Theoretical Economics 11 (2016), 711–733

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. The paper provides a justification of the salience of single-peaked preferences and evidence in favour of the Gul conjecture (\citet{barbsurvey}).

Keywords: Random social choice functions, strategy-proofness, compromise, single-peaked preferences

JEL classification: D71