# Expected utility from additive utility on semigroups

DOI: 10.1023/A:1020807903939

- Cite this article as:
- Candeal, J.C., De Miguel, J.R. & Induráin, E. Theory and Decision (2002) 53: 87. doi:10.1023/A:1020807903939

## Abstract

In the present paper we study the framework of additive utility theory, obtaining new results derived from a concurrence of algebraic and topological techniques. Such techniques lean on the concept of a connected topological totally ordered semigroup. We achieve a general result concerning the existence of continuous and additive utility functions on completely preordered sets endowed with a binary operation ``+'', not necessarily being commutative or associative. In the final part of the paper we get some applications to expected utility theory, and a representation theorem for a class of complete preorders on a quite general family of real mixture spaces.