Confidence Theory of Choice Under Risk

[abstract of the lecture given at the Laboratory for Experimental Psychology, University of Belgrade, 14. May 2009.]

In this lecture I introduce Confidence Theory as a new behavioral theory of decision making under risk. The development of decision theory in the second half of the 20th century was heavily marked by experimental research. Robust observations of behavioral deviations from normative standards of von Neumann and Morgenstern’s theory of expected utility were established. These basic empirical phenomena boldly challenged the descriptive validity of the expected utility theory. Experimental results provided evidence for human decision making not being constrained by the axioms of rational choice as proposed in von Neumann and Morgenstern’s original work. I discuss two main lines of experimental findings: the first one being related to the famous Allais paradoxes and the second one referring to Kahneman and Tversky’s demonstrations of framing effects and the phenomena of loss aversion. The first version of Prospect Theory (Kahneman & Tversky, 1979) is discussed as well as the more recent Cummulative Prospect Theory (Tversky & Kahneman, 1992). Prospect theory and its variants are of special interest to behavioral scientists since unlike other alternatives to expected utility they do not generalize it.

Confidence Theory presents an attempt at both normative and descriptive explanation of human decision making by explicitly relying on psychological processes of (i) probability representation and (ii) Bayesian belief formation, while leaving intact the decision making process as originally described in von Neumann’s and Morgenstern’s approach. Confidence Theory assumes that (i) representation, (ii) belief formation and (iii) choice are strictly separated processes in human decision making. In Confidence Theory, people are assumed to represent the statistical properties of their economical environments by relevant Pareto distributions - otherwise used in macro-economy to represent the distribution of wealth and income in particular economies. The belief formation phase assumes a rational Bayesian inference relying on subjective probabilities following an idea proposed by Viscusi in 1989. People develop their beliefs on relevant probabilities of gains and losses starting from prior Beta distributions that are parameterized according to information previously represented as parameters of respective Pareto distributions. Following rational Bayesian inference decision makers develop posterior probabilities that are used in choice processes Unlike in Prospect Theory, where decision weights (mathematically, Choquet’s capacities - in Cumulative Prospect Theory) are used to explain Allais related paradoxes, in Confidence Theory we work with proper probabilities (e.g. measures that satisfy Kolmogorov’s axioms). By assumption, gains and losses are initially represented by separate Pareto distributions, enabling the Confidence Theory to account for loss aversion phenomena. The crucial prediction of the Confidence Theory is that probability weighting phenomena are relative to the level of value (utility) and not related to values of probabilities themselves.

In two experiments where direct estimates of monetary equivalents for risky prospects of the (x,p;0,1-p) form were collected we provide empirical verification of our theoretical predictions. The Confidence Theory, which keeps the principles of von Neumann and Morgenstern’s expected utility theory intact, turns out to have more descriptive validity than Prospect Theory. In modeling both experiments the Prospect Theory was formalized by a five-parameter model and the Confidence Theory with a four-parameter one. Both group and individual data were successfully modeled. Additional data on the estimates of the probabilities of gains and losses in the relevant economical environment were modeled successfully by the Confidence Theory’s model; Prospect Theory cannot explain these data even in principle. The crucial prediction of the Confidence Theory on probability weighting relative to the level of utility and not only on the level of probability received clear experimental verification and was successfully modeled in the framework of the Confidence Theory. Again, Prospect Theory does not have any mechanisms to explain these data either. Additional experimental findings on estimates of similarity of monetary gains and losses followed by non-metric multidimensional scaling suggest that internal representation of the utility of money cannot be separated from the representation of its ecologically relevant probability. These finding provide further support for the fundamental assumptions of the Confidence Theory.

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Berger, J. O. (1980). Statistical Decision Theory and Bayesian Analysis. © Springer-Verlag New York, Inc.

Kahneman, D. & Tversky, A. (1979). Prospect Theory. An Analysis of Decision under Risk. Econometrica, 47:2, 263-91.

Tversky, A. & Kahneman, D. (1992). Cumulative Prospect Theory: An Analysis of Decision under Uncertainty. Journal of Risk and Uncertainty, 5, 297-323.

Viscusi, W. K. (1989). Prospective Reference Theory: Toward an Explanation of the Paradoxes. Journal of Risk and Uncertainty, 2, 235-264.