On Merging Strategy-Proofness

Merging operators aim at defining the beliefs/goals of a group of agents from the beliefs/goals of each member of the group. Whenever an agent of the group has preferences over the possible results of the merging process (i.e. the possible merged bases), she can try to rig the merging process by lying on her true beliefs/goals if this leads to a better merged base according to her point of view. Obviously, strategy-proof operators are highly desirable in order to guarantee a fair merging process even when some of them are not sincere. In fact, when strategy-proofness is not guaranteed, it may be questioned whether the result of the merging process actually represents the beliefs/goals of the group. In this paper, the strategy-proof landscape for many merging operators from the literature, including model-based ones and formula-based ones, is drawn. Both the general case and several restrictions on the merging process (among others, the number of agents and the presence of integrity constraints), are considered.