On random social choice functions with the tops-only property

• Main Authors: CHATTERJI, Shurojit, ZENG, Huaxia
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2018
• Subjects: Random Social Choice Functions; Unanimity; Strategy-proofness; Tops-only Property; Interior Property; Exterior Property; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/1777; https://ink.library.smu.edu.sg/context/soe_research/article/2775/viewcontent/RandomSocialChoice_Tops_onlyProperty_2018_am.pdf
• Institution: Singapore Management University

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.