计算比例否决核心
Computing the proportional veto core
AI总结：
针对社会选择中多数原则与少数群体权利保护的冲突，本文提出一种计算比例否决核心的多项式时间算法及匿名选择规则，并证明悲观者可在多项式时间内操纵核心而乐观者无法操纵。
摘要：
在社会选择中，多数原则（寻找对尽可能多的选民来说尽可能好的候选人）与保护少数群体权利（选择对特定个人或群体不过度糟糕的候选人）之间经常出现冲突。在以后者为主要关注点的情境下，基于否决的规则——赋予个人或群体从名单中划掉某些候选人的能力——是确保没有少数群体面临其认为无法容忍的结果的一种自然且有效的方法。然而，此类规则通常无法满足匿名性，或对选民和候选人的数量施加了特定限制。这些问题可以通过考虑比例否决核心来解决——这是一种合作博弈的解，其中每个联盟都被赋予否决与其规模成比例的候选人数量的权力。然而，计算否决核心的朴素算法是指数级的，并且唯一已知的在选民数量任意时从中进行选择的规则，无法满足匿名性。在本文中，我们提出了一种用于计算核心的多项式时间算法，研究了其预期大小，并提出了一种从中选择候选人的匿名规则。我们研究了与核心一致的投票规则的属性。最后，我们证明了悲观者可以在多项式时间内操纵核心，而乐观者则完全无法操纵核心。
英文摘要：
In social choice there often arises a conflict between the majority principle (the search for a candidate that is as good as possible for as many voters as possible), and the protection of minority rights (choosing a candidate that is not overly bad for particular individuals or groups). In a context where the latter is our main concern, veto-based rules -- giving individuals or groups the ability to strike off certain candidates from the list -- are a natural and effective way of ensuring that no minority is left with an outcome they find untenable. However, such rules often fail to be anonymous, or impose specific restrictions on the number of voters and candidates. These issues can be addressed by considering the proportional veto core -- the solution to a cooperative game where every coalition is given the power to veto a number of candidates proportional to its size. However, the naïve algorithm for the veto core is exponential, and the only known rule for selecting from the core, with an arbitrary number of voters, fails anonymity. In this paper we present a polynomial time algorithm for computing the core, study its expected size, and present an anonymous rule for selecting a candidate from it. We study the properties of core-consistent voting rules. Finally, we show that a pessimist can manipulate the core in polynomial time, while an optimist cannot manipulate it at all.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
