Incentives in social decision schemes with pairwise comparison preferences
研究了选民对备选方案有排序偏好时，社会决策方案如何将偏好映射到彩票上，并证明了不存在同时满足孔多塞一致性和策略防护性的方案，以及匿名中立方案无法同时满足效率与策略防护性或参与性。
Social decision schemes (SDSs) map the ordinal preferences of voters over multiple alternatives to a probability distribution over the alternatives. 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) and show that (i) no Condorcet-consistent SDS satisfies PC-strategyproofness; (ii) no anonymous and neutral SDS satisfies both PC-efficiency and PC-strategyproofness; and (iii) no anonymous and neutral SDS satisfies both PC-efficiency and strict PC-participation. 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.