We consider strategyproof social choice functions defined over product domains. If preferences are strict orderings and separable, then strategyproof social choice functions must be decomposable provided that the domain of preferences is rich. We provide several characterization results in the case where preferences are separable only with respect to the elements of some partition of the set of components and these partitions vary across individuals. We characterize the libertarian social choice function and show that no superset of the tops separable domain admits strategyproof nondictatorial social choice functions.

We study the incentives of candidates to strategically affect the outcome of a voting procedure. We show that the outcomes of every nondictatorial voting procedure that satisfies unanimity will be affected by the incentives of noncontending candidates (i.e., who cannot win the election) to influence the outcome by entering or exiting the election.