Composition of Probabilistic Preferences in Multicriteria Problems with Variables Measured in Likert Scales and Fitted by Empirical Distributions

Abstract

The aim of this article is to demonstrate the advantages of the Composition of Probabilistic Preferences method in multicriteria problems with data from Likert scales. Multicriteria decision aids require a database as a decision matrix, in which two or more alternatives are evaluated according to two or more variables selected as decision criteria. Several problems of this nature use measures by Likert scales. Depending on the method, parameters from these data (e.g., means, modes or medians) are required for calculations. This parameterization of data in ordinal scales has fueled controversy for decades between authors who favor mathematical/statistical rigor and argue against the procedure, stating that ordinal scales should not be parameterized, and scientists from other areas who have shown gains from the process that compensates for this relaxation. The Composition of Probabilistic Preferences can allay the protests raised and obtain more accurate results than descriptive statistics or parametric models can bring. The proposed algorithm in R-code involves the use of probabilities with empirical distributions and fitting histograms of data measured by Likert scales. Two case studies with simulated datasets having peculiar characteristics and a real case illustrate the advantages of the Composition of Probabilistic Preferences.