We consider the problem of choosing a subset of a finite set of indivisible objects (public projects, facilities, laws, etc.) studied by Barbera et al. (1991). Here we assume that agents' preferences are separable weak orderings. Given such a preference, objects are partitioned into three types, "goods", "bads", and "nulls". We focus on "voting rules", which rely only on this partition rather than the full information of preferences. We characterize voting rules satisfying strategy-proofness (no one can ever be better off by lying about his preference) and null-independence (the decision on each object should not be dependent on the preference of an agent for whom the object is a null). We also show that serially dictatorial rules are the only voting rules satisfying efficiency as well as the above two axioms. We show that the "separable domain" is the unique maximal domain over which each rule in the first characterization, satisfying a certain fairness property, is strategy-proof.
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