De Finetti was Right: Probability Does Not Exist

Theory and Decision 51 (2/4):89-124 (2001)
Abstract
De Finetti's treatise on the theory of probability begins with the provocative statement PROBABILITY DOES NOT EXIST, meaning that probability does not exist in an objective sense. Rather, probability exists only subjectively within the minds of individuals. De Finetti defined subjective probabilities in terms of the rates at which individuals are willing to bet money on events, even though, in principle, such betting rates could depend on state-dependent marginal utility for money as well as on beliefs. Most later authors, from Savage onward, have attempted to disentangle beliefs from values by introducing hypothetical bets whose payoffs are abstract consequences that are assumed to have state-independent utility. In this paper, I argue that de Finetti was right all along: PROBABILITY, considered as a numerical measure of pure belief uncontaminated by attitudes toward money, does not exist. Rather, what exist are de Finetti's `previsions', or betting rates for money, otherwise known in the literature as `risk neutral probabilities'. But the fact that previsions are not measures of pure belief turns out not to be problematic for statistical inference, decision analysis, or economic modeling
Keywords Probability  Beliefs  Values  Statistical inference  Decision theory
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Paul Bartha (2004). Countable Additivity and the de Finetti Lottery. British Journal for the Philosophy of Science 55 (2):301-321.
Jan von Plato (1982). The Generalization of de Finetti's Representation Theorem to Stationary Probabilities. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1982:137 - 144.
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