Characterizing the top cycle via strategyproofness

Abstract

Gibbard and Satterthwaite have shown that the only single‐valued social choice functions (SCFs) that satisfy nonimposition (i.e., the function's range coincides with its codomain) and strategyproofness (i.e., voters are never better off by misrepresenting their preferences) are dictatorships. In this paper, we consider set‐valued social choice correspondences (SCCs) that are strategyproof according to Fishburn's preference extension and, in particular, the top cycle, an attractive SCC that returns the maximal elements of the transitive closure of the weak majority relation. Our main theorem shows that, under mild conditions, the top cycle is the only non‐imposing strategyproof SCC whose outcome only depends on the quantified pairwise comparisons between alternatives. This result effectively turns the Gibbard–Satterthwaite impossibility into a complete characterization of the top cycle by moving from SCFs to SCCs. We also leverage key ideas of the proof of this statement to obtain a more general characterization of strategyproof SCCs.