Letters From Long Ago: On Causal Decision Theory and Centered Chances

In Johansson Lars-Göran (ed.), Logic, Ethics, and All That Jazz - Essays in Honour of Jordan Howard Sobel. pp. 247 - 273 (2009)
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Abstract

This paper argues that expected utility theory for actions in chancy environments should be formulated in terms of centered chances. The subjective expected utility of an option A may be seen as a weighted sum of the utilities of A in different possible worlds, with weights being the credences that the agent assigns to these worlds. The utility of A in a given world is then definable as a weighted sum of the values of A’s different possible outcomes, with weights being the conditional chances of these outcomes if A were performed. On the centered-chance view, the chances to be used as weights in the definition of utility are centered. Unlike ordinary chances, centered chances depend not only on what happens prior to the agent’s choice but also on the events that occur after the choice. Thus, to give an example, suppose that the action under consideration results in a bad outcome due to some event whose ordinary chance of occurring was very low at the time of choice. Then the utility of that action in the actual world could be high on the non-centered view, but on the centered view that utility is negative, since the centered chance of the event in question given the action was one, given that it did actually take place. A precise definition of centered chances is not easy to frame, but the concept can be made intuitively clear. The resulting decision theory is, in my opinion, philosophically more satisfactory than the extant proposals, even though it doesn’t differ much in its practical recommendations, with the exception of some rather peculiar cases.

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Wlodek Rabinowicz
Lund University

Citations of this work

The Value of Biased Information.Nilanjan Das - 2023 - British Journal for the Philosophy of Science 74 (1):25-55.
Decision and foreknowledge.J. Dmitri Gallow - 2024 - Noûs 58 (1):77-105.
The Chances of Choices.Reuben Stern - forthcoming - British Journal for the Philosophy of Science.

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References found in this work

Causal decision theory.David Lewis - 1981 - Australasian Journal of Philosophy 59 (1):5 – 30.
Counterfactuals and Two Kinds of Expected Utility.Allan Gibbard & William L. Harper - 1978 - In A. Hooker, J. J. Leach & E. F. McClennen (eds.), Foundations and Applications of Decision Theory. D. Reidel. pp. 125-162.
Imaging and conditionalization.Peter Gärdenfors - 1982 - Journal of Philosophy 79 (12):747-760.

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