
Robust Voting under Uncertainty
Abstract
This paper proposes normative criteria for voting rules under uncertainty about individual preferences to characterize a weighted majority rule (WMR). The criteria stress the significance of responsiveness, i.e., the probability that the social outcome coincides with the realized individual preferences. A voting rule is said to be robust if, for any probability distribution of preferences, the responsiveness of at least one individual is greater than onehalf. This condition is equivalent to the seemingly stronger condition requiring that, for any probability distribution of preferences and any deterministic voting rule, the responsiveness of at least one individual is greater than that under the deterministic voting rule. Our main result establishes that a voting rule is robust if and only if it is a WMR without ties. This characterization of a WMR avoiding the worst possible outcomes provides a new complement to the wellknown characterization of a WMR achieving the optimal outcomes, i.e., efficiency in the set of all random voting rules.
Introduction
Consider the choice of a voting rule on a succession of two alternatives (such as “yes” or “no”) by a group of individuals. When a voting rule is chosen, the alternatives to come in the future are unknown, and the individuals are uncertain about their future preferences. An individual votes sincerely being concerned with the probability that the outcome agrees with his or her preference, which is referred to as responsiveness (Rae, 1969). More specifically, an individual prefers a voting rule with higher responsiveness because he or she can expect that a favorable alternative is more likely to be chosen. For example, if an individual has a von NeumannMorgenstern (VNM) utility function such that the utility from the passage of a favorable issue is one and that of an unfavorable issue is zero, then the expected utility equals the responsiveness.
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