Strategy-Proofness and the Tops-Only Property

A social choice function satisfies the tops-only property if the chosen alternative only depends on each person's report of his most-preferred alternatives on the range of this function. On many domains, strategy-proofness implies the tops-only property, provided that the range of the social choice function satisfies some regularity condition. The existing proofs of this result are model specific. In this article, a general proof strategy is proposed for showing that a strategy-proof social choice function satisfies the tops-only property when everyone has the same set of admissible preferences.