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In this paper, we propose an index that measures the agreement level between an individual opinion and a collective opinion when both are expressed by rankings of a set of alternatives. This index constitutes an interesting weighted version of the well-known Kendall's ranks correlation index. The originality of the proposed index arises from the fact that it accounts for the relevance of the specific position of the alternatives in an individual order to quantify the agreement level of the individual order with respect to a collective temporary order. The paper also introduces a new consensus measure model. The core of the consensus model is the proposed agreement index. We present an illustrative example to describe the consensus process. We can obtain a faster convergence to a consensus solution using this new index compared to Kendall's index.

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Abstract. This work is based on a disaggregation approach for the ELECTRE III method for the group decision-making. We provide a procedure in which the group is supported for modifying the parameters of outranking methods in an iterative and interactive process. In this work, we provide an application of the procedure through evaluating eight municipal districts for Water Company to invest in projects of water supply. An inferring parameters model performed by NSGA-II obtains marginal information from decision makers with more disagreement, which supports the stage of parameters modification in correspondence with the preferences of the whole group (collective ranking). This paper shows how the inferring parameters model may be used to help the decision makers with different interest to iteratively reach an agreement on how to rank cities at a time, reflecting the preferences at the individual level and at the collective level.

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