The end of Sleeping Beauty’s nightmare

Groisman, Berry (2007) The end of Sleeping Beauty’s nightmare.

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Abstract

The way a rational agent changes her belief in certain proposition/hypotheses in the light of new evidence lies in the heart of Bayesian inference. The basic natural assumption, as summarized in van Fraassen’s Reflection Principle (1984), would be that in the absence of new evidence the belief should not change. Yet, there are examples that are claimed to violate this assumption. The apparent paradox presented by such examples, if not settled, would demonstrate inconsistency and/or incompleteness of the Bayesian approach and without eliminating this inconsistency the approach cannot be regarded as scientific.
The Sleeping Beauty Problem is just such an example. The existing attempts to solve the problem fall into three categories. The first two share a view that the new evidence is absent, but differ in the conclusion of whether Sleeping Beauty should change her belief or not and why. The third category is characterized by a view that, after all, a new evidence (although hidden from the initial view) is available.
My solution is radically different and does not fall into either of these categories. I deflate the paradox by arguing that the two different degrees of belief presented in the Sleeping Beauty Problem are in fact beliefs in two different propositions, i.e. there is no need to explain the (un)change of belief.

Available Versions of this Item

• The end of Sleeping Beauty’s nightmare (deposited 12 June 2007) [Currently Displayed]
  • The end of Sleeping Beauty’s nightmare (deposited 29 October 2007)