Local Strategy-proofness and Dictatorship

Abstract

We investigate preference domains under which every unanimous and locally strategy-proof social choice function (scf) satisfies dictatorship. We identify a condition on domains called connected with distinct neighbours which is necessary for dictatorship under unanimity and local strategy-proofness. Further, we show that this condition is sufficient within the class of domains where every unanimous and locally strategy-proof scf satisfies tops-onlyness. While a complete characterization remains open, we also show that on domains that are connected with distinct neighbours, unanimity and strategy-proofness (a stronger requirement) imply dictatorship.