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How to co-exist with nonexistent expectations

McCutcheon, Randall G. (2019) How to co-exist with nonexistent expectations. [Preprint]

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Dozens of articles have addressed the challenge that gambles having undefined expectation pose for decision theory. This paper makes two contributions. The first is incremental: we evolve Colyvan's ``Relative Expected Utility Theory'' into a more viable ``conservative extension of expected utility theory" by formulating and defending emendations to a version of this theory proposed by Colyvan and H\'ajek. The second is comparatively more surprising. We show that, so long as one assigns positive probability to the theory that there is a uniform bound on the utility of possible gambles (and assuming a uniform bound on the amount of utility that can accrue in a fixed amount of time), standard principles of anthropic reasoning (as formulated by Brandon Carter) place lower and upper bounds on the expected values of gambles advertised as having no expectation--even assuming that with positive probability, all gambles advertised as having infinite expected utility are administered faithfully. Should one accept the uniform bound premises, this reasoning thus dissolves (or nearly dissolves, in some cases) several puzzles in infinite decision theory.

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Item Type: Preprint
McCutcheon, Randall G.cutch17@yahoo.com0000-0002-5305-3662
Additional Information: Forthcoming in Synthese.
Keywords: St. Petersburg Game, Pasadena Game, Relative Expectation Theory, Infinite Expectation
Subjects: General Issues > Decision Theory
Specific Sciences > Probability/Statistics
Depositing User: Dr. Randall G. McCutcheon
Date Deposited: 12 May 2019 01:56
Last Modified: 12 May 2019 01:56
Item ID: 15997
Subjects: General Issues > Decision Theory
Specific Sciences > Probability/Statistics
Date: 9 May 2019

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