Incentives in Social Decision Schemes with Pairwise Comparison Preferences

• Tác giả: Felix Brandt, Patrick Lederer, Warut Suksompong
• Ngôn ngữ: eng
• Ký hiệu phân loại: 302.13 Social choice
• Thông tin xuất bản: 2022
• Bộ sưu tập: Metadata
• ID: 195000

Tóm tắt

 Comment: A preliminary version appeared in the 31st International Joint Conference on Artificial Intelligence (IJCAI), 2022. The current version is significantly extendedSocial 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.