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On random social choice functions with the tops-only property

Shurojit Chatterji and Huaxia Zeng

Games and Economic Behavior, 2018, vol. 109, issue C, 413-435

Abstract: We study the standard voting model with randomization. A Random Social Choice Function (or RSCF) satisfies the tops-only property if the social lottery under each preference profile depends only on the peaks of voters' preferences. We identify a general condition on domains of preferences (the Interior Property and the Exterior Property) which ensures that every strategy-proof RSCF satisfying unanimity has the tops-only property. We show that our condition applies to important classes of voting domains which include restricted connected domains (Sato, 2013) and the multi-dimensional single-peaked domain (Barberà et al., 1993). As an application of our result, we show that every ex-post efficient and strategy-proof RSCF defined on the multi-dimensional single-peaked domain is a random dictatorship.

Keywords: Random social choice functions; Unanimity; Strategy-proofness; The tops-only property; The interior property; The exterior property (search for similar items in EconPapers)
JEL-codes: D71 (search for similar items in EconPapers)
Date: 2018
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Handle: RePEc:eee:gamebe:v:109:y:2018:i:c:p:413-435