A characterization of possibility domains in strategic voting

We consider domains in strategic voting problems which satisfy three properties, namely top-connectedness, pervasiveness, and richness. We prove the following two results for such a domain: (i) it admits non-dictatorial, unanimous, and strategy-proof choice functions if and only if it has an inseparable top-pair, and (ii) it admits anonymous, unanimous, and strategy-proof choice functions only if it does not have any top-circuit. Finally, we establish the practical relevance of our results by applying them in the context of locating a public good or a public bad, preference aggregations, policy making, etc.