On the extension of additive utilities to infinite sets |
| |
Authors: | Jean-Yves Jaffray |
| |
Institution: | Université de Paris VI, France |
| |
Abstract: | Independence condition C is known as necessary and sufficient for the existence of an additive utility on a finite subset X of a Cartesian product. A stronger necessary condition, H, interpreted as both an independence and Archimedean condition, is derived. It is shown to be sufficient when X is countable by constructing an additive utility as the limit of a sequence of additive utilities on finite subsets of X. When X is not countable, but is a Cartesian product, another necessary condition, the existence of A, a countable perfectly (order-) dense subset of X, is added to H; an additive utility is constructed by extension to X of an additive utility on a countable set linked to A. An application to a no-solvability case is given. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|