Stable Rankings in Collective Decision Making with Imprecise Information

Abstract

The objective of the paper is to propose procedures to construct global ranking of a set of alternatives in situations in which each member of a group is able to provide imprecise information on his/her preferences about the relative importance of the criteria that have to be taken into account.

We first propose an approach based on the assumption that the final evaluation depends on the complete group since no possibility exists that the group might split into coalitions that search for more favourable solutions for the the coalitions members. To this end, the partial information on criteria weights provided by each individual is transformed into ordinal information on alternatives, and then the aggregation of individual preferences is addressed within a distance-based framework.

In a second approach, the possibility of coalition formation is considered, and the goal is to obtain rankings in which the disagreements of all the coalitions are taken into account. These rankings will exhibit an additional property of collective stability in the sense that no coalition will has the incentive to abandon the group and begin a separate evaluation process.

This last approach may be of interest in political decisions where different sectors have to be incorporated into a joint evaluation process with the desire to obtain a consensus across all possible subgroups.