Consistency of pairwise comparisons and its role in optimal detection of customers’ preferences

Abstract

Purpose: This paper analyses a problem that originates in the weighted-average model, a mathematical construct introduced by the theory of multicriteria decision-making that can be used to detect what product a customer desires. The problem occurs because the model needs to know the weight the customer assigns to each product feature, aside from the levels of all the product characteristics, in order to calculate the overall value of the product. And since by one approach the weights can be estimated by optimization, the question arises which optimization criterion to select for the procedure, as different criteria will lead to different weights and thus to different product evaluations. The paper analyses the problem in connection with the so-called consistency of pairwise comparisons, which are utilized in the optimization and describe how much the customer prefers one product feature to another. The analysis shows that the problem of which criterion to use to calculate the weights can be eliminated if the pairwise comparisons are consistent. The analysis is performed within pre-defined criteria and is supplemented with case studies supporting the findings. Methodology/Approach: Linear algebra, optimization techniques, case studies. Findings: The results represent a prescription customers can use if they want to avoid the pitfalls of selecting a specific optimization criterion when informing the product maker about what they want based on the weighted-average model. Research Limitation/Implication: The results are related to a specific decision-making model, although that model is still very general and natural. Originality/Value of paper: The problem of selecting an optimization criterion to determine decision weights is not discussed in the theory. Category: Technical paper.