A characterization of single-peaked preferences via random social choice functions
证明了每个满足妥协性质的路径连通偏好域若存在策略证明、一致且仅依赖顶点的随机社会选择函数，则该域是单峰的；反之亦然。单峰性基于任意树定义，为Gul猜想提供了证据。
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}).