Surreal Decisions


Authors
Eddy Keming Chen
University of California, San Diego
Daniel Rubio
Princeton University
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.
Keywords infinite values  Pascal's Wager  surreal numbers  expected utility theory  dominance principles  von Neumann-Morgenstern theorem  degrees of glory
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Reprint years 2018, 2020
DOI 10.1111/phpr.12510
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References found in this work BETA

Risk and Rationality.Lara Buchak - 2013 - Oxford University Press.
What Are Degrees of Belief.Lina Eriksson & Alan Hájek - 2007 - Studia Logica 86 (2):185-215.
Fair Infinite Lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.

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Citations of this work BETA

Salvaging Pascal’s Wager.Elizabeth Jackson & Andrew Rogers - 2019 - Philosophia Christi 21 (1):59-84.
Infinitesimal Probabilities.Sylvia Wenmackers - 2016 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 199-265.
Wagering Against Divine Hiddenness.Elizabeth Jackson - 2016 - European Journal for Philosophy of Religion 8 (4):85-108.

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