A critical analysis on Rank-Order-Centroid (ROC) and Rank-Sum (RS) weights in Multicriteria-Decision Analysis

Rank-Order-Centroid (ROC) weights have been celebrated several times in the literature on Multiple-
Criteria (or Multi-Attribute) Decision Analysis (MCDA), as manifesting the best performance among
other ordinal surrogate weights like Rank-Sum (RS) weights. The author expresses a strong caveat
regarding the use of ROC weights for solving practical multi-criteria or multi-attribute problems. A
previous article of the author has demonstrated that the apparent excellence of ROC weights among
surrogate weights is not all proven. It is shown there that the statistical experiments presented for
comparing the performances of surrogate weights are mainly based on the specific Point-Allocation
(PA) elicitation methodology. By contrast, Direct Rating (DR) favours Rank-Sum (RS) weights. The
present article develops this finding. Although it cannot not be mathematically proven that DR should
be preferred to PA, or equivalently RS to ROC, it appears from a practical point of view that DR is
much more natural than PA; it gives more freedom to choosing weights, and it leads to the simpler and
intuitively more convincing RS weights. This is illustrated with simulations and 2D and 3D
representations of PA and DR simplexes.