Power set extensions of dichotomous preferences

Ritxar Arlegi; Dinko Dimitrov: Dichotomous Preferences and Power Set Extensions

This paper is devoted to the study of how to extend a dichotomous partition of a universal set X into good and bad objects to an ordering on the power set of X. We introduce a family of rules that naturally take into account the number of good objects and the number of bad objects, and provide axiomatic characterizations of two rules for ranking sets in such a context. JEL Classi…cation Number:...

Structure in Dichotomous Preferences

Many hard computational social choice problems are known to become tractable when voters’ preferences belong to a restricted domain, such as those of singlepeaked or single-crossing preferences. However, to date, all algorithmic results of this type have been obtained for the setting where each voter’s preference list is a total order of candidates. The goal of this paper is to extend this line...

Weak Compactness of the Set of ε-Extensions

Approval Voting on Dichotomous Preferences

The aim of this paper is to find normative foundations of Approval Voting.In order to show that Approval Voting is the only social choice functionthat satisfies anonymity, neutrality, strategy-proofness and strict mono-tonicity we rely on an intermediate result which relates strategy-proofnessof a social choice function to the properties of Independence of IrrelevantAlte...

Collective choice under dichotomous preferences

Agents partition deterministic outcomes into good or bad. A direct revelation mechanism selects a lottery over outcomes — also interpreted as time-shares. Under such dichotomous preferences, the probability that the lottery outcome be a good one is a canonical utility representation. The utilitarian mechanism averages over all deterministic outcomes “approved” by the largest number of agents. I...