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

普雷卡帕-博雷尔定理是最近的数学发现 聚集理论。 本项目使用这些定理， 扩展和统一经济学的不同分支。 项目 将聚合理论应用于社会选择，不完美 竞争，收入分配在多部门劳动 市场，个人进入当地的自我选择 提供不同水平地方公共产品的司法管辖区 (the Tiebout假设），一阶方法的主要- 代理问题，以及需求法则的验证。 关于社会选择的研究尤其令人兴奋。 的 项目制定了社会共识的数学定义 并证明使用Prekopa-Borell定理， 结果最喜欢的平均选民不能被击败，如果一个 需要足够大的绝对多数（64%）。 这是 著名的中间选民定理的精神，最- 中间选民的首选结果总是击败任何 替代. 中间选民定理在选举中失效 不止一个问题受到威胁 在以下条件下获得的结果 该项目适用于多议题选举。 这是一个非常 这是一个重要的结果，因为它使开发一个 社会选择的积极理论基于对平均值的调查， 选民 研究一个有代表性的选民要比研究一个有代表性的选民容易得多。 调查所有选民的行为。 这项工作扩展到 在这种环境中，个体选择进入群体， 对一些问题进行投票，例如，公司股东， 地方政府的居民等。 该项目确定 在这种环境中的自我选择是否减少了 一个不可战胜的存在所需的绝对多数 提议

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.