A Characterization of Single-Peaked Preferences via Random Social Choice Functions - CHATTERJI, Shurojit (Institutional Knowledge at Singapore Management University, 2014)
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)).