Manipulating Skeptical and Credulous Consequences When Merging Beliefs

Automated reasoning techniques for multi-agent scenarios need to address the possibility that procedures for collective decision making may fall prey to manipulation by self-interested agents. In this paper we study manipulation in the context of belief merging, a framework for aggregating agents’ positions, or beliefs, with respect to a set of issues represented by propositional atoms. Within this framework agents submit their positions as propositional formulas that are to be aggregated into a single formula. To reach a final decision, we employ well-established acceptance notions and extract the skeptical and credulous consequences (i.e., atoms true in all and, respectively, at least one model) of the resulting formula. We find that, even in restricted cases, most aggregation procedures are vulnerable to manipulation by an agent acting strategically, i.e., one that is able to submit a formula not representing its true position. Our results apply when the goal of such an agent is either that of (i) affecting an atom’s skeptical or credulous acceptance status, or (ii) improving its satisfaction with the result. With respect to latter task, we extend existing work on manipulation with new satisfaction indices, based on skeptical and credulous reasoning. We also study the extent to which an agent can influence the outcome of the aggregation, and show that manipulation can often be achieved by submitting a complete formula (i.e., a formula having exactly one model), yet, the complexity of finding such a formula resides, in the general case, on the second level of the polynomial hierarchy.