Refining the PROMETHEE-scoring method: Propositions and an economic freedom assessment

The recent PROMETHEE-Scoring approach offers a method for generating cardinal scores through an outranking procedure utilizing Stochastic Multicriteria Acceptability and $\sigma$–$\mu$ analysis. In this paper, we illustrate some undesirable effects of this method and explore possible approaches to address them. First, we modify the original LP by inserting a new constraint that limits negative impacts caused by alternatives with low flow mean and standard deviation. Also, clustering is used to identify outliers in the decision matrix that may induce undesirable effects. A toy example demonstrates the issues and explores the proposed implementations. In addition, a numerical application is presented where a set of countries is ordered based on criteria from an economic freedom assessment. Both the numerical application and the toy example show that the propositions can improve the consistency of the results and prevent inconsistent outputs. The results include comparisons between the rank of alternatives when using purely the PROMETHEE-Scoring method, the proposed improvements, and the expected results from SMAA-PROMETHEE.