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An impossibility theorem for fair bidimensional representation: Towards a biproportional solution

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  • Marjorie Gassner

Abstract

This paper concerns fair (proportional) representation of a population which is divided into categories according to two criteria as is the case, for example, when an electoral system takes into account the geographical as well as the political group of the elector. Our first model leads us to the conclusion that, on the one hand, there can be no fair representation — under our very weak conditions — as soon there are more than two constituencies or more than two parties, but on the other hand, a two by two situation can always be fairly represented. As these results are mainly negative, we go on to a second model and we give a necessary and sufficient condition for the existence of a biproportional delegation.

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  • Marjorie Gassner, 1989. "An impossibility theorem for fair bidimensional representation: Towards a biproportional solution," ULB Institutional Repository 2013/232154, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/232154
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    Cited by:

    1. Oelbermann, Kai-Friederike, 2016. "Alternate Scaling algorithm for biproportional divisor methods," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 25-32.
    2. Marjorie B. Gassner, 1991. "Biproportional Delegations," Journal of Theoretical Politics, , vol. 3(3), pages 321-342, July.
    3. Federica Ricca & Andrea Scozzari & Paolo Serafini & Bruno Simeone, 2012. "Error minimization methods in biproportional apportionment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 547-577, October.

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