Robust Rankings of Multidimensional Performances

Abstract

There is a general interest in ranking performances (e.g., in sports or policy) that essentially implies aggregating several performance dimensions. The usual approach considers a “cardinal” linear weighting of the different single-dimensional performance indicators. The authors present an alternative approach, which merely requires “ordinal” information regarding the importance of the different performance dimensions. It is argued that this approach is robust with respect to alternative specifications of the (possibly nonlinear) underlying performance aggregation function. An application to Tour de France racing cyclists (in the period 1953-2004) illustrates the approach. The authors find that Eddy Merckx, Bernard Hinault, and Lance Armstrong (robustly) dominate almost all other racing cyclists in the sample, although they do not dominate each other. A net-dominance metric ranks Bernard Hinault on the first place in the sample; Eddy Merckx and Lance Armstrong follow very closely ex-aequo on the second place.