Setup and the two answers
The problem grew out of the same line of work as Piccione and Rubinstein's (1997) decision problems with imperfect recall and Aumann, Hart and Perry's (1997) discussion of the absent-minded driver. Elga (2000) argued that Beauty's credence in heads should be one-third, on the grounds that the three situations she might be in on waking, heads-Monday, tails-Monday and tails-Tuesday, are symmetric. Lewis (2001) replied that Beauty learns nothing new beyond the fact that she is awake, which was certain to happen either way, so her credence should stay at the coin's original probability of one-half. The debate turns on how Bayesian conditionalization should handle self-locating beliefs about when and where one is.
Key arguments and objections
Thirders appeal to a frequency argument, that across many repetitions only one-third of awakenings follow heads, and to a betting argument, that if Beauty makes the same bet at every waking, credences of one-third avoid a sure loss. Hitchcock (2004) analyzed the betting argument in detail, and Dorr (2002) offered a thought experiment defending Elga. Arntzenius (2002) and Briggs (2010), however, held that the rational price of a bet can depend on its structure, so betting alone cannot fix credences. Bostrom (2007) proposed a hybrid model combining the two views, Titelbaum (2008) developed a new framework for updating on self-locating information that changes over time, and Pust (2012) examined conditionalization on essentially indexical credences.
Anthropics and the wider stakes
Bostrom (2002) placed the problem within the broader framework of observation selection effects, arguing that how we treat the very fact that observers exist as evidence matters for cosmology, the Fermi paradox and the doomsday argument. Extending the thirder logic favors hypotheses with more observers, while halfer logic leads the other way. Titelbaum (2013) laid out why the problem reaches into probability theory, decision theory and even the many-worlds interpretation of quantum mechanics. Along with Newcomb's paradox, it is a leading test case for the foundations of rational belief and choice.
FAQ
- What is the Sleeping Beauty problem in simple terms?
- Someone is woken once if a coin lands heads and twice if it lands tails, forgetting each waking. When she wakes up, how likely should she think it is that the coin landed heads?
- Is the answer one-third or one-half?
- There's no consensus. Counting awakenings gives one-third, while stressing that she learns nothing new gives one-half. Many philosophers lean toward one-third, but the debate is ongoing.
Sources reviewed: 2026-10-26
References
- Elga, A. (2000). Self-locating belief and the Sleeping Beauty problem. Analysis, 60(2), 143–147.
- Lewis, D. (2001). Sleeping Beauty: Reply to Elga. Analysis, 61(3), 171–176.
- Piccione, M., & Rubinstein, A. (1997). On the interpretation of decision problems with imperfect recall. Games and Economic Behavior, 20(1), 3–24.
- Arntzenius, F. (2002). Reflections on Sleeping Beauty. Analysis, 62(1), 53–62.
- Dorr, C. (2002). Sleeping Beauty: In defence of Elga. Analysis, 62(4), 292–296.
- Bostrom, N. (2002). Anthropic Bias: Observation Selection Effects in Science and Philosophy. New York: Routledge.
- Bostrom, N. (2007). Sleeping Beauty and self-location: A hybrid model. Synthese, 157(1), 59–78.
- Titelbaum, M. G. (2008). The relevance of self-locating beliefs. Philosophical Review, 117(4), 555–606.
- Hitchcock, C. (2004). Beauty and the bets. Synthese, 139(3), 405–420.
- Briggs, R. (2010). Putting a value on Beauty. In T. S. Gendler & J. Hawthorne (Eds.), Oxford Studies in Epistemology (Vol. 3, pp. 3–34). Oxford: Oxford University Press.
- Pust, J. (2012). Conditionalization and essentially indexical credence. Journal of Philosophy, 109(4), 295–315.
- Aumann, R. J., Hart, S., & Perry, M. (1997). The absent-minded driver. Games and Economic Behavior, 20(1), 102–116.
- Titelbaum, M. G. (2013). Ten reasons to care about the Sleeping Beauty problem. Philosophy Compass, 8(11), 1003–1017.