A Characterization of Single-Peaked Preferences via Random Social Choice Functions

• Main Authors: CHATTERJI, Shurojit, SEN, Arunava, ZENG, Huaxia
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2014
• Subjects: Random Social Choice Functions; Strategy-proofness; Compromise; Singlepeaked Preferences; Economics; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/1597; https://ink.library.smu.edu.sg/context/soe_research/article/2596/viewcontent/13_2014.pdf
• Institution: Singapore Management University

The paper proves the following result: every path-connected domain of preferences that admits a strategy-proof, unanimous, tops-only random social choice function satisfying a compromise property, is single-peaked. Conversely, every single-peaked domain admits a random social choice function satisfying these properties. Single-peakedness is defined with respect to arbitrary trees. We also show that a maximal domain that admits a strategy-proof, unanimous, tops-only random social choice function satisfying a stronger version of the compromise property, is single-peaked on a line. A converse to this result also holds. The paper provides justification of the salience of single-peaked preferences and evidence in favour of the Gul conjecture (Barbera (2010)).