Consider the following principle regarding the performance of collective choice rules. "If a rule selects alternative x in situation 1, and alternative y in situation 2, there must be an alternative z, and some member of society whose appreciation of z relative to x has increased when going from...

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...