Aggregation of Partial Rankings - An Approach Based on the Kemeny Ranking Problem

Abstract

Aggregating the preference of multiple experts is a very old problem which remains without an absolute solution. This assertion is supported by the Arrow's theorem: there is no aggregation method that simultaneously satisfies three fairness criteria (non-dictatorship, independence of irrelevant alternatives and Pareto efficiency). However, it is possible to find a solution having minimal distance to the consensus, although it involves a NP-hard problem even for only a few experts. This paper presents a model based on Ant Colony Optimization for facing this problem when input data are incomplete. It means that our model should build a complete ordering from partial rankings. Besides, we introduce a measure to determine the distance between items. It provides a more complete picture of the aggregated solution. In order to illustrate our contributions we use a real problem concerning Employer Branding issues in Belgium.