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

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

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

Voting systems that combine approval and preference

Abstract Information on the rankings and information on the approval of candidates in an election, though related, are fundamentally different-one cannot be derived from the other. Both kinds of information are important in the determination of social choices. We propose a way of combining them in two hybrid voting systems, preference approval voting (PAV) and fallback voting (FV), that satisfy several desirable properties, including monotonicity. Both systems may give different winners from standard ranking and nonranking voting systems. PAV, especially, encourages candidates to take coherent majoritarian positions, but it is more information-demanding than FV. PAV and FV are manipulable through voters' contracting or expanding their approval sets, but a 3-candidate dynamic poll model suggests that Condorcet winners, and candidates ranked first or second by the most voters if there is no Condorcet winner, will be favored, though not necessarily in equilibrium