The beta stochastic utility (β-SU)

Abstract

In this article, a new model for decision making under uncertainty is presented. Here, we model human attitude toward risks to show that an individual estimate of the expected utility of a lottery follows a generalized Beta distribution with a random error that follows a similar distribution. An individual is said to maximize his stochastic utility when requested to present his preference between risky lotteries. Hypothetically, risky lotteries are those exhibiting wider ranges of rewards where human estimate will not be below the utility of the lowest reward nor above the highest of the lottery. The Beta distribution is bounded and complies to such intuitive preconditions with a variance depending on such bounds. The proposed model will overestimate/underestimate the expected utility of a lottery according to the lottery probability mass and individuals' risk attitudes. By such estimation, our model conforms to the fourfold choice pattern. The model also explains the violations present as inconsistencies in the expected utility theory, such as Allais paradox, common consequence effect, common ratio effect, and the violation of betweenness that can be found in the fourfold choice pattern. For the validation purposes, 13 datasets from literature were collected and tested. The β-SU model fits the data at least as good as other approaches such as the CPT/StEUT and presents higher prediction log-likelihoods and less sum of squared errors in most of the cases, a matter that supports the proposition that human estimates of the expected utility may be drawn out of a generalized Beta distribution.

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