Rationalizing Distance Rationalizability

Distance rationalizability is an intuitive paradigm for developing and studying voting rules: given a notion of consensus and a distance function on preference profiles, a rationalizable voting rule selects an alternative that is closest to being a consensus winner. Despite its appeal, distance rationalizability faces the challenge of connecting the chosen distance measure and consensus notion to an operational measure of social desirability. We tackle this issue via the recently introduced decision-theoretic framework of dynamic social choice, in which a social choice Markov decision process (MDP) models the dynamics of voter preferences in response to winner selection. We show that, for a prominent class of distance functions, one can construct a social choice MDP, with natural preference dynamics and reward function, such that a voting rule is (votewise) rationalizable with respect to the unanimity consensus for a given distance function iff it is a (deterministic) optimal policy in the MDP. This provides a rationale for distance rationalizability, demonstrating the equivalence of rationalizable voting rules in a static sense and winner selection to maximize societal utility in a dynamic process.