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

Rabinowicz, Wlodek LU (2009) In Logic, Ethics, and All That Jazz - Essays in Honour of Jordan Howard Sobel 56. p.247-273
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 (in that world) 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... (More)
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 (in that world) 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 (i.e. non-centered) 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 (as distinct from its expected utility), 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. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Logic, Ethics, and All That Jazz - Essays in Honour of Jordan Howard Sobel
editor
Johansson, Lars-Göran and
volume
56
pages
247 - 273
publisher
Uppsala Philosophical Studies
ISSN
1402-1110
ISBN
978-91-506-2078-8
language
English
LU publication?
yes
id
97af6041-3927-4fd1-a836-71ad76fee075 (old id 1458836)
date added to LUP
2009-09-24 10:14:24
date last changed
2016-04-16 02:42:31
@inbook{97af6041-3927-4fd1-a836-71ad76fee075,
  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 (in that world) 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 (i.e. non-centered) 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 (as distinct from its expected utility), 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.},
  author       = {Rabinowicz, Wlodek},
  editor       = {Johansson, Lars-Göran},
  isbn         = {978-91-506-2078-8},
  issn         = {1402-1110},
  language     = {eng},
  pages        = {247--273},
  publisher    = {Uppsala Philosophical Studies},
  series       = {Logic, Ethics, and All That Jazz - Essays in Honour of Jordan Howard Sobel},
  title        = {Letters from Long Ago: On Causal Decision Theory and Centered Chances},
  volume       = {56},
  year         = {2009},
}