Strategy-Proofness in Lexicographic Preferences : A Characterization

When preferences are single-peaked (Black (1948),Black et al. (1958)) or group separable Ballester and Haeringer (2011), majority voting equilibria exist. Group separability has probably not received as much attention as single-peak separability because there are no intuitive assumptions about the structure of the set of alternatives. In this article, we endow the set of alternatives with a binary partition tree structure and show that the group separability condition is equivalent to requiring individuals at each level of the tree to prefer one element of the partition to the other. Then, we represent alternatives with a vector of characteristics and show that group separability is equivalent to a general version of lexicography relative to an order that is obtained from the binary partition tree. Finally, we characterize all non-manipulable rules, which consist of a family of sequential voting by committees, with the particularity that the committee used in each situation may depend on the result of previous committees