Skip to main content

A Positive Value of Information for a Non-Bayesian Decision-Maker

  • Chapter
Beliefs, Interactions and Preferences in Decision Making

Part of the book series: Theory and Decision Library ((TDLB,volume 40))

Abstract

In the multi-prior framework, we consider that there exist two sorts of information process: revision information and focusing information. The second one is standard in economics while the former cannot be defined when there is only one prior. In this paper, we provide a coherent defmition of “revising” information structure. We show that we get a positive value of information. A partial order for those revision information structures is also proposed.

We wish to thank Main Chateauneuf, Jean-Yves Jaffray and Bernard Walliser for their helpful comments. All remaining errors are our own.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. BLACKWELL, D. (1953) “Equivalent Comparison of Experiments ”, Annals ofMathematics and Statistics, 24, 265–272.

    Article  Google Scholar 

  2. BOHNENBLUST, H.F., SHAPLEY, L.S., SHERMAN, S., (1949) Reconnaissance in Game Theory,The Rand Corporation

    Google Scholar 

  3. CHATEAUNEUF, A., JAFFRAY, J. Y., (1989) “Some characterisations of lower probabilities and other monotone capacities through the use of MSebius inversion”, Mathematical Social Sciences, 17, 263283.

    Google Scholar 

  4. DEMPSTER, A.P. (1967) “ Upper and Lower Probabilities Induced by a Multi-valued Mapping ”, Annals ofMathematical Statistics, 38, 325–339.

    Article  Google Scholar 

  5. DUBOIS, D., PRADE, H., SMETS, P., (1994) “Representing Partial Ignorance”, Mimeo, I. R.I.T, University of Toulouse.

    Google Scholar 

  6. ELLSBERG, D, (1961) “Risk, Ambiguity, and the Savage Axioms”, Quaterly Journal ofEconomics, 64, 643–669.

    Article  Google Scholar 

  7. EPSTEIN, L., LE BRETON, M., (1993) “Dynamically consistent beliefs must be bayesian”, Journal of Economic Theory, 59, 33–49.

    Article  Google Scholar 

  8. FAGIN, R., HALPERN, J. Y., (1990) “A New approach to updating beliefs”, Mimeo, IBM Research Division.

    Google Scholar 

  9. GHIRARDATO, P. (1994) “ Coping with Ignorance: Unforeseen Contingencies and Non-Additive Uncertainty ”, Mimeo, UC Berkeley.

    Google Scholar 

  10. GILBOA, I. (1987) “Expected Utility with Purely Subjective No-Additive Probabilities”, Journal of Mathematical Economics, 16, 65–88.

    Article  Google Scholar 

  11. GILBOA, I., SCHMEIDLER, D., (1989) “Maxmin Expected Utility with a non-unique prior”, Journal ofMathematical Economics, 18, 141–153.

    Google Scholar 

  12. GILBOA, I., SCHMEIDLER, D., (1993) “Updating ambiguous beliefs”, Journal of Economic Theory, 59, 33–49.

    Article  Google Scholar 

  13. HAMMOND, P.J. (1988) “Consequentialist Foundations for Expected Utility”, Theory and Decision„ 25, 25–78.

    Article  Google Scholar 

  14. JAFFRAY, J. Y., (1989) “Linear Utility Theory for Belief Functions ”, Operations Research Letters, 8, 107–112.

    Article  Google Scholar 

  15. JAFFRAY, J. Y., (1990) “Bayesian conditioning and belief functions”, Mimeo, University of Paris V I.

    Google Scholar 

  16. JAFFRAY, J. Y., WAKKER, P., (1994) “Decision Making with belief functions: Compatibility and incompatibility with the sure-thing principle”, Journal ofRisk and Uncertainly, 8, 255–271.

    Google Scholar 

  17. MACHINA, M. (1989) “Dynamic Consistency and Non-Expected Utility Models of Choice Under Uncertainty”, Journal ofEconomic Literature, 28, 1622–1668.

    Google Scholar 

  18. MACHINA, M., SCHMEIDLER, D., (1992) “A more robust definition of subjective probability”, Econometrica, 60, 745–780.

    Article  Google Scholar 

  19. MUKERJI, S., (1997) “Understanding the non additive probability decision”, Economic Theory, 59, 33–49.

    Google Scholar 

  20. SAVAGE, L.J, (1954) The Foundations of Statistics, New York: Wiley.

    Google Scholar 

  21. SHAFER, G., (1976)A Mathematical Theory of Evidence,Princeton NJ: Princeton University Press.

    Google Scholar 

  22. SCHMEIDLER, D, (1989) “Subjective probability and Expected Utility Without Additivity”, Econometrica, 57, 571–587.

    Article  Google Scholar 

  23. SEGAL, U. (1990) “Two-stage lotteries without the reduction axiom”, Econometrica, 58, 349–377.

    Article  Google Scholar 

  24. WAKKER, P, (1988) “Non expected Utility as Aversion of Information”, Journal of Behavioural Decision making, 1, 169–175.

    Article  Google Scholar 

  25. WALLISER, B., ZWIRN, D. (1995) “Les règles de révision des croyances”, Mimeo CERAS-CREA, Paris.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media New York

About this chapter

Cite this chapter

Chassagnon, A., Vergnaud, JC. (1999). A Positive Value of Information for a Non-Bayesian Decision-Maker. In: Machina, M.J., Munier, B. (eds) Beliefs, Interactions and Preferences in Decision Making. Theory and Decision Library, vol 40. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4592-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-4592-4_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-5096-3

  • Online ISBN: 978-1-4757-4592-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics