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Preference for Randomization and Ambiguity Aversion

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  • Kaito Sato
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    Abstract

    Raiffa (1961) criticizes ambiguity-averse preferences by claiming that hedging is possible with randomization of choices. We argue that the timing of randomization is crucial for hedging. Ex-ante randomizations, which are randomizations before a state is realized, could provide only ex-ante hedging but not ex-post hedging, in contrast to ex-post randomizations, which are randomizations after a state is realized. However, these two randomizations have been assumed to be indifferent under the reversal of order axiom proposed by Anscombe and Aumann (1963). We, therefore, propose a weaker axiom, the indifference axiom, which allows heterogeneous attitudes toward the timing of randomization. By using this new axiom as well as standard axioms, we provide an extension of Gilboa and Schmeidler’s (1989) Maxmin preferences that treats a preference for ex-ante randomizations separately from a preference for ex-post randomizations. In the representation, a single parameter characterizes a preference for ex-ante randomizations. By parsimoniously changing only the value of that single parameter, the representation can be consistent with Raiffa’s (1961) normative argument as well as recent experimental evidence. JEL Classification Numbers: D81, D03

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    Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1524.

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    Date of creation: 10 Apr 2011
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    Handle: RePEc:nwu:cmsems:1524

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    1. David M Kreps & Evan L Porteus, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Levine's Working Paper Archive 625018000000000009, David K. Levine.
    2. Nadja Dwenger & Dorothea Kübler & Georg Weizsäcker, 2013. "Preference for Randomization: Empirical and Experimental Evidence," SFB 649 Discussion Papers SFB649DP2013-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Adam Dominiak & Wendelin Schnedler, 2011. "Attitudes toward uncertainty and randomization: an experimental study," Economic Theory, Springer, vol. 48(2), pages 289-312, October.
    4. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    5. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
    6. Mukerji Sujoy & Shin Hyun Song, 2002. "Equilibrium Departures from Common Knowledge in Games with Non-Additive Expected Utility," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 2(1), pages 1-30, June.
    7. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
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