Abstract
This paper considers fair betting odds for certain bets that might be placed in the situation discussed in the so-called Sleeping Beauty Problem. This paper examines what Thirders, Halfers, and Double Halfers must say about the odds as determined by various decision theoretic approaches and argues that Thirders and Halfers have difficulties formulating plausible and coherent positions concerning the relevant betting odds. Double Halfers do not face this problem and that is an important consideration in favor of Double Halfers.
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Notes
It is often left open when the coin toss takes place as the timing of the toss is inessential to the problem. I stipulate it to be before Sleeping Beauty’s first waking to make exposition easier but nothing hangs on this stipulation. I stipulate that the second waking occurs on Wednesday rather than Tuesday for the sake of less confusing abbreviations.
Since you gain 1 dollar in case \(\lnot P\) and lose k dollars if P, this is, as far as the bottom line is concerned, the same as buying a bet that you win in case \(\lnot P\) at odds 1:k, or \(\frac{1}{k}:1\).
Notice that bookies have powerful reasons to lobby for such subsidies for punters: not only will the subsidies tend to encourage betting, they encourage placing bets at odds that are lucrative for bookies. There indeed are tax and other regulations that have this effect—typically more subtle than simple handouts—but that is beyond the scope of this paper.
Briggs (2010) argues for the same point though in a somewhat different manner.
References
Bostrom, N. (2007). Sleeping Beauty and self-location: A hybrid model. Synthese, 157(1), 59–78.
Bradley, D., & Leitgeb, H. (2006). When betting odds and credences come apart: More worries for Dutch Book arguments. Analysis, 66(2), 119.
Briggs, R. (2010). Putting a value on Beauty. Oxford Studies in Epistemology, 3, 3–34.
Conitzer, V. (2015). A Dutch book against sleeping beauties who are evidential decision theorists. Synthese, 192(9), 2887–2899.
Cozic, M. (2011). Imaging and Sleeping Beauty: A case for Double-Halfers. International Journal of Approximate Reasoning, 2(52), 137–143.
Draper, K., & Pust, J. (2008). Diachronic Dutch Books and Sleeping Beauty. Synthese, 164(2), 281–287.
Elga, A. (2000). Self-locating belief and the Sleeping Beauty Problem. Analysis, 60(2), 143–147.
Hitchcock, C. (2004). Beauty and the bets. Synthese, 139(3), 405–420.
Horwich, P. (1987). Asymmetries in time: Problems in the philosophy of science. Cambridge, MA: MIT Press.
Lewis, D. (2001). Sleeping Beauty: Reply to Elga. Analysis, 61(3), 171–176.
Meacham, C. J. G. (2008). Sleeping Beauty and the dynamics of de se beliefs. Philosophical Studies, 138(2), 245–269.
Pust, J. (2012). Conditionalization and essentially indexical credence. The Journal of Philosophy, 109(4), 295–315.
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Many thanks to the anonymous reviewer for insightful comments and suggestions which have made this a much better paper.
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Yamada, M. Beauty, odds, and credence. Philos Stud 176, 1247–1261 (2019). https://doi.org/10.1007/s11098-018-1061-3
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DOI: https://doi.org/10.1007/s11098-018-1061-3