Anonymous, neutral, and resolute social choice revisited

We revisit the incompatibility of anonymity and neutrality in singleton-valued social choice. We first analyze the irresoluteness structure these two axioms together with Pareto efficiency impose on social choice rules and deliver a method to refine irresolute rules without violating anonymity, neutrality, and efficiency. Next, we propose a weakening of neutrality called consequential neutrality that requires resolute social choice rules to assign each alternative to the same number of profiles. We explore social choice problems in which consequential neutrality resolves impossibilities that stem from the fundamental tension between anonymity, neutrality, and resoluteness.Series: Department of Strategy and Innovation Working Paper Serie

On Domains That Admit Well-behaved Strategy-proof Social Choice Functions

In this paper, we investigate domains which admit "well-behaved", strategy-proof social choice functions. We show that if the number of voters is even, then every domain that satisfies a richness condition and admits an anonymous, tops-only, unanimous and strategy-proof social choice function, must be semi-single-peaked. Conversely every semi-single-peaked domain admits an anonymous, tops-only, unanimous and strategy-proof social choice function. Semi-single-peaked domains are generalizations of single-peaked domains on a tree introduced by Demange (1982). We provide sharper versions of the results above when tops-onlyness is replaced by tops-selectivity and the richness condition is weakened.Voting-rules, Strategy-proofness, Restricted Domains, Tops-Only domains.

Ensuring Pareto Optimality by Referendum Voting

Abstract We consider a society confronting the decision of accepting or rejecting a list of (at least two) proposals. Assuming separability of preferences, we show the impossibility of guaranteeing Pareto optimal outcomes through anonymous referendum voting, except for the case of an odd number of voters confronting precisely two proposals. In this special case, majority voting is the only anonymous social choice rule which guarantees Pareto optimal referendum outcomes

Hyper-Stable Social Welfare Functions

We introduce a new consistency condition for neutral social welfare functions, called hyperstability. A social welfare function a selects a complete weak order from a profile PN of linear orders over any finite set of alternatives, given N individuals. Each linear order P in PN generates a linear order over orders of alternatives,called hyper-preference, by means of a preference extension. Hence each profile PN generates a hyper-profile ˙PN. We assume that all preference extensions are separable: the hyper-preference of some order P ranks order Q above order Q0 if the set of alternative pairs P and Q agree on contains the one P and Q0 agree on. A special sub-class of separable extensions contains all Kemeny extensions, which build hyper-preferences by using the Kemeny distance criterion. A social welfare function a is hyper-stable (resp. Kemeny-stable) if at any profile PN, at least one linearization of a(PN) is ranked first by a( ˙PN), where ˙PN is any separable (resp. Kemeny) hyper-profile induced from PN. We show that no scoring rule is hyper-stable, and that no unanimous scoring rule is Kemeny-stable, while there exists a hyper-stable Condorcet social welfare function

A characterization of the Copeland solution

Abstract We provide a new characterization of the Copeland solution, based on the number of steps in which candidates beat each other. A Condorcet winner is a candidate which beats every other contender in one step. In other words, given m candidates, a Condorcet winner beats all remaining contenders in a total of m 1 steps. When choosing from a tournament, there is universal agreement on the Condorcet principle which requires to pick the Condorcet winner, whenever it exists. As a Condorcet winner may fail to exist, the Condorcet principle can be extended to what we call the minisum principle: Choose the candidate(s) who beat all remaining contenders in the smallest total number of steps. We show that the minisum principle characterizes the Copeland solution

Positively responsive collection choice rules and majority rule: a generalization of May's theorem to many alternatives

A collective choice rule selects a set of alternatives for each collective choice problem. Suppose that the alternative ’x’, is in the set selected by a collective choice rule for some collective choice problem. Now suppose that ‘x’ rises above another selected alternative ‘y’ in some individual’s preferences. If the collective choice rule is “positively responsive”, ‘x’ remains selected but ‘y’ is no longer selected. If the set of alternatives contains two members, an anonymous and neutral collective choice rule is positively responsive if and only if it is majority rule (May 1952). If the set of alternatives contains three or more members, a large set of collective choice rules satisfy these three conditions. We show, however, that in this case only the rule that assigns to every problem its strict Condorcet winner satisfies the three conditions plus Nash’s version of “independence of irrelevant alternatives” for the domain of problems that have strict Condorcet winners. Further, no rule satisfies the four conditions for the domain of all preference relations

On Domains that Admit Well-Behaved Strategy-Proof Social Choice Functions

Published in Journal of Economic Theory, 2013, https://doi.org/10.1016/j.jet.2012.10.005</p