Expected utility from additive utility on semigroups

Theory and Decision 53 (1):87-94 (2002)
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
Keywords Preordered sets  utility funtions  continuous and additive utility  expected utility  semigroups
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