Disjunctive merging: Quota and Gmin merging operators

When aggregating information from a group of agents, accepting the pieces of information shared by all agents is a natural requirement. In this paper, we investigate such a unanimity condition in the setting of propositional merging. We discuss two interpretations of the unanimity condition. We show that the first interpretation is captured by existing postulates for merging. But the second interpretation is not, and this leads to the introduction of a new disjunction postulate (Disj). It turns out that existing operators satisfying (Disj) do not perform well with respect to the standard criteria used to evaluate merging operators: logical properties, computational complexity and strategy-proofness. To fill this gap, we introduce two new families of propositional merging operators, quota operators and Gmin operators, which satisfy (Disj), and achieve interesting trade-offs with respect to the logical, computational, and strategy-proofness criteria.