Inspired by Aumann's agreement theorem, Scott Aaronson studied the amount of communication necessary for two Bayesian experts to approximately agree on the expectation of a random variable. Aaronson showed that, remarkably, the number of 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 the estimate they would settle on if they were to share all of their information. We show that if the experts' signals are \emph{substitutes} -- meaning the experts' information has diminishing marginal returns -- then it is the case that if the experts are close to agreement then they are close to the truth. We prove this result for a broad class of agreement and accuracy measures that includes squared distance and KL divergence. Additionally, we show that although these measures capture fundamentally different kinds of agreement, Aaronson's agreement result generalizes to them as well.

翻译：在Aumann协议理论的启发下,Scott Aaronson研究了两名巴伊西亚专家大致商定随机变量预期所需的通信量。Aaronson指出,明显的是,位数并不取决于每名专家可获得的信息量。然而,一般而言,商定的估计可能不准确:如果专家的信号是/emph{substities} -- -- 即专家的信息减少了边际回报 -- -- 那么,如果专家接近于同意,那么他们就会接近于真理。我们证明,这一结果产生了广泛的一致和准确性措施,其中包括平方距离和KL差异。此外,我们表明,虽然这些措施反映了截然不同的一致,但Aaronson的协议也对它们作了概括。