The interference problem for the betting interpretation of degrees of belief
- 254 Downloads
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.
KeywordsBelief Probability Bets Betting interpretation Betting rate Conditionals Causal decision theory Sleeping beauty Ramsey de Finetti
Unable to display preview. Download preview PDF.
- 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.Google Scholar
- Blamey, J. (2011). Challenging the assumption of stake-size invariance. draft.Google Scholar
- de Finetti, B. (1990). Theory of probability, Vol. I (1st edn, 1974). New York: Wiley.Google Scholar
- Eriksson L., Hajek A. (2007) What are degrees of belief?. Studia Logica 86: 185–215Google Scholar
- 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.Google Scholar
- Hájek, A. (ms). Most counterfactuals are false. book manuscript.Google Scholar
- 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 173–195Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- Kant, I. (1929 ). Critique of pure reason. London: Macmillan.Google Scholar
- 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: 25–40Google Scholar
- Levi I. (1997) The covenant of reason. Cambridge University Press, CambridgeGoogle Scholar
- Putnam H. (1965) Brains and behavior. In: Butler R. J. (eds) Analytical philosophy, second series. Barnes and Noble, New York, pp 1–19Google Scholar
- 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.Google Scholar
- Strawson G. (1994) Mental reality. MIT Press, CambridgeGoogle Scholar
- van Fraassen B. (1980) Review of Brian Ellis, ‘rational belief systems’. Canadian Journal of Philosophy 10: 497–511Google Scholar