Strategic manipulation in judgment aggregation under higher-level reasoning

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.