Robust Voting under Uncertainty

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 one-half. 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 well-known characterization of a WMR achieving the optimal outcomes, i.e., efficiency in the set of all random voting rules.