The role of absolute continuity in "merging of opinions" and "rational learning"

D. Blackwell and L. Dubins (1962, Ann. Math. Statist. 38, 882-886) showed t hat opinions merge when priors are absolutely continuous. E. Kalai and E. L ehrer (1993. Econometrica 61, 1019-1045) use this result to show that playe rs in a repeated game eventually play like a Nash equilibrium. We provide a n alternative proof of merging of opinions that clarifies the role of absol ute continuity while casting doubt on the relevance of the result. Persiste nt disagreement, the opposite of merging, allows the construction of a sequ ence of mutually favorable "bets." By a law of large numbers, both agents a rt certain they will win these bets on average. This certain disagreement v iolates absolute continuity. Journal of Economic Literature Classification Numbers: C11, C69, C72, D83. (C) 1999 Academic Press.