David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Theory and Decision 63 (3):233-263, (2007)
This paper provides new foundations for Bayesian Decision Theory based on a representation theorem for preferences defined on a set of prospects containing both factual and conditional possibilities. This use of a rich set of prospects not only provides a framework within which the main theoretical claims of Savage, Ramsey, Jeffrey and others can be stated and compared, but also allows for the postulation of an extended Bayesian model of rational belief and desire from which they can be derived as special cases. The main theorem of the paper establishes the existence of a such a Bayesian representation of preferences over conditional prospects, i.e. the existence of a pair of real-valued functions respectively measuring the agent’s degrees of belief and desire and which satisfy the postulated rationality conditions on partial belief and desire. The representation of partial belief is shown to be unique and that of partial desire, unique up to a linear transformation.
|Keywords||Bayesian decision theory conditionals probability desirability representation theorem|
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References found in this work BETA
David K. Lewis (1973). Counterfactuals. Blackwell Publishers.
Richard Jeffrey (1983). The Logic of Decision. University of Chicago Press.
Leonard J. Savage (1954). The Foundations of Statistics. Wiley Publications in Statistics.
James Joyce (1999). The Foundations of Causal Decision Theory. Cambridge University Press.
John Broome (1991). Weighing Goods: Equality, Uncertainty and Time. Wiley-Blackwell.
Citations of this work BETA
Richard Bradley & H. Orri Stefánsson (forthcoming). Counterfactual Desirability. British Journal for the Philosophy of Science:axv023.
Ittay Nissan-Rozen (forthcoming). A Triviality Result for the “Desire by Necessity” Thesis. Synthese:1-22.
Gabriel Frahm (2015). A Theoretical Foundation of Portfolio Resampling. Theory and Decision 79 (1):107-132.
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