  Moses & Nachum ([7]) identify conceptual flaws in Bacharach's generalization
([3]) of Aumann's seminal "agreeing to disagree" result ([1]). Essentially,
Bacharach's framework requires agents' decision functions to be defined over
events that are informationally meaningless for the agents. In this paper, we
argue that the analysis of the agreement theorem should be carried out in
information structures that can accommodate for counterfactual states. We
therefore develop a method for constructing such "counterfactual structures"
(starting from partitional structures), and prove a new agreement theorem
within such structures. Furthermore, we show that our approach also resolves
the conceptual flaws in the sense that, within our framework, decision
functions are always only defined over events that are informationally
meaningful for the agents.
