The interference problem for the betting interpretation of degrees of belief
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
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.
Supplementary Material (0)
- Arntzenius F. (2002) Reflections on sleeping beauty. Analysis 62: 53–62 CrossRef
- Aumann R. J., Hart, S., & Perry, M. (2005). Conditioning and the sure-thing principle. Discussion paper series DP-393. Jerusalem: Center for Rationality and Interactive Decision Theory, Hebrew University.
- Blamey, J. (2011). Challenging the assumption of stake-size invariance. draft.
- Bovens L., Rabinowicz W. (2010) The puzzle of the hats. Synthese 172: 57–78 CrossRef
- Bradley D., Leitgeb H. (2006) When betting odds and credences come apart: More worries for Dutch book arguments. Analysis 66: 27–119 CrossRef
- de Finetti, B. (1990). Theory of probability, Vol. I (1st edn, 1974). New York: Wiley.
- Egan A. (2007) Some counterexamples to causal decision theory. Philosophical Review 116: 93–114 CrossRef
- Eriksson L., Hajek A. (2007) What are degrees of belief?. Studia Logica 86: 185–215
- Gibbard, A., & Harper, W. (1981 ). Counterfactuals and two kinds of expected utility. In W. Harper, R. Stalnaker & G. Pearce (Eds.), Ifs (pp. 153–190). Dordrecht: Reidel.
- Hájek, A. (ms). Most counterfactuals are false. book manuscript.
- Hájek Alan (2008) Dutch book arguments. In: Anand P., Pattanaik P., Puppe C. (eds) The Oxford handbook of rational and social choice. Oxford University Press, Oxford, pp 173–195
- Hájek, A. (2009). Interpretations of probability. In Stanford encyclopedia of philosophy. Retrieved July 23, 2009 from http://www.science.uva.nl/~eop/entries/probability-interpret/.
- Hammond, P. (2008). Isolation, assurance and rules. In B. Kaushik & K. Ravi (Eds.), Arguments for a better world: Essays in honor of Amartya Sen, Vol 1; ethics, welfare, and measurement, Chap. 28 (pp. 523–534). Oxford: Oxford University Press.
- Jeffrey R. (1956) Valuation and acceptance of scientific hypotheses. Philosophy of Science 23: 237–246 CrossRef
- Joyce J. M. (1998) A nonpragmatic vindication of probabilism. Philosophy of Science 65: 575–603 CrossRef
- Joyce, J. M. (2011). Regret and instability in causal decision theory. In H. Arlo-Costa & J. Helzner (Eds.), Synthese on the foundations of decision theory. Cambridge: Harvard University Press.
- Kant, I. (1929 ). Critique of pure reason. London: Macmillan.
- Kant, I. (1904 ). Kritik der Reinen Vernunft. Akademieausgabe, III. http://www.korpora.org/kant/aa03/.
- Lewis D. (1979) Prisoner’s dilemma is a Newcomb problem. Philosophy and Public Affairs 8: 25–40
- Levi I. (1997) The covenant of reason. Cambridge University Press, Cambridge
- Masel J. (2007) A Bayesian model of quasi-magical thinking can explain observed cooperation in the public good game. Journal of Economic Behavior and Organization 64: 31–216 CrossRef
- Morris M. W., Sim D. L. H., Girotto V. (1998) Distinguishing sources of cooperation in the one-round prisoner’s dilemma: Evidence for cooperative decisions based on the illusion of control. Journal of Experimental Social Psychology 34: 494–512 CrossRef
- Putnam H. (1965) Brains and behavior. In: Butler R. J. (eds) Analytical philosophy, second series. Barnes and Noble, New York, pp 1–19
- Rabinowicz W. (2002) Does practical deliberation crowd out self-prediction?. Erkenntnis 57: 91–122 CrossRef
- Ramsey, F. P. (1931 ). Truth and probability. In F. Ramsey & R. B. Braithwaite (Eds.), Foundations of mathematics and other essays (pp. 156–98). London: Kegan, Paul, Trench, Trubner & Co. & New York: Harcourt, Brace and Company.
- Shafir E., Tversky A. (1992) Thinking through uncertainty: Nonconsequential reasoning and choice. Cognitive Psychology 24: 449–474 CrossRef
- Spohn W. (1977) Where Luce and Krantz do really generalize Savage’s decision model. Erkenntnis 11: 34–113 CrossRef
- Strawson G. (1994) Mental reality. MIT Press, Cambridge
- van Fraassen B. (1980) Review of Brian Ellis, ‘rational belief systems’. Canadian Journal of Philosophy 10: 497–511
About this Article
- The interference problem for the betting interpretation of degrees of belief
Volume 190, Issue 5 , pp 809-830
- Cover Date
- Print ISSN
- Online ISSN
- Springer Netherlands
- Additional Links
- Betting interpretation
- Betting rate
- Causal decision theory
- Sleeping beauty
- de Finetti
- Industry Sectors