Baumann on the Monty Hall Problem and Single-Case Probabilities

Synthese 158 (1):139-151 (2007)

Authors
Ken M. Levy
Louisiana State University
Abstract
Peter Baumann uses the Monty Hall game to demonstrate that probabilities cannot be meaningfully applied to individual games. Baumann draws from this first conclusion a second: in a single game, it is not necessarily rational to switch from the door that I have initially chosen to the door that Monty Hall did not open. After challenging Baumann's particular arguments for these conclusions, I argue that there is a deeper problem with his position: it rests on the false assumption that what justifies the switching strategy is its leading me to win a greater percentage of the time. In fact, what justifies the switching strategy is not any statistical result over the long run but rather the "causal structure" intrinsic to each individual game itself. Finally, I argue that an argument by Hilary Putnam will not help to save Baumann's second conclusion above.
Keywords Monty Hall  probability  rigidity  causal structure  Peter Baumann  Hilary Putnam
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DOI 10.1007/s11229-006-9065-5
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References found in this work BETA

Paradoxes from A to Z.Michael Clark - 2004 - Revue Philosophique de la France Et de l'Etranger 194 (3):374-375.
Three Doors, Two Players, and Single-Case Probabilities.Peter Baumann - 2005 - American Philosophical Quarterly 42 (1):71 - 79.

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