Risk: compensation and the expected utility hypothesis

Abstract

The formula for Fair Risk-Compensation (hereafter, FRC) in betting situations is usually expressed as B/p(W), where B is the amount bet and p(W) is the probability of winning. (The psychological interpretation is clear. If an individual has 1 - p(W) chances of losing his investment-- where 1 - p(W)≫p(W), he must stand to gain, should he win, in proportion to his chances of winning; otherwise there is no point to undertaking the risk in the first place.) This formula is highly misleading. It is a trivial matter to construct betting policies where p(L) # 1 - p(W). (I. e. - where the probability of having to pay out money is not equal to the probability of not taking in money.)