Further Analysis of the Markowitz Model of Utility with a Small Degree of Probability Distortion

Explanation of the Allais paradox and the preference of many for multiple prize lottery tickets provide a rationale for why a model of agent's choice under uncertainty should embody the assumption that they distort probabilities. However the degree of probability distortion required to explain gambling on long shots in Cumulative Prospect Theory appears problematic since it implies subjective expected rates of return are dramatically higher than objective returns. Here we show that a Markowitz model of expected utility, supplemented by a small degree of probability distortion, has qualitatively similar predictions as Cumulative Prospect Theory for numerous experimental outcomes as well as the indifference curves between expected return and objective probabilities for a given stake gamble. In addition we show how a small degree of probability distortion can lead to a preference for a multiple prize lottery which has a rather different prize structure and associated probabilities than the optimally chosen one prize lottery even though the utility gain is small.