Dynamic Coherence

  • Brian Skyrms
Chapter
Part of the The University of Western Ontario Series in Philosophy of Science book series (WONS, volume 35)

Abstract

Ramsey (1931) and de Finetti (1937) founded the notion of personal probability on static coherence. Someone’s betting quotients over a boolean algebra of propositions are coherent if and only if it is not possible for a bettor to make a dutch book against him by means of a finite number of bets; i.e. there are a finite number of bets which he judges fair or favorable such that his net payoff from them is negative in every possible outcome. The classical dutch book theorem shows that betting quotients are coherent in this sense if and only if they constitute a finitely additive probability measure (de Finetti, 1937; Kemeny, 1955; Lehman, 1955; Shimony, 1955). Adams (1962) showed that the result can be strengthened to require countable additivity if the concept of coherence is modified to allow count ably many bets. These betting quotients can be thought of as degrees of belief, in the dispositional sense of belief, as Ramsey suggested. The degrees of belief are held fixed for the classical dutch book argument; we are dealing with degrees of belief at a time. The notion of coherence involved is static; all betting is done at the same time with reference to the same set of degrees of belief. What is established is that coherent degrees of belief, in the sense at issue, are probabilities.

What can be said about changes in degrees of belief? Rules for changing degrees of belief in response to new evidence, such as Bayes’ rule of conditionalization, play a central role in Bayesian reasoning. What about coherence concepts and results for rules for changing degrees of belief? This is what I am calling the question of dynamic coherence. It appears that this question has not even been considered seriously until recently. Hacking (1967) called attention to the problem of providing a justification of Bayesian conditionalization by means of a coherence argument, but was skeptical of the possibility of a positive result. Since Hacking’s discussion, questions of dynamic coherence have been discussed by both philosophers and statisticians, and some fundamentals results have been established.

Keywords

True Color Dutch Book Coherence Concept Additive Probability Measure Discrimination Information 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© D. Reidel Publishing Company 1987

Authors and Affiliations

  • Brian Skyrms
    • 1
  1. 1.Department of PhilosophyUniversity of California at IrvineIrvineUSA

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