Ignoring ignorance and Agreeing to Disagree *

A model of information structure and common knowledge is presented which does not take states of the world as primitive. Rather, these states are constructed as sets of propositions, including propositions which describe knowledge. In this model information structure and measurability structure are endogenously defined in terms of the relation between the propositions. In particular, when agents are ignorant of their own ignorance, the information structure is not a partition of the state space. We show that Aumann’s (Ann. Statist. 4 (1976), 1236-1239) famous result on the impossibility of agreeing to disagree, which was proved for partitions, can be extended to such information structures. Journal of Economic Literature Classification Numbers: 021, 026.