Comment on “Correlated information, mechanism design and informational rents” [J. Econ. Theory 123 (2) (2005) 210-217]

We amend an error in [S. Parreiras, Correlated information, mechanism design and informational rents, J. Econ. Theory 123 (2005) 210-217]. Consequently, it is in general not possible to reinterpret a mechanism design model that violates the spanning condition of Crémer and McLean [J. Crémer, R. McLean, Full extraction of the surplus in bayesian, dominant strategy auctions, Econometrica 56 (1988) 1247-1258] as one in which agents hold private information about the informativeness of their signals about other agentsʼ types. Instead, such an interpretation is warranted only when the weights used to span an agentʼs set of beliefs stand in a singular relation with the prior type distribution that is known as an alternative characterization of Blackwell dominance.