Abstract
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.
Highlights
In many instances of their social life, individuals—being members of various groups—need to reach collective decisions by aggregating their private judgments on several issues: from choosing what kind of food to have during a dinner with friends, to reaching an agreement with their colleagues about what policy their company should implement
For any type of partial information that may manifest itself in a given scenario, we prove two main results: first, on the positive side, any aggregation rule that is immune to manipulation under first-level reasoning will remain resistant to manipulation under all higher levels of reasoning; that is, higher-level reasoning is never detrimental to a rule’s immunity to manipulation
Given any type of information the individuals may hold about the truthful judgments of their peers, we investigate the logical connections between first-level and higherlevel reasoning with regard to the strategyproofness of aggregation rules
Summary
In many instances of their social life, individuals—being members of various groups—need to reach collective decisions by aggregating their private judgments on several issues: from choosing what kind of food to have during a dinner with friends, to reaching an agreement with their colleagues about what policy their company should implement. The leader could think that—since the deputy knows that she wants the position but he prefers to not have it announced yet—the deputy has an incentive to lie by declaring that he agrees with the new position, so that the rule prevents it from being announced (this thought of the leader corresponds to level-2 reasoning). An incentive for the leader to lie is created She may think that the deputy has already followed the previous reasoning in his mind, expecting her to lie and making the decision to tell the truth that he does not want the position. It would again be better for the leader to tell the truth as well.
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