Incentives in Social Decision Schemes with Pairwise Comparison Preferences

Felix Brandt, Patrick Lederer and Warut Suksompong

Papers from arXiv.org

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.

Date: 2022-04, Revised 2024-08
New Economics Papers: this item is included in nep-des, nep-mic and nep-upt
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Published in Games and Economic Behavior, 142:266-291 (2023)

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