Counterfactuals in “agreeing to disagree” type results

Moses and Nachum (1990) identified conceptual flaws (later echoed by Samet, 2010) in Bacharach's (1985) generalization of Aumann's (1976) seminal “agreeing to disagree” result by demonstrating that the crucial assumptions of like-mindedness and the Sure-Thing Principle are not meaningfully expressible in standard partitional information structures. This paper presents a new agreement theorem couched in “counterfactual information structures” that resolves these conceptual flaws. The new version of the Sure-Thing Principle introduced here, which accounts for beliefs at counterfactual states, is also shown to sit well with the intuition of the original version proposed by Savage (1972).