Paper: arXiv 2510.15911

Authors: Ben Abramowitz

Abstract

The Sleeping Beauty problem is a problem of imperfect recall that has received considerable attention. One approach to solving the Sleeping Beauty problem is to allow Sleeping Beauty to make decisions based on her beliefs, and then characterize what it takes for her decisions to be “rational”. In particular, she can be allowed to make monetary bets based on her beliefs, with the assumption that she wants to gain wealth rather than lose it. However, this approach is often coupled with the assumption that Sleeping Beauty should maximize the expected value of her bets. Here, show that Sleeping Beauty maximizes the expected growth rate of her wealth as a “thirder” sizing bets using the Kelly Criterion under multiplicative dynamics. Furthermore, this position is shown to be impervious to Dutch books. By contrast, the “halfer” position is shown to be vulnerable to Dutch books under similar circumstances.

Complexity vs Empirical Score

  • Math Complexity: 3.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Philosophers — conceptual discussion, limited math and data

Why this score: The paper provides a clever and novel perspective on the classic Sleeping Beauty paradox by framing it through ergodic economics and the Kelly Criterion rather than standard expected utility theory. However, it is fundamentally a theoretical/philosophical inquiry with simple algebra rather than an empirical or computationally rigorous finance paper.

Research Flowchart

  flowchart TD
    A[Research Goal: Determine Rational Bet Sizing for Sleeping Beauty] --> B[Inputs: Multiplicative Wealth Dynamics & Sleeping Beauty Setup]
    B --> C[Methodology: Apply Kelly Criterion for Growth Rate Maximization]
    C --> D[Compute Optimal Bet Sizes & Test Against Dutch Books]
    D --> E[Outcome 1: Thirder Position Maximizes Expected Growth Rate]
    D --> F[Outcome 2: Thirder is Impervious to Dutch Books while Halfer is Vulnerable]

Cited References (25)

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and 17 more
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  4. Sleeping beauty: reply to Elga (2001)
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  11. Observer Theory (2023)
  12. Mathematica, V ersion 14.1 — link
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  15. A devastating example for the Halfer Rule (2015)
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0 of 25 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.