Updating Probability: Tracking Statistics as Criterion

• Published in: The British journal for the philosophy of science 2017-09, Vol.68 (3), p.725-743
• Main Authors: van Fraassen, Bas C., Halpern, Joseph Y.
• Format: Article
• Language: English
• ISSN: 0007-0882; 1464-3537
• DOI: 10.1093/bjps/axv027

For changing opinion, represented by an assignment of probabilities to propositions, the criterion proposed is motivated by the requirement that the assignment should have, and maintain, the possibility of matching in some appropriate sense statistical proportions in a population. This 'tracking' criterion implies limitations on policies for updating in response to a wide range of types of new input. Satisfying the criterion is shown equivalent to the principle that the prior must be a convex combination of the possible posteriors. Furthermore, this is equivalent to the requirement that prior expected values must fall inside the range spanned by possible posterior expected values. The tracking criterion is liberal; it allows for, but does not require, a policy such as Bayesian conditionalization, and can be offered as a general constraint on policies for managing opinion over time. Examples are given of non-Bayesian policies, both ones that satisfy and ones that violate the criterion.