The Agreement Theorem Aumann (1976 Ann. Stat. 4 , 1236–1239. ( doi:10.1214/aos/1176343654 )) states that if two Bayesian agents start with a common prior, then they cannot have common knowledge that they hold different posterior probabilities of some underlying event of interest. In short, the two agents cannot ‘agree to disagree’. This result applies in the classical domain where classical probability theory applies. But in non-classical domains, such as the quantum world, classical probability theory does not apply. Inspired principally by their use in quantum mechanics, we employ signed probabilities to investigate the epistemics of the non-classical world. We find that here, too, it cannot be common knowledge that two agents assign different probabilities to an event of interest. However, in a non-classical domain, unlike the classical case, it can be common certainty that two agents assign different probabilities to an event of interest. Finally, in a non-classical domain, it cannot be common certainty that two agents assign different probabilities, if communication of their common certainty is possible—even if communication does not take place. This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.

中文翻译：

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非经典世界中的同意和分歧

一致定理 Aumann (1976安. 统计。 4，1236–1239。（doi:10.1214/aos/1176343654)) 指出，如果两个贝叶斯代理以共同的先验开始，那么他们就无法拥有共同的知识，即他们对某些感兴趣的潜在事件持有不同的后验概率。简而言之，两个代理人不能“求同存异”。这个结果适用于经典概率论应用的经典领域。但在非经典领域，例如量子世界，经典概率论并不适用。主要受到它们在量子力学中的应用的启发，我们采用有符号概率来研究非经典世界的认知论。我们发现，两个代理为感兴趣的事件分配不同的概率也不能成为常识。然而，在非经典领域中，与经典情况不同，两个代理为感兴趣的事件分配不同的概率是普遍确定的。最后，在非经典领域，如果两个代理分配不同概率的共同确定性是可能的，那么即使没有发生通信，它们也不能是共同确定性的。本文是“量子背景、因果关系和选择自由”主题的一部分。