This article shows that a social choice function defined on a domain of separable preferences which satisfies a relatively weak domain-richness condition on a product set of alternatives is (i) strategy-proof and only depends on the tops of the individual preferences if and only if (ii) the range of the social choice function is a product set and the social choice function can be decomposed into the product of one-dimensional, strategy-proof, nontop-insensitive social choice functions.

JEL Classification Number: D71.