Alternative Ways of Information Processing as a Source of Sustainable and Rational Peer Disagreement

Consider an event of interest B and another event A which is viewed as information for B. When a decision maker (DM) evaluates the effect of A on B, she evaluates the degree to which she asserts the indicative conditional "if A then B", written as A ---> B. In the context of the standard Bayesian confirmation theory, the degree of assertability, As(A ---> B) is given by DM's subjective conditional probability P(B | A). However, the Bayesian interpretation is not the only rational interpretation of As(A ---> B). An alternative interpretation is that As(A ---> B) goes by the probability that the proposition A ---> B is true, that is by DM's unconditional probability P(A ---> B). It is now widely accepted that there is no interpretation of "--->" that ensures the genral validity of P(A ---> B) = P(B | A). Hence, there are multiple truth-conditional interpretations of "--->" each corresponding to a distinct way of information processing. One of these interpretations, namely the material implication of the Propositional Logic, competes favorably with the Bayesian interpretation on normative grounds. As a result, two decision makers can disagree about their posterior probabilities of B even if they share the same information A and have identical prior probability functions.