Multiple-criteria performance ranking based on profile distributions: An application to university research evaluations

This article addresses a category of multi-criteria ranking problems in which performance evaluations of the 'objects' or 'alternatives' to be ranked are not given by unique numbers but by performance profile distributions running over an ordered set of performance score levels. The numerical values to be given to score levels are not specified a priori using cardinal scales. A weighted sum approach is developed based on order statistics to combine the individual profile distributions. In this way, a global ranking indicator is obtained, considering not only mean distribution values but also standard deviations. As a test of feasibility, the resulting Profile Ranking with Order Statistics Evaluations (PROSE) approach has been applied to the performance profile distributions provided by the UK Research Excellence Framework 2014, evaluating the quality of UK research.