Apportionment methods

Niemeyer, Horst; Niemeyer, Alice C.

doi:10.1016/j.mathsocsci.2008.03.003

Cited by 18 publications

(25 citation statements)

References 7 publications

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“…Blondel 1969;Taagepera and Laakso 1980;Taagepera and Shugart 1989;Gallagher 1991;Pennisi 1998;Benoit 2000), or in terms of their formal properties (e.g. Loosemore and Hanby 1971;Balinski and Young 1982;Lijphart 1986;Ibaraki and Katoh 1988;Gallagher 1992;Schuster et al 2003;Grilli di Cortona et al 1999;Niemeyer and Niemeyer 2008). This paper takes the second approach.…”

Section: The D'hondt Methods Within a Mixture Generalizationmentioning

confidence: 99%

Rethinking the D'Hondt method

Medzihorský

2019

Political Research Exchange

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The D'Hondt method is the most popular proportional apportionment procedure, as well as one of the oldest. Despite this, the method is not fully understood, with serious normative and empirical implications for democratic representation. This paper provides insights into the D'Hondt method through a generalization that is based on a finite mixture model, extends to situations with missing data (e.g. imperfect records), and applies to allocation problems outside of elections. The generalization disproves several widely accepted beliefs, clarifying that the method maximizes the fraction of exactly proportionally represented votes, and providing intuitive measures of overall and party-level disproportionality. The crucial insights of this interpretation are easily communicated in natural language without any mathematical formalisms, which makes it particularly useful for lay audiences and civic education. I illustrate these features with the 1999-2014 British European Parliament elections.

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Section: The D'hondt Methods Within a Mixture Generalizationmentioning

confidence: 99%

Rethinking the D'Hondt method

Medzihorský

2019

Political Research Exchange

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“…[1], [18] and [20]. Theorems 3.7 and 3.16 yield by the continuous mapping theorem asymptotic distributions for many such functionals for the methods treated here, under our standard assumptions that p 1 , .…”

Section: Some Other Goodness-of-fit Functionalsmentioning

confidence: 99%

Asymptotic bias of some election methods

Janson

2012

Ann Oper Res

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Abstract. Consider an election where N seats are distributed among parties with proportions p1, . . . , pm 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 N pi that yields exact proportionality. Our approach is to keep p1, . . . , pm 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.

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“…Some other goodness-of-fit functionals Many election methods, including the ones treated here, can be characterised as minimising various functionals, see e.g. [1], [18] and [20]. Theorems 3.7 and 3.16 yield by the continuous mapping theorem asymptotic distributions for many such functionals for the methods treated here, under our standard assumptions that p 1 , .…”

Section: The Sainte-laguë Divergencementioning

confidence: 99%

Asymptotic bias of some election methods

Janson¹

2011

Preprint

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Consider an election where N seats are distributed among parties with proportions p1, . . . , pm 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 N pi that yields exact proportionality. Our approach is to keep p1, . . . , pm 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.

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Apportionment methods

Cited by 18 publications

References 7 publications

Rethinking the D'Hondt method

Rethinking the D'Hondt method

Asymptotic bias of some election methods

Asymptotic bias of some election methods

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