Theory and Decision

, Volume 53, Issue 1, pp 87–94 | Cite as

Expected utility from additive utility on semigroups

  • Juan C. Candeal
  • Juan R. De Miguel
  • Esteban Induráin


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 sets utility funtions continuous and additive utility expected utility semigroups 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alimov, N.G. (1950), On ordered semigroups (In Russian), Izv. Akad. Nauk SSSR Ser. Math. 14, 569–576.Google Scholar
  2. Araujo, A. (1985), Lack of Pareto optimal allocations in economies with infinitely many commodities: the need for impatience, Econometrica 53(2), 455–461.Google Scholar
  3. Brown, D.J. and Lewis, L.M. (1981), Myopic economic agents, Econometrica 49(2), 359–368.Google Scholar
  4. Candeal, J.C., De Miguel, J.R. and Induráin, E. (1997), Topological additively representable semigroups, Journal of Mathematical Analysis and Applications 210, 375–389.Google Scholar
  5. Candeal, J.C., De Miguel, J.R., Induráin, E. and Olóriz, E. (1997), Associativity equation revisited, Publicationes Mathematicae Debrecen 51(12), 133–144.Google Scholar
  6. Candeal, J.C., and Induráin, E. (1995), A note on linear utility, Economic Theory 6, 519–522.Google Scholar
  7. De Miguel, J.R., Candeal, J.C., and Induráin, E. (1996), Archimedeaness and additive utility on totally ordered semigroups, Semigroup Forum 52, 335–347.Google Scholar
  8. Einy, E. (1989), On preferences relations which satisfy weak independent property, Journal of Mathematical Economics 18, 291–300.Google Scholar
  9. Fishburn, P.C. (1982), The Foundations of Expected Utility. Dordrecht, The Netherlands, D. Reidel.Google Scholar
  10. Fuhrken, G., and Richter, M.K. (1991), Additive utility, Economic Theory 1, 83–105.Google Scholar
  11. Gottinger, H. (1976), Existence of a utility on a topological semigroup, Theory and Decision 7, 145–158.Google Scholar
  12. Herstein, I.N., and Milnor, J. (1953), An axiomatic approach to measurable utility, Econometrica 21, 291–297.Google Scholar
  13. Krantz, D.H., Luce, R.D., Suppes, P. and Tversky, A. (1971), Foundations of measurement. Academic Press, New York.Google Scholar
  14. Narens, L. (1985), Abstract Measurement Theory. Cambridge, MA: MIT Press.Google Scholar
  15. Neuefeind, W. and Trockel, W. (1995), Continuous linear representability of binary relations, Economic Theory 6, 351–356.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Juan C. Candeal
    • 1
  • Juan R. De Miguel
    • 2
  • Esteban Induráin
    • 2
  1. 1.Departamento de Análisis EconómicoUniversidad de ZaragozaZaragozaSpain
  2. 2.Departamento de Matemática e InformáticaUniversidad Pública de NavarraPamplonaSpain

Personalised recommendations