A unified Bayesian decision theory

Bradley, Richard ORCID: 0000-0003-2184-7844 (2006) A unified Bayesian decision theory. LSE Choice Group working paper series (vol. 1, no. 1). The Centre for Philosophy of Natural and Social Science (CPNSS), London, 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, Je¤rey 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.

Item Type:	Monograph (Working Paper)
Official URL:	http://www2.lse.ac.uk/CPNSS/Home.aspx
Additional Information:	© 2006 The author
Divisions:	LSE
Subjects:	B Philosophy. Psychology. Religion > B Philosophy (General)
Date Deposited:	15 May 2009 12:32
Last Modified:	13 Sep 2024 20:00
URI:	http://eprints.lse.ac.uk/id/eprint/23914

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