Bounded single-peaked width and proportional representation
Cornaz, Denis; Galand, Lucie; Spanjaard, Olivier (2012), Bounded single-peaked width and proportional representation, COMSOC 2012, 2012-09, Cracovie, Poland
TypeCommunication / Conférence
Conference titleCOMSOC 2012
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Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)This paper is devoted to the proportional representation (PR) problem when the preferences are clustered single-peaked. PR is a “multi-winner” election problem, that we study in Chamberlin and Courant’s scheme . We deﬁne clustered single-peakedness as a form of single-peakedness with respect to clusters of candidates, i.e. subsets of candidates that are consecutive (in arbitrary order) in the preferences of all voters. We show that the PR problem becomes polynomial when the size of the largest cluster of candidates (width) is bounded. Furthermore, we establish the polynomiality of determining the single-peaked width of a preference proﬁle (minimum width for a partition of candidates into clusters compatible with clustered single-peakedness) when the preferences are narcissistic (i.e., every candidate is the most preferred one for some voter).
Subjects / Keywordssingle-peaked; proportional representation; election problem; multi-winner
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