Avec Éric Kamwa (Université des Antilles, LC2S)
The Chamberlin-Courant rule and the k-scoring rules: agreement and Condorcet Committee Efficiency
Co-auteurs : Mostapha Diss (GATE and UJM Saint-Etienne) - Abdelmonaim Tlidi (University of Marrakech, National School of Applied Science)
Résumé : For committee or multiwinner elections, the Chamberlin-Courant rule (CCR) which combines the Borda rule and the proportional representation, aims to pick the most representative committee (Chamberlin and Courant, 1983). Chamberlin and Courant (1983) have shown that given m>=3 candidates, if the size of the committee to be elected is k=1, the CCR is equivalent to the Borda rule; Kamwa and Merlin (2014) claimed that if k=m-1, the CCR is equivalent to the Plurality rule. In this paper, we explore what happen for 1<k<m-1 by computing the probability of agreement between the CCR and four k-scoring rules: the k-Plurality, the k-Borda, the k-Negative Plurality and the Bloc. Our results support the hypothesis that for committees of at least two members, the CCR rule leads in most cases to a committee recommended by the k-Plurality rule. As for the probability of electing the Condorcet committee when it exists, the RCC does less well than the k-Borda rule and the Bloc rule but better than the k-Plurality and the k-Negative Plurality rules. The Condorcet committee is a fixed size subset of candidates such that every member defeats every non-member in pairwise comparisons.