A Subjective Spin on Roulette Wheels

Creators: Ghirardato, Paolo; Maccheroni, Fabio; Marinacci, Massimo; Sinsicalchi, Marciano

Abstract

We provide a behavioral foundation to the notion of 'mixture' of acts, which is used to great advantage in the decision setting introduced by Anscombe and Aumann. Our construction allows one to formulate mixture-space axioms even in a fully subjective setting, without assuming the existence of randomizing devices. This simplifies the task of developing axiomatic models which only use behavioral data. Moreover, it is immune from the difficulty that agents may 'distort' the probabilities associated with randomizing devices. For illustration, we present simple subjective axiomatizations of some models of choice under uncertainty, including the maxmin expected utility model of Gilboa and Schmeidler, and Bewley's model of choice with incomplete preferences.

Additional Information

An earlier version of this paper was circulated with the title "Subjective Foundations for Objective Randomization: A New Spin on Roulette Wheels". We thank Mark Machina and the audiences at the V SAET Conference (Ischia, July 2001) and the RUD 2001 Conference (Venezia, July 2001) for helpful comments. Maccheroni thanks the Department of Economics at Boston University and the Division of HSS at Caltech, while Siniscalchi thanks the MEDS Department at the Kellogg Graduate School of Management (Northwestern University), for their hospitality while this paper was being written. Published as Ghirardato, P., Maccheroni, F., Marinacci, M., & Siniscalchi, M. (2003). A subjective spin on roulette wheels. Econometrica, 71(6), 1897-1908.

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