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Fair Proportional Representation Problems with Mixture Operators

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Hugo Gilbert
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Abstract

This paper deals with proportional representation problems in which a set of winning candidates must be selected according to the ballots of the voters. We investigate the use of a new class of optimization criteria to determine the set of winning candidates, namely mixture operators. In a nutshell, mixture operators are similar to weighted means where the numerical weights are replaced by weighting functions. In this paper: (1) we give the mathematical condition for which a mixture operator is fair and provide several instances of this operator satisfying this condition; (2) we show that when using a mixture operator as optimization criterion, one recovers the same complexity results as in the utilitarian case (i.e., maximizing the sum of agent's utilities) under a light condition ; (3) we present solution methods to find an optimal set of winners w.r.t. a mixture operator under both Monroe and Chamberlin-Courant multi-winner voting rules and test their computational efficiency.
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Dates and versions

hal-01560630 , version 1 (11-07-2017)

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  • HAL Id : hal-01560630 , version 1

Cite

Hugo Gilbert. Fair Proportional Representation Problems with Mixture Operators. 5th International Conference on Algorithmic Decision Theory (ADT 2017), Oct 2017, Luxembourg, Luxembourg. ⟨hal-01560630⟩
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