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Highest averages method
| A joint Politics and Economics series |
| Social choice and electoral systems |
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 Mathematics portal |
The highest averages, divisor, or divide-and-round methods[1] are a family of apportionment algorithms that aim to fairly divide a legislature between several groups, such as political parties or states.[1][2] More generally, divisor methods can be used to round shares of a total, e.g. percentage points (which must add up to 100).[2]
The methods aim to treat voters equally by ensuring legislators represent an equal number of voters by ensuring every party has the same seats-to-votes ratio (or divisor).[3]: 30 Such methods divide the number of votes, by the number of votes-per-seat, then round the total to get the final apportionment. In doing so, the method approximately maintains proportional representation, so that a party with e.g. twice as many votes as another should win twice as many seats.[3]: 30
The divisor methods are generally preferred by social choice theorists to the largest remainder methods, as they produce more-proportional results by most metrics and are less susceptible to apportionment paradoxes.[4][5][6] In particular, divisor methods satisfy vote-ratio monotonicity and participation, i.e. voting for a party can never cause it to lose seats, unlike in the largest remainders methods; in addition, they are not sensitive to spoiler effects.[5]
- ^ a b Pukelsheim, Friedrich (2017), Pukelsheim, Friedrich (ed.), "Divisor Methods of Apportionment: Divide and Round", Proportional Representation: Apportionment Methods and Their Applications, Cham: Springer International Publishing, pp. 71–93, doi:10.1007/978-3-319-64707-4_4, ISBN 978-3-319-64707-4, retrieved 2021-09-01
- ^ a b Pukelsheim, Friedrich (2017), "From Reals to Integers: Rounding Functions, Rounding Rules", Proportional Representation: Apportionment Methods and Their Applications, Springer International Publishing, pp. 71–93, doi:10.1007/978-3-319-64707-4_4, ISBN 978-3-319-64707-4, retrieved 2021-09-01
- ^ 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.
- ^ 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
- ^ a b 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
- ^ 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.
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