将置信度聚合为信念：不可能性结果的议程条件
Aggregating Credences into Beliefs: Agenda Conditions for Impossibility Results
AI总结：
本文用议程理论方法研究信念二值化聚合中不可能性定理的精确议程条件，分别确定了寡头结果、平凡性结果和不可能性结果对应的路径连通性与偶可否定性、否定连通性及阻塞性条件。
摘要：
信念二值化聚合研究如何将个体概率性信念理性地聚合为集体二值信念。与判断聚合理论的发展类似，在信念二值化聚合中，制定公理化要求、证明不可能性定理以及识别不可能性定理的精确议程条件，是自然且重要的研究课题。基于我们先前对不可能性定理的研究，我们采用议程理论方法来推广这些结果，并确定议程中各议题之间逻辑互连的必要且充分水平，以使不可能性定理得以出现。我们证明：(1) 路径连通性和偶可否定性构成了寡头结果的精确议程条件，该结果指出，在次要条件下，满足命题独立性（proposition-wise independence）和集体信念演绎封闭性的信念二值化聚合会产生寡头；(2) 否定连通性是通过在寡头结果上添加匿名性而得到的平凡性结果的条件；(3) 阻塞性是通过添加集体信念的完备性和一致性而得到的不可能性结果的条件。此外，我们将这些新发现与判断聚合和信念二值化中现有的议程理论刻画定理进行了比较。
英文摘要：
Binarizing belief aggregation addresses how to rationally aggregate individual probabilistic beliefs into collective binary beliefs. Similar to the development of judgment aggregation theory, formulating axiomatic requirements, proving impossibility theorems, and identifying exact agenda conditions of impossibility theorems are natural and important research topics in binarizing belief aggregation. Building on our previous research on impossibility theorems, we use an agenda-theoretic approach to generalize the results and to determine the necessary and sufficient level of logical interconnection between the issues in an agenda for the impossibility theorems to arise. We demonstrate that (1) path-connectedness and even-negatability constitute the exact agenda condition for the oligarchy result stating that binarizing belief aggregation satisfying proposition-wise independence and deductive closure of collective beliefs yields the oligarchies under minor conditions; (2) negation-connectedness is the condition for the triviality result obtained by adding anonymity to the oligarchy result; and (3) blockedness is the condition for the impossibility result, which follows by adding completeness and consistency of collective beliefs. Moreover, we compare these novel findings with existing agenda-theoretic characterization theorems in judgment aggregation and belief binarization.
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