MoL-2011-08: Information and Representation in Computational Social Choice

MoL-2011-08: Frank, Ilan (2011) Information and Representation in Computational Social Choice. [Report]

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Voting rules are functions aggregating the preferences of voters regarding a set of alternatives, and the theoretical properties of these objects are investigated in voting theory, as well as in computational social choice, where we study their computational aspects. The question of how much information such rules actually need in order to compute their result has been studied from various angles in recent years, via concepts such as the communication complexity (Conitzer and Sandholm), compilation complexity (Chevaleyre et al.), and informational size (Sato). We review these concepts and analyze the relations between them. That will lead us to a discussion about representation of information: We describe different representations for different voting rules and construct a hierarchy of those representations. We then discuss generalized scoring rules (introduced by Xia and Conitzer), and show how they relate to our previous discussion. Finally, we build a correspondence between one representation for voting rules and subgroups of the symmetric group, thus showing a connection between group theory and informational representations in voting theory. We use that correspondence to prove a theorem posed by Sato in his paper on informational size.

Item Type: Report
Report Nr: MoL-2011-08
Series Name: Master of Logic Thesis (MoL) Series
Year: 2011
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38

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