Realistic utility versus game utility: a proposal for dealing with the spread of uncertain prospects
AbstractThe author develops the properties and implications of a proposal, concerning a summary statistic of the random prospect of utilities. Following a suggestion of Allais, such a statistic is increasing with expected utility, and decreasing – for most people, who are risk averse – with the mean absolute deviation of utilities; a parameter multiplying this disper sion measure allows for risk averse or risk prone behaviour, according to its sign, and also for more or less departure from a certain prospect. It is demonstrated that this statistic (a) satisfies the first stochastic dominance, (b) satisfies the independence condition, (c) satisfies the so called “problem of probabilistic insurance”, (d) resolves the paradoxes of Allais, Ellsberg and Kahneman-Tversky (paradox of the substitution axiom), (e) is compatible with Quiggin’s approach of rank-dependent expected utility models, (f) the mean absolute deviation cannot be replaced by the standard deviation
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