On the Logic of Merging: Quota and Gmin Operators

In this paper, two families of merging operators are considered: quota operators and Gmin operators. Quota operators rely on a simple idea: any possible world is viewed as a model of the result of the merging when it satisfies “sufficiently many” bases from the given profile (a multi-set of bases). Each interpretation of the “sufficiently many” gives rise to a specific operator. Each Gmin operator is parameterized by a pseudo-distance and each of them is intended to refine the quota operators (i.e., to preserve more information). Quota and Gmin operators are evaluated and compared along four dimensions: rationality, computational complexity, strategy-proofness, and discriminating power. Those two families are shown as interesting alternatives to the formula-based merging operators (which selects some formulas in the union of the bases).