False-Name-Proof and Strategy-Proof Voting Rules Under Separable Preferences

We consider the problem of a society that uses a voting rule to select a subset from a given set of objects (candidates, binary issues or alike). We assume that voters' preferences over subsets of objects are separable: Adding an object to a set leads to a better set if and only if the object is good (as a singleton set, the object is better than the empty set). A voting rule is strategy-proof if no voter benefits by not revealing its preferences truthfully and it is false-name-proof if no voter gains by submitting several votes under other identities. We characterize all voting rules that verify false-name-proofness, strategy-proofness, unanimity, anonymity, and neutrality as either the class of voting by quota one (all voters can be decisive for all objects) or the class of voting by full quota (all voters can veto all objects)