We analyse the incentives of individuals to misrepresent their truthful judgments when engaged in collective decision-making. Our focus is on scenarios in which individuals reason about the incentives of others before choosing which judgments to report themselves. To this end, we introduce a formal model of strategic behaviour in logic-based judgment aggregation that accounts for such higher-level reasoning as well as the fact that individuals may only have partial information about the truthful judgments and preferences of their peers. We find that every aggregation rule must belong to exactly one of three possible categories: it is either (i) immune to strategic manipulation for every level of reasoning, or (ii) manipulable for every level of reasoning, or (iii) immune to manipulation only for every kth level of reasoning, for some natural number k greater than 1.

我们分析了个人在参与集体决策时歪曲其真实判断的动机。我们的重点是个人在选择报告自己的判断之前对他人的激励进行推理的情况。为此，我们在基于逻辑的判断聚合中引入了一种正式的战略行为模型，该模型解释了这种更高层次的推理以及个人可能只有部分关于其同龄人的真实判断和偏好的信息的事实。我们发现每个聚合规则必须恰好属于三个可能的类别之一：它要么（i）对每个推理级别的策略操纵免疫，要么（ii）对每个推理级别都可操纵，或（iii）不受操纵仅对每k第 1 级推理，对于某个大于 1 的自然数 k。