International audienceReasoning on multiple criteria is a key issue in groupdecision to take into account the multidimensional nature ofreal-world decision-making problems. In order to reduce theinduced information overload, in multicriteria decisionanalysis, criteria are in general aggregated, in many casesby a simple discriminant function of the form of a weightedsum. It requires to, a priori and completely, elicitpreferences of decision makers. That can be quite arbitrary.In everyday life, to reduce information overload peopleoften use a heuristic, called ``Take-the-best'': theytake criteria in a predefined order, the first criterionwhich discriminates the alternatives at stake is used tomake the decision. Although useful, the heuristic can bebiased. This article proposes the Logical Multicriteria Sort process to supportmulticriteria sorting within islands of agreement. Ittherefore does not require a complete and consistent apriori set of preferences, but rather supports groups toquickly identify the criteria for which an agreement exists.The process can be seen as a generalization ofTake-the-best. It also proposes to consider one criterion ata time but once a criterion has been found discriminating itis recorded, the process is iterated and relevant criteriaare logically combined. Hence, the biases of Take-the-bestare reduced. The process is supported by a GDSS, based onLogical Information Systems, which gives instantaneousfeedbacks of each small decision and keeps tracks of all ofthe decisions taken so far. The process is incremental,each step involves low information load. It guarantees somefairness because all considered alternatives aresystematically analyzed along the selected criteria. Asuccessful case study is reported