Group Manipulation in Judgment Aggregation
Sirin Botan, Arianna Novaro, Ulle Endriss

Abstract:
We introduce the concept of group manipulation into the study of judgment aggregation and investigate the circumstances under which an aggregation rule may be subject to strategic misrepresentation of judgments by a group of agents. Our focus is on neutral aggregation rules, which treat all propositions to be judged symmetrically, and we assume that agents strategise to minimise the number of propositions on which they disagree with the outcome of a rule. We find that strategic manipulation by groups of two agents can be ruled out for the independent and monotonic aggregation rules. This family of rules, which is precisely the family of rules for which manipulation by a single agent can be ruled out, includes the widely used uniform quota rules. When three or more agents may coordinate their manipulation, on the other hand, essentially all attractive rules are susceptible to strategic manipulation. However, we are able to recover the family of independent and monotonic rules as being immune to manipulation, if we add the assumption that the members of a group of manipulating agents fear that the others might opt out of the jointly agreed plan.