Derivation of probability weighting and value functions by Decision by Sampling model: Model comparison with Bayesian statistical modeling

Abstract

Cumulative prospect theory predicts that probabilities presented objectively are subjectively transformed to facilitate decision-making. Two types of probability weighting functions have been proposed: those derived from axiomatic approaches and those from psychological mechanisms. However, interpreting many model parameters through psychological theories remains challenging. Thus, this study aims to introduce a new probability weighting function and value function based on the Decision by Sampling (DbS) model, which elucidates the information processing mechanism in cognitive psychology. Initially, it assumes that the value of probabilistic information can be represented by the amount of Kullback-Leibler (KL) information. A probability weighting function was consequently derived from the DbS model, yielding a cumulative distribution function characterized by a beta distribution. Similarly, the value function is expressed as a cumulative distribution function of the beta distribution, grounded in the assumptions of DbS and the mental ruler theory. Results from Bayesian statistical model comparison indicated that the probability weighting function of our proposed model exhibited relatively lower prediction accuracy compared to previously proposed models. However, the value function’s accuracy significantly improved. Moreover, comparisons with the Gaussian process model suggest that the overall proposed model possesses adequate forecasting accuracy. This study’s proposed model is significant, offering a mechanism within prospect theory that is both highly accurate in predictions and psychologically interpretable.