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Synthese

, Volume 196, Issue 1, pp 265–271 | Cite as

De Finetti coherence and the product law for independent events

  • Daniele MundiciEmail author
Article

Abstract

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.

Keywords

De 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 Classification

Primary: 60A05 60B05 Secondary: 18A30 28A60 

Notes

Acknowledgements

The author is grateful to the two referees for their valuable remarks and suggestions for improvement.

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Copyright information

© Springer Nature B.V. 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science “Ulisse Dini”University of FlorenceFlorenceItaly

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