Multi-dimensional social choice under frugal information: The Tukey median as Condorcet winner ex ante by

We study a voting model with partial information in which the evaluation of social welfare must be based on information about agents' top choices plus qualitative background conditions on preferences. The former is elicited individually, while the latter is not. The social evaluator is modeled as an imprecise Bayesian characterized by a set of priors over voters' complete ordinal preference profiles. We apply this 'frugal aggregation' model to multi-dimensional budget allocation problems and propose a solution concept of 'ex-ante' Condorcet winners. We show that if the social evaluator has symmetrically ignorant beliefs over profiles of quadratic preferences, the ex-ante Condorcet winners refine the set of Tukey medians (Tukey, 1975).