [[Electoral system|electoral systems]], the '''Droop quota''' (sometimes called the [[Eduard Hagenbach-Bischoff|'''Hagenbach-Bischoff''']], '''Britton''', or '''Newland-Britton quota'''<ref name="mw-2007">{{Cite journal |last1=Lundell |first1=Jonathan |last2=Hill |first2=ID |title=Notes on the Droop quota |url=http://www.mcdougall.org.uk/voting-matters/ISSUE24/ISSUE24.pdf#page=7 |journal=Voting Matters |publication-date=October 2007 |issue=24 |pages=3–6}}</ref>{{efn|name="exact"|Some authors use the terms "Newland-Britton quota" or "exact Droop quota" to refer to the quantity described in this article, and reserve the term "Droop quota" for the archaic or rounded form of the Droop quota (the original found in the works of Henry Droop).<ref name="pukelsheim-2017-quota">{{cite book |doi=10.1007/978-3-319-64707-4_5 |chapter=Quota Methods of Apportionment: Divide and Rank |title=Proportional Representation |date=2017 |last1=Pukelsheim |first1=Friedrich |pages=95–105 |isbn=978-3-319-64706-7 }}</ref>}}) is the [[Infimum|minimum]] number of votes a party or candidate needs to receive in a district to guarantee they will win at least one seat.<ref>{{Citation |title=Droop Quota |date=2011 |encyclopedia=The Encyclopedia of Political Science |url=http://dx.doi.org/10.4135/9781608712434.n455 |access-date=2024-05-03 |place=2300 N Street, NW, Suite 800, Washington DC 20037 United States |publisher=CQ Press|doi=10.4135/9781608712434.n455 |isbn=978-1-933116-44-0 |url-access=subscription }}</ref><ref name="droop-1881">{{cite journal |last=Droop |first=Henry Richmond |year=1881 |title=On methods of electing representatives |url=http://www.votingmatters.org.uk/ISSUE24/I24P3.pdf |journal=[[Journal of the Statistical Society of London]] |volume=44 |issue=2 |pages=141–196 [Discussion, 197–202] [33 (176)] |doi=10.2307/2339223 |jstor=2339223}} Reprinted in ''[[Voting matters]] Issue 24'' (October 2007) pp.&nbsp;7–46.</ref>

The Droop quota is used to extend the concept of a [[majority]] to [[multiwinner elections]], taking the place of the 50% bar in single-winner elections. Just as any candidate with more than half of all votes is guaranteed to be declared the winner in single-seat election, any candidate with more than a Droop quota's worth of votes is guaranteed to win a seat in a [[Multiwinner voting|multiwinner election]].<ref name="droop-1881"></ref>

Besides establishing winners, the Droop quota is used to define the number of [[excess vote]]s, i.e. votes not needed by a candidate who has been declared elected. In proportional [[electoral quota|quota]]-based systems such as [[Single transferable vote|STV]] or [[expanding approvals rule|expanding approvals]], these excess votes can be transferred to other candidates to prevent them from [[Wasted vote|being wasted]].<ref name="droop-1881"></ref>

The Droop quota was first suggested by the English lawyer and mathematician [[Henry Richmond Droop]] (1831–1884) as an alternative to the [[Hare quota]].<ref name="droop-1881"></ref>

Today, the Droop quota is used in almost all STV elections, including those in [[Australia]],<ref>{{Cite web |title=Proportional Representation Voting Systems of Australia's Parliaments |url=https://www.ecanz.gov.au/electoral-systems/proportional |url-status=live |archive-url=https://web.archive.org/web/20240706104711/https://www.ecanz.gov.au/electoral-systems/proportional |archive-date=6 July 2024 |website=Electoral Council of Australia & New Zealand}}</ref> the [[Republic of Ireland]], [[Northern Ireland]], and [[Malta]].<ref>{{Cite web|url=https://electoral.gov.mt/ElectionResults/General|title=Electoral Commission of Malta|website=electoral.gov.mt|accessdate=2025-01-20}}</ref> It is also used in [[South Africa]] to allocate seats by the [[largest remainder method]].<ref>{{Cite book |last=Pukelsheim |first=Friedrich |url=http://archive.org/details/proportionalrepr0000puke |title=Proportional representation : apportionment methods and their applications |date=2014 |publisher=Cham ; New York : Springer |others=Internet Archive |isbn=978-3-319-03855-1}}</ref><ref>{{Cite web |title=IFES Election Guide {{!}} Elections: South African National Assembly 2014 General |url=https://www.electionguide.org/elections/id/2721/ |access-date=2024-06-02 |website=www.electionguide.org}}</ref>

Although common, the quota's use in [[proportional representation]] has been criticized both for its bias toward large parties<ref name="pukelsheim-2017-bias" /> and for its ability to create [[no-show paradox|no-show paradoxes]], situations where a candidate or party loses a seat as a result of having won too ''many'' votes. This occurs regardless of whether the quota is used with [[Largest remainders method|largest remainders]]<ref>{{Cite journal |last=Dančišin |first=Vladimír |date=2017-01-01 |title=No-show paradox in Slovak party-list proportional system |url=https://www.degruyter.com/document/doi/10.1515/humaff-2017-0002/html |journal=Human Affairs |language=en |volume=27 |issue=1 |pages=15–21 |doi=10.1515/humaff-2017-0002 |issn=1337-401X|url-access=subscription }}</ref> or [[single transferable vote|STV]].<ref>{{Cite journal |last=Ray |first=Dipankar |date=1983-07-01 |title=Hare's voting scheme and negative responsiveness |url=https://www.sciencedirect.com/science/article/abs/pii/016548968390032X |journal=Mathematical Social Sciences |volume=4 |issue=3 |pages=301–303 |doi=10.1016/0165-4896(83)90032-X |issn=0165-4896|url-access=subscription }}</ref>