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.
KeywordsCoherence Betting systems Finite additivity Countable additivity
Mathematics Subject Classification (2010)60A05
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 .
- 4.de Finetti, B.: Sul significato soggettivo della probabilità. Fundam. Math. 17, 298–329 (1931)Google Scholar