Expert-elicited weights in multi-criteria decision analysis: theory and practice

The expert weighting method has been applied in decision-making for years but lacks a firm theoretical basis. This study introduces a mathematical framework to address this gap. Due to the additive-only nature of the five-point Likert scale, a 100-point system was adopted. Experts rated each variable based on a baseline of 1, and matrix multiplication was used to generate proportional importance values, overcoming the limits of ordinal comparisons. Mathematical induction shows that, with equal initial scores, variables with higher variance receive lower importance. This supports the logic of the weighting process and improves the scale's sensitivity in distinguishing variable significance. By analysing internal variance, the method allows for clearer importance ranking and enhances evaluation precision. While the Likert scale is common, its statistical limits reduce reliability. Incorporating the expert weighting method addresses these flaws and improves evaluation tools.