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Asymptotic bias of some election methods

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  • Svante Janson

Abstract

Consider an election where N seats are distributed among parties with proportions p 1 ,…,p m of the votes. We study, for the common divisor and quota methods, the asymptotic distribution, and in particular the mean, of the seat excess of a party, i.e. the difference between the number of seats given to the party and the (real) number Np i that yields exact proportionality. Our approach is to keep p 1 ,…,p m fixed and let N→∞, with N random in a suitable way. In particular, we give formulas showing the bias favouring large or small parties for the different election methods. Copyright Springer Science+Business Media, LLC 2014

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  • Svante Janson, 2014. "Asymptotic bias of some election methods," Annals of Operations Research, Springer, vol. 215(1), pages 89-136, April.
    • Handle: RePEc:spr:annopr:v:215:y:2014:i:1:p:89-136:10.1007/s10479-012-1141-2
    DOI: 10.1007/s10479-012-1141-2
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    1. Udo Schwingenschlögl & Mathias Drton, 2004. "Seat allocation distributions and seat biases of stationary apportionment methods for proportional representation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(2), pages 191-202, September.
    2. Lothar Heinrich & Udo Schwingenschlögl, 2006. "Goodness-of-fit Criteria for the Adams and Jefferson Rounding Methods and their Limiting Laws," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(2), pages 191-207, October.
    3. Grimmett, Geoffrey R., 2012. "European apportionment via the Cambridge Compromise," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 68-73.
    4. Schwingenschlögl, Udo & Drton, Mathias, 2006. "Seat excess variances of apportionment methods for proportional representation," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1723-1730, October.
    5. Niemeyer, Horst F. & Niemeyer, Alice C., 2008. "Apportionment methods," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 240-253, September.
    6. Gaffke, Norbert & Pukelsheim, Friedrich, 2008. "Divisor methods for proportional representation systems: An optimization approach to vector and matrix apportionment problems," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 166-184, September.
    7. Mathias Drton & Udo Schwingenschlögl, 2005. "Asymptotic seat bias formulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(1), pages 23-31, September.
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    Cited by:

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    2. David F. Muñoz & Héctor Gardida & Hugo Velázquez & Jorge D. Ayala, 2022. "Simulation models to support the preliminary electoral results program for the Mexican Electoral Institute," Annals of Operations Research, Springer, vol. 316(2), pages 1141-1156, September.
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    4. Jarosław Flis & Wojciech Słomczyński & Dariusz Stolicki, 2020. "Pot and ladle: a formula for estimating the distribution of seats under the Jefferson–D’Hondt method," Public Choice, Springer, vol. 182(1), pages 201-227, January.

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