This paper addresses how multiple individual credences on logically related issues should be aggregated into collective binary beliefs. We call this binarizing belief aggregation. It is vulnerable to dilemmas such as the discursive dilemma or the lottery paradox: proposition-wise independent aggregation can generate inconsistent or not deductively closed collective judgments. Addressing this challenge using the familiar axiomatic approach, we introduce general conditions on a binarizing belief aggregation rule, including rationality conditions on individual inputs and collective outputs, and determine which rules (if any) satisfy different combinations of these conditions. Furthermore, we analyze similarities and differences between our proofs and other related proofs in the literature and conclude that the problem of binarizing belief aggregation is a free-standing aggregation problem not reducible to judgment aggregation or probabilistic opinion pooling.

本文讨论了如何将逻辑相关问题上的多个个体信念聚合成集体二元信念。我们称之为二值化信念聚合。它很容易陷入诸如话语困境或彩票悖论之类的困境：命题明智的独立聚合可能会产生不一致或非演绎封闭的集体判断。使用熟悉的公理方法解决这一挑战，我们引入了二值化信念聚合规则的一般条件，包括个体输入和集体输出的合理性条件，并确定哪些规则（如果有）满足这些条件的不同组合。此外，我们分析了我们的证明与文献中其他相关证明之间的异同，并得出结论：二值化信念聚合问题是一个独立的聚合问题，不能简化为判断聚合或概率意见池。