Learning Conditional Evidence

Learning indicative conditionals and learning relative frequencies have one thing in common: they are examples of conditional evidence, that is, evidence that includes a suppositional element. Standard Bayesian theory does not describe how such evidence affects rational degrees of belief, and natural solutions run into major problems. We propose that conditional evidence is best modeled by a combination of two strategies: First, by generalizing Bayesian Conditionalization to minimizing an appropriate divergence between prior and posterior probability distribution. Second, by representing the relevant causal relations and the implied conditional independence relations in a Bayesian network that constrains both prior and posterior. We show that this approach solves several well-known puzzles about learning conditional evidence (e.g., the notorious Judy Benjamin problem) and that learning an indicative conditional can often be described adequately by conditionalizing on the associated material conditional.

Learning from Conditionals

In this article, we address a major outstanding question of probabilistic Bayesian epistemology: how should a rational Bayesian agent update their beliefs upon learning an indicative conditional? A number of authors have recently contended that this question is fundamentally underdetermined by Bayesian norms, and hence that there is no single update procedure that rational agents are obliged to follow upon learning an indicative conditional. Here we resist this trend and argue that a core set of widely accepted Bayesian norms is sufficient to identify a normatively privileged updating procedure for this kind of learning. Along the way, we justify a privileged formalization of the notion of ‘epistemic conservativity’, offer a new analysis of the Judy Benjamin problem, and emphasize the distinction between interpreting the content of new evidence and updating one’s beliefs on the basis of that content.