In this paper we consider the standard voting model with a finite set of alternatives A and n voters and address the following question: what are the characteristics of domains D that induce the property that every strategy-proof social choice function f : Dn → A satisfying unanimity, has the tops-only property? We first impose a minimal richness condition which ensures that for every alternative a, there exists an admissible ordering where a is maximal. We identify conditions on D that are sufficient for strategy-proofness and unanimity to imply tops onlyness in the general case of n voters and in the special case, n = 2. We provide an algorithm for constructing tops-only domains from connected graphs with elements of A as nodes. We provide several applications of our results. Finally, we relax the minimal richness assumption and partially extend our results.
Voting-rules, Strategy-proofness, Restricted domains, Tops-only domains
Singapore Management University Economics and Statistics Working Paper Series, Paper No. 06-2009
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CHATTERJI, Shurojit and SEN, Arunava.
Tops-Only Domains. (2009). 1-33. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1139
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