Tops-Only Domains

• Main Authors: CHATTERJI, Shurojit, SEN, Arunava
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2009
• Subjects: Voting-rules; Strategy-proofness; Restricted domains; Tops-only domains; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/1139; https://ink.library.smu.edu.sg/context/soe_research/article/2138/viewcontent/topsfeb09_2_.pdf
• Institution: Singapore Management University

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.