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The interference problem for the betting interpretation of degrees of belief

Eriksson, Lina and Rabinowicz, Wlodek LU (2013) In Synthese 190(5). p.809-830
Abstract
The paper's target is the historically influential betting interpretation of subjective probabilities due to Ramsey and de Finetti. While there are several classical and well-known objections to this interpretation, the paper focuses on just one fundamental problem: There is a sense in which degrees of belief cannot be interpreted as betting rates. The reasons differ in different cases, but there's one crucial feature that all these cases have in common: The agent's degree of belief in a proposition A does not coincide with her degree of belief in a conditional that A would be the case if she were to bet on A, where the belief in this conditional itself is conditioned on the supposition that the agent will have an opportunity to make such... (More)
The paper's target is the historically influential betting interpretation of subjective probabilities due to Ramsey and de Finetti. While there are several classical and well-known objections to this interpretation, the paper focuses on just one fundamental problem: There is a sense in which degrees of belief cannot be interpreted as betting rates. The reasons differ in different cases, but there's one crucial feature that all these cases have in common: The agent's degree of belief in a proposition A does not coincide with her degree of belief in a conditional that A would be the case if she were to bet on A, where the belief in this conditional itself is conditioned on the supposition that the agent will have an opportunity to make such a bet. Even though the two degrees of belief sometimes can coincide (they will coincide in those cases when the bet has no expected causal bearings on the proposition A and the opportunity to bet have no evidential bearings on that proposition), it is the latter belief rather than the former that guides the agent's rational betting behaviour. The reason is that this latter belief takes into consideration potential interferences that bet opportunities and betting itself might create with regard to the proposition to be betted on. It is because of this interference problem that the agent's degree of belief in A cannot be interpreted as her betting rate for A. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Belief, Probability, Bets, Betting interpretation, Betting rate, Conditionals, Causal decision theory, Sleeping beauty, Ramsey, de, Finetti
in
Synthese
volume
190
issue
5
pages
809 - 830
publisher
Springer
external identifiers
  • wos:000316201500003
  • scopus:84874948962
ISSN
0039-7857
DOI
10.1007/s11229-012-0187-7
language
English
LU publication?
yes
id
973db421-a396-4322-9f1c-d80c64a84350 (old id 3636631)
date added to LUP
2013-04-24 14:35:54
date last changed
2017-01-01 05:25:04
@article{973db421-a396-4322-9f1c-d80c64a84350,
  abstract     = {The paper's target is the historically influential betting interpretation of subjective probabilities due to Ramsey and de Finetti. While there are several classical and well-known objections to this interpretation, the paper focuses on just one fundamental problem: There is a sense in which degrees of belief cannot be interpreted as betting rates. The reasons differ in different cases, but there's one crucial feature that all these cases have in common: The agent's degree of belief in a proposition A does not coincide with her degree of belief in a conditional that A would be the case if she were to bet on A, where the belief in this conditional itself is conditioned on the supposition that the agent will have an opportunity to make such a bet. Even though the two degrees of belief sometimes can coincide (they will coincide in those cases when the bet has no expected causal bearings on the proposition A and the opportunity to bet have no evidential bearings on that proposition), it is the latter belief rather than the former that guides the agent's rational betting behaviour. The reason is that this latter belief takes into consideration potential interferences that bet opportunities and betting itself might create with regard to the proposition to be betted on. It is because of this interference problem that the agent's degree of belief in A cannot be interpreted as her betting rate for A.},
  author       = {Eriksson, Lina and Rabinowicz, Wlodek},
  issn         = {0039-7857},
  keyword      = {Belief,Probability,Bets,Betting interpretation,Betting rate,Conditionals,Causal decision theory,Sleeping beauty,Ramsey,de,Finetti},
  language     = {eng},
  number       = {5},
  pages        = {809--830},
  publisher    = {Springer},
  series       = {Synthese},
  title        = {The interference problem for the betting interpretation of degrees of belief},
  url          = {http://dx.doi.org/10.1007/s11229-012-0187-7},
  volume       = {190},
  year         = {2013},
}