Aggregation of incomplete preference rankings: Robustness analysis of the ZMII-technique

Abstract

A common group decision-making problem is that in which: (a) several judges express their subjective preference rankings regarding some objects of interest and (b) these rankings should then be aggregated into a collective judgement. The authors recently developed an aggregation technique – denominated “ZM_II” – aggregating these rankings into a ratio scaling of the objects, which represents the solution to the decision-making problem of interest. This technique also includes a flexible response mode, which tolerates incomplete rankings and can, therefore, be adapted to various practical contexts, such as quality improvement activities, field surveys, product-comparison surveys, etc.

The aim of this article is proposing an original approach to verify the robustness of the ZM_II-technique under the influence of various factors, especially those concerned with the degree of “completeness” of preference rankings (e.g., number of objects identified by judges, whether these objects are ordered or not, etc.). The methodology in use relies on the simulation of several thousand decision-making problems, in order to organically study the effect of the factors of interest. Results show a certain robustness of the ZM_II-technique, even under relatively “unfavourable” practical conditions, characterized by very incomplete preference rankings. Description is supported by instructive examples.