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

In situations where noisy signals of some underlying variable are observed, Paul Milgrom (The Bell Journal of Economics, 12(2): 380–391) showed that a higher signal implies a higher posterior (in the sense of first-order stochastic dominance) for every non-degenerate prior if and only if the conditional distribution satisfies the strict monotone likelihood ratio property (MLRP). We show that for any non-degenerate prior with bounded support there exists a symmetric and quasiconcave conditional distribution such that a higher signal implies a lower posterior. Thus, when the prior is known but the conditional distribution is unrestricted it is always possible that “good” signals may be “bad” news.