Theoretical Economics, Volume 4, Number 2 (June 2009)

Theoretical Economics 4 (2009), 127–163

Strategy-proofness and single-crossing

Alejandro Saporiti


This paper analyzes strategy-proof collective choice rules when individuals have single-crossing preferences on a finite and ordered set of social alternatives. It shows that a social choice rule is anonymous, unanimous, and strategy-proof on a maximal single-crossing domain if and only if it is an extended median rule with n-1 fixed ballots distributed over the individuals' most preferred alternatives. As a by-product, the paper also proves that strategy-proofness implies the tops-only property. It also offers a strategic foundation for the so-called "single-crossing version" of the Median Voter Theorem, by showing that the median ideal point can be implemented in dominant strategies by a direct mechanism in which every individual reveals his true preferences.

Keywords: Single-crossing, strategy-proofness, tops-only, peak rules

JEL classification: C72, D71, D78

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