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The quota or divide-and-rank methods are a family of apportionment rules, i.e. algorithms for distributing seats in a legislative body between several groups (e.g. parties or federal states). The quota methods begin by calculating an entitlement (ideal 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). Then, leftover seats are distributed by rounding up the apportionment for some parties. These rules are typically contrasted with the more popular highest averages methods (also called divisor methods).[1]
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 remainders, i.e. most leftover votes).[2] When using the Hare quota, this rule is called Hamilton's method, and is the third-most common apportionment rule worldwide (after Jefferson's method and Webster's method).[1]
Despite their intuitive definition, quota methods are generally disfavored by social choice theorists as a result of apportionment paradoxes.[1][3] In particular, the largest remainder methods exhibit the no-show paradox, i.e. voting for a party can cause it to lose seats.[3][4] The largest remainders methods are also vulnerable to spoiler effects and can fail 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).[3][4]: Cor.4.3.1
- ^ a b c Pukelsheim, Friedrich (2017), Pukelsheim, Friedrich (ed.), "Quota Methods of Apportionment: Divide and Rank", Proportional Representation: Apportionment Methods and Their Applications, Cham: Springer International Publishing, pp. 95–105, doi:10.1007/978-3-319-64707-4_5, ISBN 978-3-319-64707-4, retrieved 2024-05-10
- ^ Tannenbaum, Peter (2010). Excursions in Modern Mathematics. New York: Prentice Hall. p. 128. ISBN 978-0-321-56803-8.
- ^ a b c Pukelsheim, Friedrich (2017), Pukelsheim, Friedrich (ed.), "Securing System Consistency: Coherence and Paradoxes", Proportional Representation: Apportionment Methods and Their Applications, Cham: Springer International Publishing, pp. 159–183, doi:10.1007/978-3-319-64707-4_9, ISBN 978-3-319-64707-4, retrieved 2024-05-10
- ^ a b Balinski, Michel L.; Young, H. Peyton (1982). Fair Representation: Meeting the Ideal of One Man, One Vote. New Haven: Yale University Press. ISBN 0-300-02724-9.