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Hierarchical Maximization of Two Kinds of Expected Utility

Published online by Cambridge University Press:  01 April 2022

Paul Weirich
Paul Weirich*
Affiliation:
Department of Philosophy University of Missouri
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Abstract

Causal decision theory produces decision instability in cases such as Death in Damascus where a decision itself provides evidence concerning the utility of options. Several authors have proposed ways of handling this instability. William Harper (1985 and 1986) advances one of the most elegant proposals. He recommends maximizing causal expected utility among the options that are causally ratifiable. Unfortunately, Harper's proposal imposes certain restrictions; for instance, the restriction that mixed strategies are freely available. To obtain a completely general method of handling decision instability, I step outside the confines of pure causal decision theory. I introduce a new kind of backtracking expected utility and propose maximizing it among the options that are causally ratifiable. In other words, I propose a hierarchical maximization of (1) conditional causal expected utility and (2) the new backtracking expected utility. I support this proposal with some intuitive considerations concerning the distinction between optimality and conditional optimality. And I prove that the proposal yields a solution in every finite decision problem.

Type
Research Article
Information
Philosophy of Science , Volume 55 , Issue 4 , December 1988 , pp. 560 - 582
Copyright
Copyright © 1988 by the Philosophy of Science Association

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Footnotes

†

I presented a precursor of this paper at the 1986 Western APA meeting. William Harper was the commentator. I am grateful to him and the audience for an enlightening discussion. Also, I am indebted to Ellery Eells and Reed Richter for stimulating correspondence on decision instability. And finally, I would like to thank the referees for many helpful suggestions.

References

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