Expected Utility from Multinomial Second–order Probability Distributions

 

David Sundgren

 

University of Gävle, Sweden. (dsn@hig.se).

 

Manuscript received June 8, 2010.
Manuscript accepted for publication July 25, 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.

Key words: Imprecise probability. second–order probability, discrete probability distributions, multinomial distributions, expected utilty.

 

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