On the Robustness of ‘ Good News and Bad News ’ ∗

Paul Milgrom (The Bell Journal of Economics, 12(2): 380–391) showed that if the strict monotone likelihood ratio property (MLRP) does not hold for a signal structure then there exists some non-degenerate prior and a pair of signals where the highersignal posterior does not stochastically dominate the lower-signal posterior. We show here that for any non-degenerate prior with bounded support there exists an additive signal structure (satisfying other natural properties) and pair of signals such that a higher signal implies a lower posterior. Thus, higher signals can be “bad” news when the prior is fixed but the signal structure is not.