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Incentives in Social Decision Schemes with Pairwise Comparison Preferences

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  • Felix Brandt
  • Patrick Lederer
  • Warut Suksompong

Abstract

Social decision schemes (SDSs) map the ordinal preferences of individual voters over multiple alternatives to a probability distribution over the alternatives. In order to study the axiomatic properties of SDSs, we lift preferences over alternatives to preferences over lotteries using the natural -- but little understood -- pairwise comparison (PC) preference extension. This extension postulates that one lottery is preferred to another if the former is more likely to return a preferred outcome. We settle three open questions raised by Brandt (2017): (i) there is no Condorcet-consistent SDS that satisfies PC-strategyproofness; (ii) there is no anonymous and neutral SDS that satisfies PC-efficiency and PC-strategyproofness; and (iii) there is no anonymous and neutral SDS that satisfies PC-efficiency and strict PC-participation. All three impossibilities require $m\geq 4$ alternatives and turn into possibilities when $m\leq 3$. We furthermore settle an open problem raised by Aziz et al. (2015) by showing that no path of PC-improvements originating from an inefficient lottery may lead to a PC-efficient lottery.

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  • Felix Brandt & Patrick Lederer & Warut Suksompong, 2022. "Incentives in Social Decision Schemes with Pairwise Comparison Preferences," Papers 2204.12436, arXiv.org, revised Aug 2024.
    • Handle: RePEc:arx:papers:2204.12436
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