Rules: Invention and Analysis

规则：发明和评估当个人遵循导致合理结果的规则时，人类机构是成功的。靠左行驶，一起吃饭，银行和信贷通常会产生有利于参与者的结果。可以根据规则所引发结果的性质来评估规则；可以发明和比较新的规则。本研究计划的总体目标是发展和分析规则，特别是行为规则，以改善制度的功能。行为规则（如果你想要X，做A；如果你想要Y，做B等）通过约束个人选择来反映个人偏好来调节社会系统。规则的正式模型生成了从偏好概况到结果的映射，可以根据“公平性”和其他属性进行评估，使我们能够询问其他规则是否会做得更好。该项目将专注于四类规则，但将寻找更广泛的应用。公平分配：具有不同偏好的个人能否以“公平”的方式共同分配资产？如果可以，如何分配？这个项目解决了分配不可分割的物体的问题，比如硬糖、橱柜位置或艺术品。一般来说，公平的分配是没有嫉妒的（没有人会严格地喜欢别人的份额）和帕累托最优的（任何其他分配对某人来说都严格地更差）；有时也会寻求其他属性。根据上下文和定义，公平分配可能不存在。本文的出发点是最近的一项综合综述，该综述评估了所有已知的两人平衡联合分配算法。选举制度：多名获胜者的选举应如何进行？本研究的重点是多赢家选举的选票和计票，这是一个特别有趣的问题，因为对获胜集的两个自然要求之间存在紧张关系：每个获胜者都应该得到选民的良好支持，但对整个获胜集的支持应该是多样化的，以避免“多数人的暴政”。该项目将寻找新的投票系统和财产。服务体育：比赛应该如何组织以奖励能力，同时保持兴趣？发球运动是一种双方比赛，球被来回击打，直到一方失败；然后另一方得一分。发球通常是有利的。在标准规则下，下一个发球者是前一分的赢家；在追赶规则下，下一个发球者是前一分的输家。获胜概率保持不变，但追赶通常会增加游戏的预期长度。这两条规则影响长度，但不影响公平，但其他规则似乎改变了这两种衡量标准。冲突解决的图模型：个人应该遵循规则吗？这个广泛用于建模和分析战略冲突的系统将与博弈论一起应用于评估这一维度上的规则。

Rules: Invention and Assessment Human institutions are successful when individuals follow rules that lead to reasonable outcomes. Driving on the left side of the road, taking meals together, and banking and credit generally produce outcomes that benefit actors. Rules can be assessed according to the properties of the outcomes they induce; new rules can be invented and compared. The overall objective of this research program is to develop and analyze rules, especially behavioral rules, in order to improve the functioning of institutions. Behavioral rules (If you want X, do A; If you want Y, do B; etc.) regulate social systems by constraining individual choices to reflect individual preferences. Formal models of rules produce a mapping from preference profiles to outcomes that can be evaluated for "fairness" and other properties, enabling us to ask whether other rules would do better. The program will focus on four classes of rules, but will look for applications further afield. Fair Division: Can individuals with different preferences jointly allocate assets in a "fair" way and, if so, how? This project addresses the problem of allocating indivisible objects, such as hard candies, cabinet positions, or objets d'art. Generally, a fair division is envy-free (no one would strictly prefer someone else's share) and Pareto-optimal (any other division would be strictly worse for someone); sometimes other properties are also sought. Fair allocations may not exist, depending on the context and the definition. The starting point is a recent comprehensive review that assesses all known algorithms for two-person balanced joint allocation. Electoral Systems: How should elections with multiple winners be conducted? This study focuses on ballots and ballot-counting for multi-winner elections, which are of special interest because of the tension between two natural requirements on the winning set: each winner should be well-supported by the voters, but support for the winning set as a whole should be diverse, to avoid "tyranny of the majority." The project will search for new voting systems and properties. Service Sports: How should competitions be structured to reward ability and at the same time maintain interest? A service sport is a two-sided competition in which a ball is hit back and forth until one side fails; the other side then gains a point. It is usually an advantage to serve. Under the Standard Rule, the next server is the winner of the previous point; under the Catch-Up Rule, the next server is the loser of the previous point. Win probability remains the same, but Catch-Up typically increases the expected length of the game. These two rules affect length but not fairness, but other rules appear to alter both measures. Graph Model for Conflict Resolution: Should an individual follow a rule? This widely used system for modeling and analyzing strategic conflicts will be applied, along with game theory, to assess rules on this dimension.