Vote par approbation pour les élections à vainqueurs multiples. Une famille générale de règles, leur complexité algorithmique et leur manipulabilité

Abstract : Approval voting is a well-known voting procedure used, among others, for electing committees, where each voter casts a ballot consisting of a set of approved candidates (without any cardinality constraint). Two prominent rules for electing committees using approval voting are the standard rule (also called minisum), which selects the set of candidates (possibly subject to some cardinality constraint) with the highest number of approvals, and the minimax rule, where the set of elected candidates minimizes the maximum, over all voters, of the Hamming distance to the voter’s ballot. As these two rules are in some way too extreme, we generalize them into a continuum of rules, by using ordered weighted averaging operators (OWA). The rule is parameterized by a weight vector w, which allows us to model voting procedures between minisum and minimax. We focus on non decreasing weight vectors, and in particular, vectors of the form w(i) = (0; ::; 0; 1; ::; 1), where i is the number of 0’s. We address the computational aspects of finding a winning committee and all the winning committees for rules associated with the w(i) vectors. We show that finding a winning committee for these rules is NP-hard whereas it is computationally easy for minisum. Finally, we address the issue of manipulating the rules when parameterized by non decreasing and strictly increasing weight vectors.
Document type :
Journal articles
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01493014
Contributor : Christine Okret-Manville <>
Submitted on : Monday, March 20, 2017 - 6:03:48 PM
Last modification on : Thursday, February 13, 2020 - 2:02:12 PM

Identifiers

Citation

Nathanaël Barrot, Jérôme Lang, Bernard Ries. Vote par approbation pour les élections à vainqueurs multiples. Une famille générale de règles, leur complexité algorithmique et leur manipulabilité. Revue d'intelligence artificielle, 2015, 29 (3-4), ⟨10.3166/RIA.29.265-291⟩. ⟨hal-01493014⟩

Share

Metrics

Record views

154