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.
