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- Title
Uncertainty and binary stochastic choice.
- Authors
Ryan, Matthew
- Abstract
Experimental evidence suggests that decision-making has a stochastic element and is better described through choice probabilities than preference relations. Binary choice probabilities admit a <italic>strong utility representation</italic> if there exists a utility function <italic>u</italic> such that the probability of choosing <italic>a</italic> over <italic>b</italic> is a strictly increasing function of the utility difference u(a)-u(b)<inline-graphic></inline-graphic>. Debreu (Econometrica 26(3):440-444, <xref>1958</xref>) obtained a simple set of sufficient conditions for the existence of a strong utility representation when alternatives are drawn from a suitably rich domain. Dagsvik (Math Soc Sci 55:341-370, <xref>2008</xref>) specialised Debreu’s result to the domain of lotteries (risky prospects) and provided axiomatic foundations for a strong utility representation in which the underlying utility function conforms to expected utility. This paper considers general <italic>mixture set</italic> domains. These include the domain of lotteries, but also the domain of Anscombe-Aumann acts: uncertain prospects in the form of state-contingent lotteries. For the risky domain, we show that one of Dagsvik’s axioms can be weakened. For the uncertain domain, we provide axiomatic foundations for a strong utility representation in which the utility function represents <italic>invariant biseparable</italic> preferences (Ghirardato et al. in J Econ Theory 118:133-173, <xref>2004</xref>). The latter is a wide class that includes subjective expected utility, Choquet expected utility and maxmin expected utility preferences. We prove a specialised strong utility representation theorem for each of these special cases.
- Subjects
STOCHASTIC processes; DECISION making; UTILITY functions; MATHEMATICAL logic; AXIOM of choice
- Publication
Economic Theory, 2018, Vol 65, Issue 3, p629
- ISSN
0938-2259
- Publication type
Article
- DOI
10.1007/s00199-017-1033-4