Strong and Weak Expectations

Abstract

Fine has shown that assigning any value to the Pasadena game is consistent with a certain standard set of axioms for decision theory. However, I suggest that it might be reasonable to believe that the value of an individual game is constrained by the long-run payout of repeated plays of the game. Although there is no value that repeated plays of the Pasadena game converges to in the standard strong sense, I show that there is a weaker sort of convergence it exhibits, and use this to define a notion of ‘weak expectation’ that can give values to the Pasadena game and many others, though not to all games that fail to have a strong expectation in the standard sense.

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