Toward a Rational-Choice Foundation of Non-Additive Theories
AbstractA classical argument of de Finetti holds that Rationality implies Subjective Expected Utility (SEU). In contrast, the Knightian distinction between Risk and Ambiguity suggests that a rational decision maker would obey the SEU paradigm when the information available is in some sense good, and would depart from it when the information available is not good. Unlike de Finetti's, however, this view does not rely on a formal argument. In this paper, we study the set of all information structures that might be availabe to a decision maker, and show that they are of two types: those compatible with SEU theory and those for which SEU theory must fail. We also show that the former correspond to "good" information, while the latter correspond to information that is not good. Thus, our results provide a formalization of the distinction between Risk and Ambiguity. As a consequence of our main theorem (Theorem 2, Section 8), behavior not-conforming to SEU theory is bound to emerge in the presence of Ambiguity. We give two examples of situations of Ambiguity. One concerns the uncertainty on the class of measure zero events, the other is a variation on Ellberg's three-color urn experiment. We also briefly link our results to two other strands of literature: the study of ambiguous events and the problem of unforeseen contingencies. We conclude the paper by re-considering de Finetti?s argument in light of our findings.
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Bibliographic InfoPaper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 13-2009.
Length: 37 pages
Date of creation: 2009
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Other versions of this item:
- AMARANTE, Massimiliano, 2009. "Toward a Rational-Choice Foundation of Non-Additive Theories," Cahiers de recherche 2009-12, Universite de Montreal, Departement de sciences economiques.
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- David Schmeidler, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Levine's Working Paper Archive
7662, David K. Levine.
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1202, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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- Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
- Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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