Local Strategy-proofness and Dictatorship

Abstract

We investigate preference domains on which every unanimous and locally strategy-proof social choice function (scf) is dictatorial. We identify a condition on domains, connected with distinct neighbours, that is necessary for this property. We then show that the condition is also sufficient on L-tops-only domains, i.e., domains on which every unanimous and locally strategy-proof scf is tops-only. Whether every connected with distinct neighbours domain is L-tops-only remains open; if some are not, our sufficiency result is silent on them. We show, however, that every connected with distinct neighbours domain, L-tops-only or not, is a dictatorial domain, i.e., unanimity and strategy-proofness (a stronger requirement than local strategy-proofness) force dictatorship on it.