Monty hall drives a wedge between Judy Benjamin and the sleeping beauty: A reply to Bovens

Analysis 70 (3):473 - 481 (2010)
Luc Bovens
University of North Carolina, Chapel Hill
In “Judy Benjamin is a Sleeping Beauty” (2010) Bovens recognises a certain similarity between the Sleeping Beauty (SB) and the Judy Benjamin (JB). But he does not recognise the dissimilarity between underlying protocols (as spelled out in Shafer (1985). Protocols are expressed in conditional probability tables that spell out the probability of coming to learn various propositions conditional on the actual state of the world. The principle of total evidence requires that we not update on the content of the proposition learned but rather on the fact that we learn the proposition in question. Now attention to protocols drives a wedge between the SB and the JB. We have shown that the solution to a close variant of the SB which involves a clear protocol is P*(Heads) = 1/3 and since Beauty’s has precisely the same information at her disposal in the original SB at the time that she is asked to state her credence for Heads, the same solution should hold. The solution to the JB, on the other hand, is dependent on Judy’s probability distribution over protocols. One reasonable protocol yields P(Red) = 1/2, but Judy could also defend alternative values or a range of values in the interval [1/3, 1/2] depending on her probability distribution over protocols.
Keywords Judy Benjamin  Shafer  Protocols  Updating Credences  Monty Hall  Sleeping Beauty
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DOI 10.1093/analys/anq020
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References found in this work BETA

Judy Benjamin is a Sleeping Beauty.Luc Bovens - 2010 - Analysis 70 (1):23-26.
A Problem for Relative Information Minimizers in Probability Kinematics.Bas C. van Fraassen - 1981 - British Journal for the Philosophy of Science 32 (4):375-379.

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Confirmation in a Branching World: The Everett Interpretation and Sleeping Beauty.Darren Bradley - 2011 - British Journal for the Philosophy of Science 62 (2):323-342.
Sleeping Beauty Should Be Imprecise.Daniel Jeremy Singer - 2014 - Synthese 191 (14):3159-3172.
Natural Language and Logic of Agency.Johan van Benthem - 2014 - Journal of Logic, Language and Information 23 (3):367-382.

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