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  1. Peter Baumann (2008). Single-Case Probabilities and the Case of Monty Hall: Levy's View. Synthese 162 (2):265 - 273.
    In Baumann (American Philosophical Quarterly 42: 71–79, 2005) I argued that reflections on a variation of the Monty Hall problem throws a very general skeptical light on the idea of single-case probabilities. Levy (Synthese, forthcoming, 2007) puts forward some interesting objections which I answer here.
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  2. L. Bovens & J. L. Ferreira (2010). Monty Hall Drives a Wedge Between Judy Benjamin and the Sleeping Beauty: A Reply to Bovens. Analysis 70 (3):473-481.
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  3. Darren Bradley (2007). Bayesianism And Self-Locating Beliefs. Dissertation, Stanford University
    How should we update our beliefs when we learn new evidence? Bayesian confirmation theory provides a widely accepted and well understood answer – we should conditionalize. But this theory has a problem with self-locating beliefs, beliefs that tell you where you are in the world, as opposed to what the world is like. To see the problem, consider your current belief that it is January. You might be absolutely, 100%, sure that it is January. But you will soon believe it (...)
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  4. Darren Bradley & Branden Fitelson (2003). Monty Hall, Doomsday and Confirmation. Analysis 63 (277):23–31.
    We give an analysis of the Monty Hall problem purely in terms of confirmation, without making any lottery assumptions about priors. Along the way, we show the Monty Hall problem is structurally identical to the Doomsday Argument.
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  5. Darren Bradley & Branden Fitelson (2003). Monty Hall, Doomsday and Confirmation. Analysis 63 (1):23-31.
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  6. Charles B. Cross (2000). A Characterization of Imaging in Terms of Popper Functions. Philosophy of Science 67 (2):316-338.
    Despite the results of David Lewis, Peter Gärdenfors, and others, showing that imaging and classical conditionalization coincide only in the most trivial probabilistic models of belief revision, it turns out that imaging on a proposition A can always be described via Popper function conditionalization on a proposition that entails A. This result generalizes to any method of belief revision meeting certain minimal requirements. The proof is illustrated by an application of imaging in the context of the Monty Hall Problem.
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  7. José Luis Ferreira (2010). Monty Hall Drives a Wedge Between Judy Benjamin and the Sleeping Beauty: A Reply to Bovens. Analysis 70 (3):473 - 481.
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  8. Branden Fitelson (2007). Likelihoodism, Bayesianism, and Relational Confirmation. Synthese 156 (3):473 - 489.
    Likelihoodists and Bayesians seem to have a fundamental disagreement about the proper probabilistic explication of relational (or contrastive) conceptions of evidential support (or confirmation). In this paper, I will survey some recent arguments and results in this area, with an eye toward pinpointing the nexus of the dispute. This will lead, first, to an important shift in the way the debate has been couched, and, second, to an alternative explication of relational support, which is in some sense a "middle way" (...)
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  9. Ana Franco-Watkins, Peter Derks & Michael Dougherty (2003). Reasoning in the Monty Hall Problem: Examining Choice Behaviour and Probability Judgements. Thinking and Reasoning 9 (1):67 – 90.
    This research examined choice behaviour and probability judgement in a counterintuitive reasoning problem called the Monty Hall problem (MHP). In Experiments 1 and 2 we examined whether learning from a simulated card game similar to the MHP affected how people solved the MHP. Results indicated that the experience with the card game affected participants' choice behaviour, in that participants selected to switch in the MHP. However, it did not affect their understanding of the objective probabilities. This suggests that there is (...)
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  10. Jeffrey N. Howard, Charles G. Lambdin & Darcee L. Datteri (2007). Let's Make a Deal: Quality and Availability of Second-Stage Information as a Catalyst for Change. Thinking and Reasoning 13 (3):248 – 272.
    The Monty Hall Problem (MHP), a process of two-stage decision making, was presented in atypical form via a custom software game. Differing from the normal three-box MHP, the game added one additional box on-screen for each game—culminating on game 23 with 25 on-screen boxes to initially choose from. A total of 108 participants played 23 games (trials) in one of four conditions; (1) “Vanish” condition—all non-winning boxes totally removed from the screen; (2) “Empty” condition—all non-winning boxes remain on-screen, but with (...)
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  11. Ken Levy (2007). Baumann on the Monty Hall Problem and Single-Case Probabilities. Synthese 158 (1):139 - 151.
    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 (...)
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  12. Brian Skyrms (1966). Choice and Chance. Belmont, Calif.,Dickenson Pub. Co..
  13. Jan Sprenger (2010). Probability, Rational Single-Case Decisions and the Monty Hall Problem. Synthese 174 (3):331 - 340.
    The application of probabilistic arguments to rational decisions in a single case is a contentious philosophical issue which arises in various contexts. Some authors (e.g. Horgan, Philos Pap 24:209–222, 1995; Levy, Synthese 158:139–151, 2007) affirm the normative force of probabilistic arguments in single cases while others (Baumann, Am Philos Q 42:71–79, 2005; Synthese 162:265–273, 2008) deny it. I demonstrate that both sides do not give convincing arguments for their case and propose a new account of the relationship between probabilistic reasoning (...)
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