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Surreal Decisions

Chen, Eddy Keming and Rubio, Daniel (2020) Surreal Decisions. Philosophy and Phenomenological Research, 100 (1). pp. 54-74.

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Abstract

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Chen, Eddy Kemingeddykemingchen@ucsd.edu0000-0001-5144-0952
Rubio, Daniel
Keywords: decision theory, dominance principles, in nite values, surreal numbers, Pascal's Wager, mixed strategies, representation theorem, pragmatic argument
Subjects: General Issues > Decision Theory
General Issues > Evidence
General Issues > Game Theory
Specific Sciences > Probability/Statistics
Depositing User: Dr. Eddy Keming Chen
Date Deposited: 24 Oct 2021 03:44
Last Modified: 24 Oct 2021 03:44
Item ID: 19741
Journal or Publication Title: Philosophy and Phenomenological Research
Official URL: https://doi.org/10.1111/phpr.12510
DOI or Unique Handle: 10.1111/phpr.12510
Subjects: General Issues > Decision Theory
General Issues > Evidence
General Issues > Game Theory
Specific Sciences > Probability/Statistics
Date: 2020
Page Range: pp. 54-74
Volume: 100
Number: 1
URI: http://philsci-archive.pitt.edu/id/eprint/19741

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