Chen, Eddy Keming and Rubio, Daniel (2020) Surreal Decisions. Philosophy and Phenomenological Research, 100 (1). pp. 54-74.
|
Text
Surreal Decisions PPR Final Archive.pdf Download (349kB) | Preview |
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.
| Export/Citation: | EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL |
| Social Networking: |
| Item Type: | Published Article or Volume | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Creators: |
|
|||||||||
| 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: | https://philsci-archive.pitt.edu/id/eprint/19741 |
Monthly Views for the past 3 years
Monthly Downloads for the past 3 years
Plum Analytics
Altmetric.com
Actions (login required)
 |
View Item |
![[feed]](http://philsci-archive.pitt.edu/style/images/feed-icon-32x32.png){kind=icon}