Joint consensus evaluation of multiple objects on an ordinal scale: An approach driven by monotonicity

In this paper, we consider the problem of obtaining the consensus evaluation of multiple objects based on the evaluations expressed by several experts. This problem is of relevance to several fields, in particular to the field of sensory evaluation, such as in food quality appraisal, and to the field of recommender systems, such as in movie recommendation and online dating systems. Unlike existing methods for obtaining a consensus evaluation, which strongly rely on a chosen distance function, we adhere to the natural property of monotonicity, resulting in an intuitively appealing consensus evaluation method in which the labels expressed for all objects are considered simultaneously. Three real-life and three synthetic examples illustrate the search for such consensus evaluation.