On the utility of gambling: extending the approach of Meginniss (1976)

J. R. Meginniss modified expected utility to accommodate a concept of the utility of gambling that led to a representation composed of a utility expectation term plus an entropy of degree κ term. He imposed several apparently strong assumptions. One of these is that a number of unknown generating functions are identical. A second is that he assumed he was working with given probabilities. Here we follow his general framework but weaken considerably those assumptions. Our problem is reduced to solving some functional equations induced by gamble decomposition. From the solutions, we obtain the representation of the utility function. Further axiomatic restrictions are imposed that lead ultimately to Meginniss' earlier result.