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The quota methods are a family of apportionment rules, i.e. algorithms for distributing the seats in a legislative body among a number of administrative divisions. The quota methods are based on calculating a fixed electoral quota, i.e. a given number of votes needed to win a seat. These rules are typically contrasted with the more popular highest averages methods (also called divisor methods).[1] This is used to calculate each party's seat entitlement. Every party is assigned the integer portion of this entitlement, and any seats left over are distributed according to a specified rule.
By far the most common quota method is the largest remainders or quota-shift method, which assigns any leftover seats to the "plurality" winners (those parties with the largest remainders, i.e. most leftover votes).[2] When using the Hare quota, the method 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, by increasing the size of the electoral quota.[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 state 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.