Unanimity and local incentive compatibility in sparsely connected domains

This paper studies the implications of imposing unanimity and local incentive compatibility on a deterministic social choice function. In an environment with strict ordinal preferences over a finite set of alternatives, we find that tops-onlyness and full incentive compatibility necessarily follow from unanimity and local incentive compatibility in sparsely connected domains. Furthermore, we identify a property of preference domains that completely characterizes dictatorial domains within sparsely connected domains.