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Inspired by Aumann's agreement theorem, Scott Aaronson studied the amount ofcommunication necessary for two Bayesian experts to approximately agree on theexpectation of a random variable. Aaronson showed that, remarkably, the numberof bits does not depend on the amount of information available to each expert.However, in general the agreed-upon estimate may be inaccurate: far from theestimate they would settle on if they were to share all of their information.We show that if the experts' signals are \emph{substitutes} -- meaning theexperts' information has diminishing marginal returns -- then it is the casethat if the experts are close to agreement then they are close to the truth. Weprove this result for a broad class of agreement and accuracy measures thatincludes squared distance and KL divergence. Additionally, we show thatalthough these measures capture fundamentally different kinds of agreement,Aaronson's agreement result generalizes to them as well.

Agreement Implies Accuracy for Substitutable Signals