Belief Update Methods and Rules—Some Comparisons
Leszek Wroński · Ergo an Open Access Journal of Philosophy · 2016
We tackle two open questions from Leitgeb and Pettigrew (2010b) regarding what the belief update framework described in that paper mandates as correct responses to two problems.One of them concerns credences in overlapping propositions and is known in the literature as the "simultaneous update problem".The other is the well known "Judy Benjamin" problem concerning conditional credences.We argue that our results concerning the problems point to deficiencies of the framework.More generally, we observe that the method of minimizing inverse relative entropy seems to work better than (or at least equally well as) its competitors in many situations.S uppose that an agent at a certain time has credences in propositions which form a Boolean algebra.These credences, or degrees of belief (we will use these terms interchangeably), are given by a "belief function" b.Suppose that subsequently the agent obtains evidence which entails constraints that b does not meet.Which belief function should the agent adopt?This paper will be concerned with problems of this kind ("belief update problems"), and in particular with two specificic issues posed as open problems at the end of Leitgeb and Pettigrew (2010b).Some belief update problems have answers with which many people feel comfortable; the most common example would be that if, for some proposition E, the agent learns that E (and nothing more), she should update her belief function by conditionalization, provided that her initial credence in E was not equal to zero (more on this in Section 1).However, with respect to other problems intuitions may vary wildly.What if the evidence entails (only) new credences in two overlapping propositions?(This is the "simultaneous update problem".)Or what if it entails (only) a new conditional credence?(This is the "Judy Benjamin problem".)Some might want to say that in such cases there is no unique answer; that is, that the evidence underdetermines the choice of the new belief function.Still, some answers may be more reasonable than others.Given a belief update