Expected Utility from Multinomial Second-order Probability Distributions
Authors: David Sundgren
Polibits, 42, pp. 71-75, 2010.
Abstract: We consider the problem of maximizing expected utility when utilities and probabilities are given by discrete probability distributions so that expected utility is a discrete stochastic variable. As for discrete second-order distributions, that is probability distributions where the variables are themselves probabilities, the multinomial family is a reasonable choice at least if first-order probabilities are interpreted as relative frequencies. We suggest a decision rule that reflects the uncertainty present in distribution-based probabilities and utilities and we show an example of this rule in action with multinomial second-order distributions.
Keywords: Imprecise probability; second-order probability; discrete probability distributions; multinomial distributions; expected utilty
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