Local Strategy-proofness and Dictatorship

TL;DR

This paper characterizes preference domains where unanimous, locally strategy-proof social choice functions are necessarily dictatorships, identifying a key domain condition called connected with distinct neighbours.

Contribution

It introduces a necessary and sufficient condition on domains for dictatorship under local strategy-proofness and unanimity, advancing the understanding of strategy-proof social choice functions.

Findings

Connected with distinct neighbours is necessary for dictatorship.

On such domains, unanimity and strategy-proofness imply dictatorship.

Complete characterization of all such domains remains open.

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.