A Unified Bayesian Decision Theory |
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Authors: | Richard Bradley |
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Institution: | (1) Department of Philosophy, Logic and Scientific Method, London School of Economics, Houghton Street, London, WC2A 2AE, UK |
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Abstract: | 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. |
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Keywords: | Bayesian decision theory conditionals probability desirability representation theorem |
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