A linear programming model to reduce rank violations while eliciting preference from pairwise comparison matrix

Abstract

Rank violation is a crucial criterion to decide the ordinal consistency of a priority vector derived from a pairwise comparison matrix. Popular prioritisation methods, such as the eigenvalue method, logarithmic least squares, and weighted least squares have not guaranteed minimal rank violations even with cardinal consistency examination. This article closes this gap by proposing a linear-programming-based procedure to update a priority vector obtained by one of the popular prioritisation methods with a better one that ensures minimal rank violations. Taking advantage of rank preservation in an improved linear programming model, the proposed procedure can examine the feasibility of including inconsistent constraints with respect to a given priority vector, and hence determines the existence of a better priority vector with reduced rank violations. The process of obtaining updated priority vectors by the proposed procedure is demonstrated in classic examples.

Keywords:

• Multiple criteria analysis
• priority vector
• rank violation
• pairwise comparison matrix
• linear programming