Cohesiveness in group decision makin problems: its measurement and its achievement

Abstract

[EN] The general objective of this doctoral thesis is to develop novel approaches for measuring cohesiveness / consensus and for accomplishing social consensus solutions in group decision making problems. In this line, this thesis expects to broaden the scope of the traditional and related methodologies. These general issues are then addressed in the three following contributions.

In the first contribution, the problem of measuring the degree of consensus/ dissensus in a context where experts or agents express their opinions on alternatives or issues by means of cardinal evaluations is studied. The assumption of considering cardinal evaluations to measure the cohesiveness had not been previously examined in literature. To this end, a new class of distance-based consensus methods, the family of the Mahalanobis dissensus measures for profiles of cardinal values is proposed. The main advantage of this proposal is that it takes into account the effects of differences in scale and possible interrelated issues. Moreover, some meaningful properties of the Mahalanobis dissensus measures are set forth. Finally, an application over a real empirical example is presented and discussed.

In the second contribution, a new approach to the measurement of consensus based on the Pearson correlation coeffcient is studied under the assumption of experts' opinions modelled via reciprocal preference relations. The new correlation consensus degree measures the concordance between the intensities of preference for pairs of alternatives. Although a detailed study of the formal properties of the new correlation consensus degree shows that it verifies relevant and desirable properties common either to distance or to similarity functions, it is also proved that it is different to traditional consensus measures. In order to emphasise the novelty of our work, an application to Clinical Decision-Making realm is presented.

In the third contribution, three basic essentials are addressed: the management of experts' opinions when they are expressed by ordinal information; the measurement of the degree of dissensus among such opinions; and the achievement of a group solution that conveys the minimum dissensus to the experts' group. Accordingly, a new procedure to codify ordinal information is characterised. Likewise, a new measurement of the degree of dissensus among individual preferences based on the Mahalanobis distance is designed in such a way that it is especially indicated for the case of possibly correlated alternatives. Finally, a procedure to obtain a social consensus solution, that also includes the possibility of alternatives that are correlated, is investigated. In addition, we examine the main traits of the dissensus measurement as well as the social solution proposed. The operational character and intuitive interpretation of these approaches are illustrated by an explanatory example.