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Fair Proportional Representation Problems with Mixture Operators

Hugo Gilbert 1
1 DECISION
LIP6 - Laboratoire d'Informatique de Paris 6
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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Submitted on : Tuesday, July 11, 2017 - 5:12:02 PM
Last modification on : Friday, January 8, 2021 - 5:32:07 PM
Long-term archiving on: : Wednesday, January 24, 2018 - 11:27:18 PM

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  • HAL Id : hal-01560630, version 1
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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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