Surreal Decisions

• URL: http://arxiv.org/abs/2111.00862v1
• Date: Sat, 23 Oct 2021 18:37:20 GMT
• Title: Surreal Decisions
• Authors: Eddy Keming Chen and Daniel Rubio
• Abstract summary: We argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. We then bring our theory to bear on one of the more venerable decision problems in the literature: Pascal's Wager.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• A decision-theoretic approach to dealing with uncertainty in quantum mechanics [42.166654559515244]
  We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. We show that measurements play the role of acts with an uncertain outcome. We discuss the mathematical implications of our findings.
  arXiv  Detail & Related papers  (2025-03-26T14:53:06Z)
• Algorithmic idealism: what should you believe to experience next? [0.0]
  I argue for an approach to the Foundations of Physics that puts the question in the title center stage, rather than asking "what is the case in the world?" Algorithmic Idealism is a conceptual framework, based on two postulates that admit several possible mathematical formalizations.
  arXiv  Detail & Related papers  (2024-12-03T20:44:32Z)
• Machine learning and information theory concepts towards an AI Mathematician [77.63761356203105]
  The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. This essay builds on the idea that current deep learning mostly succeeds at system 1 abilities. It takes an information-theoretical posture to ask questions about what constitutes an interesting mathematical statement.
  arXiv  Detail & Related papers  (2024-03-07T15:12:06Z)
• Betting on what is neither verifiable nor falsifiable [18.688474183114085]
  We propose an approach to betting on such events via options, or equivalently as bets on the outcome of a "verification-falsification game" Our work thus acts as an alternative to the existing framework of Garrabrant induction for logical uncertainty, and relates to the stance known as constructivism in the philosophy of mathematics.
  arXiv  Detail & Related papers  (2024-01-29T17:30:34Z)
• A new foundation of quantum decision theory [0.0]
  It is assumed that each accessible variable can be seen as a function of a specific inaccessible variable. Two basic assumptions behind the Born rule are 1) the likelihood principle, 2) the actor in question has motivations that can be modeled by a hypothetical perfectly rational higher being.
  arXiv  Detail & Related papers  (2023-10-19T14:08:02Z)
• Logic meets Wigner's Friend (and their Friends) [49.1574468325115]
  We take a fresh look at Wigner's Friend thought-experiment and some of its more recent variants and extensions. We discuss various solutions proposed in the literature, focusing on a few questions.
  arXiv  Detail & Related papers  (2023-07-04T13:31:56Z)
• Connecting classical finite exchangeability to quantum theory [69.62715388742298]
  Exchangeability is a fundamental concept in probability theory and statistics. We show how a de Finetti-like representation theorem for finitely exchangeable sequences requires a mathematical representation which is formally equivalent to quantum theory.
  arXiv  Detail & Related papers  (2023-06-06T17:15:19Z)
• The Smoothed Likelihood of Doctrinal Paradox [34.534516291695155]
  We show that under mild conditions, the smoothed likelihood of the doctrinal paradox is either $0$, $exp(-Theta(n))$, $Theta(n-1/2)$ or $Theta(1)$. Our main theorem states that under mild conditions, the smoothed likelihood of the doctrinal paradox is either $0$, $exp(-Theta(n))$, $Theta(n-1/2)$ or $Theta(1)$.
  arXiv  Detail & Related papers  (2021-05-11T15:55:47Z)
• The view from a Wigner bubble [0.0]
  I argue that the key distinction between QBism and realist interpretations of quantum mechanics is best understood in terms of their adherence to different theories of truth. The notion of reality afforded by QBism will correspond to the invariant elements of any theory that has pragmatic value to all rational agents.
  arXiv  Detail & Related papers  (2020-08-12T04:21:33Z)
• Moore's Paradox and the logic of belief [0.0]
  Moores Paradox is a test case for any formal theory of belief. I argue that Hintikkas interpretation of one of the doxastic operators is philosophically problematic.
  arXiv  Detail & Related papers  (2020-06-19T20:41:19Z)
• Non-Boolean Hidden Variables model reproduces Quantum Mechanics' predictions for Bell's experiment [91.3755431537592]
  Theory aimed to violate Bell's inequalities must start by giving up Boolean logic. "Hard" problem is to predict the time values when single particles are detected. "Soft" problem is to explain the violation of Bell's inequalities within (non-Boolean) Local Realism.
  arXiv  Detail & Related papers  (2020-05-20T21:46:35Z)
• Epistemic Phase Transitions in Mathematical Proofs [0.0]
  We show that under a cognitively-plausible belief formation mechanism, belief in mathematical arguments can undergo a dramatic and rapidly-propagating jump from uncertainty to near-complete confidence at reasonable levels of claim-to-claim error rates. Our results bear both on recent work in the history and philosophy of mathematics on how we understand proofs, and on a question, basic to cognitive science, of how we justify complex beliefs.
  arXiv  Detail & Related papers  (2020-03-31T18:39:56Z)
• Indeterminism and Undecidability [0.0]
  Chaitin's follow-up to Goedel's (first) incompleteness theorem can be proved. The main point is that Bell and others did not exploit the full empirical content of quantum mechanics.
  arXiv  Detail & Related papers  (2020-03-07T11:06:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.