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arXiv cs/0203013cs.AIcs.LO
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表示和聚合验证信念

Representing and Aggregating Conflicting Beliefs

Pedrito Maynard-Reid, Daniel Lehmann

摘要:

我们考虑代表集体信念和聚合这些信念的双重问题。我们提出了模块化的,集体信念的传递关系。它们允许我们表示相互冲突的观点,并且它们具有清晰的语义。我们将它们与社会选择中经常使用的准传递关系进行比较。然后,我们描述了一种方法来构建一个代理人的信念状态通知一组不同程度的可靠性的来源。这种构造以令人满意的方式规避了阿罗不可能定理。最后,我们给出了一个简单的集合论为基础的运营商结合多个代理的信息。我们表明,该操作符满足理想的不变量的恒等式,交换性和结合性,因此,是行为良好的迭代时,我们描述了一个计算有效的方式计算所产生的信念状态。

英文摘要:

We consider the two-fold problem of representing collective beliefs and aggregating these beliefs. We propose modular, transitive relations for collective beliefs. They allow us to represent conflicting opinions and they have a clear semantics. We compare them with the quasi-transitive relations often used in Social Choice. Then, we describe a way to construct the belief state of an agent informed by a set of sources of varying degrees of reliability. This construction circumvents Arrow's Impossibility Theorem in a satisfactory manner. Finally, we give a simple set-theory-based operator for combining the information of multiple agents. We show that this operator satisfies the desirable invariants of idempotence, commutativity, and associativity, and, thus, is well-behaved when iterated, and we describe a computationally effective way of computing the resulting belief state.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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