Breaking the cycle of behaviour in decision making under uncertainty

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g charles-cadogan

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Dec 1, 2012, 11:00:58 AM12/1/12

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Dear DT Forumites:

The attached draft contains the bibliographical references which are reviewed as indicated. Basically, the paper proves mathematically what we know from experience: Breaking the cycle of behavior causes us not to engage in the same pattern of conduct when faced with the same stimuli. The paper is motivated (in part) by the problem of selecting a coherent set of priors via the maximum entropy principle proposed by Good (1963), and employed by Jaynes (1968) to address shortcomings of Savage’s (1954, 1972) personal probability theory. It introduces a harmonic probability weighting function (HPWF) that provides a theoretical explanation for Kahneman and Tversky (1979, pg. 282) “quantal effect” or fluctuation near the end points 0 and 1 of probability weighting functions. A working paper by al-Nowaihi and Dharni (2010) proposes a synthesis of prospect theory and cumulative prospective theory to explain that result. The HPWF generates the same probabilities at discrete cycles. However, when those cycles are broken different probabilities are generated. In psychology, one way of breaking the cycle is via interruption of circadian cycles. If so, then from an experimental economics perspective, time of day may affect probabilistic preferences for subjects facing the same underlying stimuli in repeated experiments.

The paper also identifies a cluster set of fixed point probabilities that constitute a linear subspace in the space of probability measures. Thus, the complementary space is nonlinear probabilities. So we have a de facto “probability hyperplane separation” result. Intuitively, in two dimensions, this coincides with Tversky and Wakker (1995, Fig. 3) where the “middle portion” of the weighting function is a straight line but it is nonlinear elsewhere. Perhaps more important, it provides a probabilistic preference foundation for Loomes Sugden (1982) and Koszegi and Rabin (2006) type hybridized models of expected utility and nonexpected utility theories. For example, the EUT component of those models rests on the cluster set of fixed point probabilities, i.e. a linear subspace, while the nonexpected utility component is supported by the complimentary nonlinear probability subspace.