Hierarchical Structures in Multicriteria Decision Making

Abstract

Confronted with decisions involving many criteria in real life, people sometimes apply a ranking of importance to the criteria, instead of trying to balance the criteria on some common scale. The principle “first things first” is at the heart of any hierarchical procedure and one may ask for the reasons people are applying it. Beside empirical investigation, an answer may also be given by looking analytically for possible appealing features which hierarchical structures could possess. In this respect, not only the individual decision taker is of interest, but also his cultural environment, including e.g. the dictionary or the decimal system both being based on lexicographical ordering. It is the main result of the present paper that hierarchical decision procedures may be characterized by some specific stability property. Roughly speaking, the latter means that a decision taken in favor of one alternative against the other, is not upset by a small perturbation in the assessment of any of the criteria. For the result, we have to assume the decision rule under consideration yields decisions in sufficiently many cases of conflict between the different criteria. Without this assumption the stability property is not very demanding and it is shared by various different rules.