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Theory and Decision

, Volume 26, Issue 2, pp 99–105 | Cite as

Coherent bets under partially resolving uncertainty and belief functions

  • Jean-Yves Jaffray
Article

Abstract

By considering situations of partially resolving uncertainty, a one-to-one correspondence between belief functions and coherent betting systems à la de Finetti is shown to exist.

Keywords

decision theory uncertainty betting system Dutch book belief function 

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References

  1. 1.
    A. P. Dempster: 1967, ‘Upper and lower probabilities induced by a multivalued mapping’, Annals of Mathematical Statistics 38, 325–339.Google Scholar
  2. 2.
    B. de Finetti: 1974, Theory of Probabilities, Vol. 1, Wiley, New York.Google Scholar
  3. 3.
    D. Gale: 1960, The Theory of Linear Economic Models, McGraw Hill, New York.Google Scholar
  4. 4.
    L. J. Savage: 1972, The Foundations of Statistics (2d ed.), Dover Publications, New York.Google Scholar
  5. 5.
    G. Shafer: 1976, A Mathematical Theory of Evidence, Princeton University Press, Princeton.Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Jean-Yves Jaffray
    • 1
  1. 1.Université P. et M. CurieParisFrance

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