## Research Collection School Of Economics

#### Title

Tops-Only Domains

Journal Article

12-2009

#### Abstract

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 $${\mathcal D}$$ that induce the property that every strategy-proof social choice function $${f: {\mathcal D}^n \rightarrow A}$$ 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 $${\mathcal D}$$ 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.

#### Keywords

Voting-rules - Strategy-proofness - Restricted domains - Tops-only domains

Econometrics

Economic Theory

Economic Theory

46

255

282

0938-2259

#### Identifier

10.1007/s00199-009-0509-2

Springer Verlag