Group belief dynamics under iterated revision: fixed points and cycles of joint upgrades

A. Baltag, S. Smets
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引用次数: 68

Abstract

What happens if in the Muddy Children story [22] we drop the assumption that the public announcements (made by the father and by the children) are commonly known to be always true, and instead we simply assume that they are true and commonly believed to be true? More generally, what happens in the long term with a group's beliefs, knowledge and "epistemic states" (fully describable in fact by conditional beliefs), when receiving (or exchanging) a sequence of public announcements of truthful but uncertain information? Do the agents' beliefs (or knowledge, or conditional beliefs, or other doxastic attitudes such as "strong beliefs") reach a fixed point? Or do they exhibit instead a cyclic behavior, oscillating forever?
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迭代修正下的群体信念动力学:联合升级的不动点与周期
如果在泥泞的孩子的故事b[22]中,我们放弃了众所周知的公开声明(由父亲和孩子们发布)总是真实的假设,而是简单地假设它们是真实的,并且通常被认为是真实的,会发生什么?更一般地说,当接收(或交换)一系列真实但不确定的公开信息时,一个群体的信念、知识和“认知状态”(实际上完全可以通过条件信念来描述)在长期内会发生什么?代理人的信念(或知识,或条件信念,或其他矛盾的态度,如“强烈信念”)是否达到一个固定点?还是它们表现出一种循环行为,永远振荡?
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