Editing Quota method (section)

[[Category:Party-list proportional representation]]
[[Category:Apportionment methods]]
{{Short description|Proportional-representation voting system}}
{{more citations needed|date=November 2011}} {{Electoral systems}}

The '''quota''' or '''divide-and-rank methods''' make up a category of [[Apportionment (politics)|apportionment rules]], i.e. algorithms for allocating seats in a legislative body among multiple groups (e.g. [[Political party|parties]] or [[Federal state|federal states]]). The quota methods begin by calculating an [[Entitlement (fair division)|entitlement]] (basic number of seats) for each party, by dividing their vote totals by an [[electoral quota]] (a fixed number of votes needed to win a seat, as a unit). Then, leftover seats, if any are allocated by rounding up the apportionment for some parties. These rules are typically contrasted with the more popular [[Highest averages method|highest averages methods]] (also called divisor methods).<ref name=":12">{{Citation |last=Pukelsheim |first=Friedrich |title=Quota Methods of Apportionment: Divide and Rank |date=2017 |work=Proportional Representation: Apportionment Methods and Their Applications |pages=95–105 |editor-last=Pukelsheim |editor-first=Friedrich |url=https://doi.org/10.1007/978-3-319-64707-4_5 |access-date=2024-05-10 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-64707-4_5 |isbn=978-3-319-64707-4}}</ref>

By far the most common quota method are the '''largest remainders''' or '''quota-shift methods''', which assign any leftover seats to the "plurality" winners (the parties with the largest [[Remainder|remainders]], i.e. most leftover votes).<ref name=":02">{{cite book |last=Tannenbaum |first=Peter |url=http://www.mypearsonstore.com/bookstore/product.asp?isbn=9780321568038 |title=Excursions in Modern Mathematics |publisher=Prentice Hall |year=2010 |isbn=978-0-321-56803-8 |location=New York |pages=128}}</ref> 

When using the [[Hare quota]], this rule is called '''[[Alexander Hamilton|Hamilton]]'s method''', and is the third-most common apportionment rule worldwide (after [[Jefferson's method]] and [[Webster's method]]).<ref name=":12" />

Despite their intuitive definition, quota methods are generally disfavored by [[Social choice theory|social choice theorists]] as a result of [[Apportionment paradox|apportionment paradoxes]].<ref name=":12" /><ref name=":52">{{Citation |last=Pukelsheim |first=Friedrich |title=Securing System Consistency: Coherence and Paradoxes |date=2017 |work=Proportional Representation: Apportionment Methods and Their Applications |pages=159–183 |editor-last=Pukelsheim |editor-first=Friedrich |url=https://doi.org/10.1007/978-3-319-64707-4_9 |access-date=2024-05-10 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-64707-4_9 |isbn=978-3-319-64707-4}}</ref> In particular, the largest remainder methods exhibit the [[Participation criterion|no-show paradox]], i.e. voting ''for'' a party can cause it to ''lose'' seats.<ref name=":52" /><ref name=":02222">{{cite book |last1=Balinski |first1=Michel L. |url=https://archive.org/details/fairrepresentati00bali |title=Fair Representation: Meeting the Ideal of One Man, One Vote |last2=Young |first2=H. Peyton |publisher=Yale University Press |year=1982 |isbn=0-300-02724-9 |location=New Haven |url-access=registration}}</ref> The largest remainders methods are also vulnerable to [[Spoiler effect|spoiler effects]] and can fail [[Resource monotonicity|resource]] or [[house monotonicity]], which says that increasing the number of seats in a legislature should not cause a party to lose a seat (a situation known as an [[Alabama paradox]]).<ref name=":52" /><ref name=":02222" />{{Rp|Cor.4.3.1}}