A representation theorem for a decision theory with conditionals

Synthese 116 (2):187-229 (1998)
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.
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
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Reprint years 2004
DOI 10.1023/A:1005030124500
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Counterfactual Desirability.Richard Bradley & H. Orri Stefánsson - 2017 - British Journal for the Philosophy of Science 68 (2):485-533.
A Unified Bayesian Decision Theory.Richard Bradley - 2007 - Theory and Decision 63 (3):233-263,.
Conditionals in Causal Decision Theory.John Cantwell - 2013 - Synthese 190 (4):661-679.
Desirability of Conditionals.H. Orri Stefánsson - 2016 - Synthese 193 (6):1967-1981.
Logic with Numbers.Colin Howson - 2007 - Synthese 156 (3):491-512.

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