Probabilistic Extention of the Cumulative Prospect Theory

Abstract

A number of experiments indicate probabilistic preferences in cases where no one alternative is absolutely optimal. The task of predicting the choice of one of the alternatives among multiple alternatives is then practically important and not trivial. It can occur in situations of choice under risk when no one lottery stochastically dominates others.For risky lotteries there are several complicated models of probabilistic binary preference. For the first time, we herein propose the probabilistic extension of the cumulative prospect theory (CPT). The presented visual graphic justification of this model is intuitively clear and does not use sophisticated cumulative summing or a Choquet integral. Here we propose a model of selecting from a set of alternatives by continuous Markov random walks. It makes predicting the results of a choice easy because it fully uses dates received by probabilistic extension of СPT. The proposed methods are quite simple and do not require a large amount of data for practical use.