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Discounting Desirable Gambles

Wheeler, Gregory (2021) Discounting Desirable Gambles. [Preprint]


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The desirable gambles framework offers the most comprehensive foundations for the theory of lower previsions, which in turn affords the most general ac- count of imprecise probabilities. Nevertheless, for all its generality, the theory of lower previsions rests on the notion of linear utility. This commitment to linearity is clearest in the coherence axioms for sets of desirable gambles. This paper considers two routes to relaxing this commitment. The first preserves the additive structure of the desirable gambles framework and the machinery for coherent inference but detaches the interpretation of desirability from the multiplicative scale invariance axiom. The second strays from the additive combination axiom to accommodate repeated gambles that return rewards by a non-stationary processes that is not necessarily additive. Unlike the first approach, which is a conservative amendment to the desirable gambles framework, the second is a rad- ical departure. Yet, common to both is a method for describing rewards called discounted utility.

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Item Type: Preprint
Wheeler, Gregory
Keywords: Desirability, ergodicity, non-linear utility, lower previsions, imprecise probability
Subjects: General Issues > Decision Theory
Specific Sciences > Probability/Statistics
Depositing User: Gregory Wheeler
Date Deposited: 23 Sep 2021 03:54
Last Modified: 23 Sep 2021 03:54
Item ID: 19606
Official URL:
Subjects: General Issues > Decision Theory
Specific Sciences > Probability/Statistics
Date: July 2021

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