Author: Gopakumar Achuthankutty and Souvik Roy
Title: Strategy-Proof Rules On Partially Single-Peaked Domains
Abstract: We consider domains that exhibit single-peakedness only over a subset of linearly ordered set of alternatives. We call such domains partially single-peaked and provide a characterization of the unanimous and strategy-proof social choice functions on these domains. We obtain the following interesting auxiliary results: (i) we characterize all unanimous and strategyproof social choice functions on generalized top-connected domains, which are an important sub-class of the maximal single-peaked domain, (ii) we show that strategy-proofness and group strategy-proofness are equivalent on partially single-peaked domains, and (iii) lastly, we identify and characterize the unanimous and strategy-proof SCFs on partially single-peaked domains that are close to being anonymous. As an application of this result, we obtain a characterization of the unanimous and strategy-proof social choice functions on multi-peaked domains (Stiglitz (1974), Epple and Romano (1996a)), multiple single-peaked domains (Reffgen (2015)) and single-peaked domains on graphs (Demange (1982), Schummer and Vohra (2002)).
Keywords: D71, D82.
JEL Code: Partially single-peaked domain, strategy-proofness, group strategy-proofness, partly dictatorial min-max rules.