A representation theorem for a decision theory with conditionals

Synthese 116 (2):187-229 (1998)
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Abstract

This paper investigates the role of conditionals in hypothetical reasoning and rational decision making. Its main result is a proof of a representation theorem for preferences defined on sets of sentences (and, in particular, conditional sentences), where an agent’s preference for one sentence over another is understood to be a preference for receiving the news conveyed by the former. The theorem shows that a rational preference ordering of conditional sentences determines probability and desirability representations of the agent’s degrees of belief and desire that satisfy, in the case of non-conditional sentences, the axioms of Jeffrey’s decision theory and, in the case of conditional sentences, Adams’ expression for the probabilities of conditionals. Furthermore, the probability representation is shown to be unique and the desirability representation unique up to positive linear transformation.

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Richard Bradley
London School of Economics

Citations of this work

Decision Theory.Johanna Thoma - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 57-106.
Counterfactual Desirability.Richard Bradley & H. Orii Stefansson - 2017 - British Journal for the Philosophy of Science 68 (2):485-533.
Decision Theory.Katie Steele & H. Orri Stefánsson - 2012 - In Peter Adamson (ed.), Stanford Encyclopedia of Philosophy. Stanford Encyclopedia of Philosophy.
The Logic of Conditional Negation.John Cantwell - 2008 - Notre Dame Journal of Formal Logic 49 (3):245-260.
A unified Bayesian decision theory.Richard Bradley - 2007 - Theory and Decision 63 (3):233-263,.

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References found in this work

The Logic of Decision.Richard C. Jeffrey - 1965 - New York, NY, USA: University of Chicago Press.
Truth and probability.Frank Ramsey - 1926 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge. pp. 52-94.
The Logic of Conditionals.Ernest Adams, Ernest W. Adams, Jaakko Hintikka & Patrick Suppes - 1965 - Journal of Symbolic Logic 39 (3):609-611.
Conditional probabilities and compounds of conditionals.Vann McGee - 1989 - Philosophical Review 98 (4):485-541.

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