A New Approach to Aggregation with Applications to ImperfectCompetition, Majority Voting, and the Distribution of Income

Prekopa-Borell定理是最近在聚集理论中的数学发现。本项目使用这些定理来扩展和统一经济学的不同分支。该项目将聚合理论应用于社会选择、不完全竞争、多部门劳动力市场中的收入分配、个人进入提供不同水平当地公共产品的地方司法管辖区的自我选择（Tiebout假说）、委托-代理问题的一阶方法、以及需求法则的验证。关于社会选择的研究尤其令人兴奋。该项目制定了社会共识的数学定义，并使用Prekopa-Borell定理证明，如果需要足够大的超级多数（64%），那么普通选民最喜欢的结果就不会被击败。这符合著名的中位数选民定理的精神，即中位数选民最喜欢的结果总是胜过任何其他选择。在涉及多个议题的选举中，中间选民定理就失效了。在这个项目下获得的结果适用于多议题选举。这是一个非常重要的结果，因为它使基于对中庸选民的调查发展社会选择的积极理论成为可能。研究一个有代表性的选民要比调查所有选民的行为容易得多。这项工作被扩展到这样的环境中，在这种环境中，个人选择进入群体，然后对一些问题进行投票，例如，公司股东，当地政府的居民等。该项目决定了在这种环境下的自我选择是否减少了一个无与伦比的提案存在所需的超级多数的规模。

The Prekopa-Borell theorems are recent mathematical discoveries in aggregation theory. This project uses these theorems to extend and unify diverse branches of economics. The project applies aggregation theory to social choice, imperfect competition, the distribution of income in a multi-sector labor market, the self-selection of individuals into local jurisdictions providing different levels of local public goods (the Tiebout hypothesis), the first-order approach to Principal- Agent problems, and verification of the Law of Demand. The research on social choice is especially exciting. The project formulates a mathematical definition of social consensus and demonstrates using the Prekopa-Borell theorems that the outcome most-preferred by the mean voter cannot be defeated if a sufficiently large super-majority (64%) is required. This is in the spirit of the famous median-voter theorem that the most- preferred outcome of the median voter always beats any alternative. The median-voter theorem breaks down in an election with more than one issue at stake. The results obtained under this project hold for multi-issue elections. This is a very important result because it makes it possible to develop a positive theory of social choice based on investigations of mean- voters. It is much easier to study a representative voter than investigate the behavior of all voters. This work is extended to environments in which individuals select into groups that then vote on some set of issues, e.g., corporate shareholders, residents of local governments, etc.. The project determines whether the self-selection in such environments reduces the size of the super-majority required for the existence of an unbeatable proposal.