On random social choice functions with the tops-only property
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...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
2018
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| Subjects: | |
| 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 |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | 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. |
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