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arXiv · 2204.12436

Incentives in Social Decision Schemes with Pairwise Comparison Preferences

Felix Brandt·Patrick Lederer·Warut Suksompong
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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. 2022-04-26. Incentives in Social Decision Schemes with Pairwise Comparison Preferences. https://doi.org/10.1016/j.geb.2023.08.009

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