De Finetti coherence and the product law for independent events
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In an earlier paper the present author proved that de Finetti coherence is preserved under taking products of coherent books on two finite sets of independent events. Conversely, in this note it is proved that product is the only coherence preserving operation on coherent books. Our proof shows that the traditional definition of stochastically independent classes of events actually follows from the combination of two more basic notions: boolean algebraic independence and de Finetti coherent betting system.
KeywordsDe Finetti Dutch Book theorem Coherent book Coherent probability assessment Product law for independent events Stochastic independence Belief-distributions Subjective probability function Foundations of Bayesianism
Mathematics Subject ClassificationPrimary: 60A05 60B05 Secondary: 18A30 28A60
The author is grateful to the two referees for their valuable remarks and suggestions for improvement.
- Feller, W. (1957). An introduction to probability theory and its applications (3rd ed.). New York: Wiley.Google Scholar
- Kac, M. (1959). Statistical independence in probability, analysis and number theory. In The Carus mathematical monographs, Vol. 12, The Mathematical Association of America. New York: Wiley.Google Scholar
- Koppelberg, S. (1989). General theory of Boolean algebras. In J. D. Monk & R. Bonnet (Eds.), Handbook of Boolean algebras (Vol. 1). Amsterdam: Elsevier.Google Scholar
- Loéve, M. (1977). Probability theory I. In Graduate texts in mathematics (4th ed., Vol. 45). Berlin: Springer.Google Scholar
- Mundici, D.(2016). Coherence of de Finetti coherence. Synthese. Published online, June 1, doi: 10.1007/s11229-016-1126-9.