Incentives in Social Decision Schemes with Pairwise Comparison Preferences
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866913478041665536 |
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| author | Brandt, Felix Lederer, Patrick Suksompong, Warut |
| author_facet | Brandt, Felix Lederer, Patrick Suksompong, Warut |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_12436 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Incentives in Social Decision Schemes with Pairwise Comparison Preferences Brandt, Felix Lederer, Patrick Suksompong, Warut Computer Science and Game Theory Theoretical Economics 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. |
| title | Incentives in Social Decision Schemes with Pairwise Comparison Preferences |
| topic | Computer Science and Game Theory Theoretical Economics |
| url | https://arxiv.org/abs/2204.12436 |