IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2510.15911.html

The Sleeping Beauty Problem: Sleeping Kelly is a Thirder

Author

Listed:
  • 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.

Suggested Citation

  • Ben Abramowitz, 2025. "The Sleeping Beauty Problem: Sleeping Kelly is a Thirder," Papers 2510.15911, arXiv.org, revised Jan 2026.
    • Handle: RePEc:arx:papers:2510.15911
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2510.15911
    File Function: Latest version
    Download Restriction: no
    ---><---

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2510.15911. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.