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.
Random Social Choice Functions, Unanimity, Strategy-proofness, Tops-only Property, Interior Property, Exterior Property
Games and Economic Behavior
CHATTERJI, Shurojit and ZENG, Huaxia.
On random social choice functions with the tops-only property. (2018). Games and Economic Behavior. 1-39. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/2156
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