I give a Dutch book argument for CDT thirders in the context of a generalized Sleeping Beauty scenario. In combination with the Briggs (2010) Dutch book for EDT thirders, this amounts to a purely decision-theoretic argument for halfing in Sleeping Beauty. In combination with the Hitchcock (2004) Dutch book for CDT halfers, this amounts to a Dutch book argument against CDT. The combined Dutch book against CDT invites a plausible diagnosis of the reasons for CDT’s failure: CDT is incompatible with (...) the Dutch book requirement because it allows the values of epistemically impossible outcomes influence one’s decision. (shrink)

The Sleeping Beauty problem has attracted considerable attention in the literature as a paradigmatic example of how self-locating uncertainty creates problems for the Bayesian principles of Conditionalization and Reflection. Furthermore, it is also thought to raise serious issues for diachronic Dutch Book arguments. I show that, contrary to what is commonly accepted, it is possible to represent the Sleeping Beauty problem within a standard Bayesian framework. Once the problem is correctly represented, the ‘thirder’ solution satisfies standard rationality principles, vindicating why (...) it is not vulnerable to diachronic Dutch Book arguments. Moreover, the diachronic Dutch Books against the ‘halfer’ solutions fail to undermine the standard arguments for Conditionalization. The main upshot that emerges from my discussion is that the disagreement between different solutions does not challenge the applicability of Bayesian reasoning to centered settings, nor the commitment to Conditionalization, but is instead an instance of the familiar problem of choosing the priors. (shrink)

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.

Significant controversy remains about what constitute correct self-locating beliefs in scenarios such as the Sleeping Beauty problem, with proponents on both the “halfer” and “thirder” sides. To attempt to settle the issue, one natural approach consists in creating decision variants of the problem, determining what actions the various candidate beliefs prescribe, and assessing whether these actions are reasonable when we step back. Dutch book arguments are a special case of this approach, but other Sleeping Beauty games have also been constructed (...) to make similar points. Building on a recent article :491–508, 2013), I show that in general we should be wary of such arguments, because unintuitive actions may result for reasons that are unrelated to the beliefs. On the other hand, I show that, when we restrict our attention to additive games, then a thirder will necessarily maximize her ex ante expected payout, but a halfer in some cases will not . I conclude that this does not necessarily settle the issue and speculate about what might. (shrink)

Newcomb’s problem has spawned a debate about which variant of expected utility maximisation should guide rational choice. In this paper, we provide a new argument against what is probably the most popular variant: causal decision theory. In particular, we provide two scenarios in which CDT voluntarily loses money. In the first, an agent faces a single choice and following CDT’s recommendation yields a loss of money in expectation. The second scenario extends the first to a diachronic Dutch book against CDT.