Tops-only domains - CHATTERJI, Shurojit (Institutional Knowledge at Singapore Management University, 2011)
In this paper we consider the standard voting model with a finite set of alternativesA and n voters and address the following question: what are the characteristics ofdomains D that induce the property that every strategy-proof social choice functionf : Dn → A satisfying unanimity, has the tops-only property? We first impose aminimal richness condition which ensures that for every alternative a, there exists anadmissible ordering where a is maximal. We identify conditions on D that are sufficientfor strategy-proofness and unanimity to imply tops onlyness in the general case of nvoters and in the special case, n = 2. We provide an algorithm for constructing tops-onlydomains from connected graphs with elements of A as nodes. We provide severalapplications of our results. Finally, we relax the minimal richness assumption andpartially extend our results.