Additive representations on a simplex
研究了在单纯形等内部为空的乘积空间子集上，偏好关系存在可加表示的条件，给出了一个充要条件，并应用于蛋糕分割问题帕累托前沿上的功利主义刻画。
We characterize additive representations on subsets of product spaces with an empty interior such as simplexes and certain homeomorphisms thereof. Previously, all additive representation theorems only applied to spaces in which any coordinate can be changed without changing any of the other coordinates. We identify a novel preference condition that is necessary and sufficient for the existence of additive representations. Our results provide, for instance, a characterization of utilitarianism on the Pareto frontier of a cake division problem.