Theory and Decision

, Volume 53, Issue 1, pp 87–94

Expected utility from additive utility on semigroups


  • Juan C. Candeal
    • Departamento de Análisis EconómicoUniversidad de Zaragoza
  • Juan R. De Miguel
    • Departamento de Matemática e InformáticaUniversidad Pública de Navarra
    • Departamento de Matemática e InformáticaUniversidad Pública de Navarra

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


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.

Preordered setsutility funtionscontinuous and additive utilityexpected utilitysemigroups
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© Kluwer Academic Publishers 2002