Before revision:  First, if private signal distributions are diverse enough across agents , then Bayesian learning achieves good information aggregation as long as individuals observe sufficiently many others . Second, without such diversity,  Bayesian information aggregation can fall far short of good aggregation benchmarks, and can be Pareto-inefficient .
After revision:  First, if private signal distributions are diverse enough across agents , then Bayesian learning achieves good information aggregation as long as individuals observe sufficiently many others . Second, without such diversity, Bayesian information aggregation necessarily falls far short of good aggregation benchmarks, and can be Pareto-inefficient .