Journal of Theoretical Probability

, Volume 28, Issue 2, pp 520–538 | Cite as

Coherence of Countably Many Bets



De Finetti’s betting argument is used to justify finitely additive probabilities when only finitely many bets are considered. Under what circumstances can countably many bets be used to justify countable additivity? In this framework, one faces issues such as the convergence of the returns of the bet. Generalizations of de Finetti’s (Fundam Math 17:298–329, 1931) argument depend on what types of conditions on convergence are required of the bets under consideration. Two new such conditions are compared with others presented in the literature.


Coherence Betting systems Finite additivity Countable additivity 

Mathematics Subject Classification (2010)




We thank the two anonymous referees, Jessi Cisewski, Georg Goerg, Rafael Izbicki, Mark Schervish, Teddy Seidenfeld and Julio Stern for their valuable comments. In particular, we thank Teddy Seidenfeld for pointing us toward [1].


  1. 1.
    Adams, E.: On rational betting systems. Arch. Math. Log. 6(1–2), 7–29 (1962)CrossRefGoogle Scholar
  2. 2.
    Beam, J.: Unfair gambles in probability. Stat. Probab. Lett. 77, 681–686 (2007)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Billingsley, P.: Probability and Measure, 2nd edn. Wiley, New York (1986)MATHGoogle Scholar
  4. 4.
    de Finetti, B.: Sul significato soggettivo della probabilità. Fundam. Math. 17, 298–329 (1931)Google Scholar
  5. 5.
    Heath, D.C., Sudderth, W.D.: On a theorem of de finettti, oddsmaking, and game theory. Ann. Math. Stat. 43, 2072–2077 (1972)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of StatisticsCarnegie Mellon UniversityPittsburghUSA

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