Rules: Invention and Analysis

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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.