Axiomatic properties of inconsistency indices for pairwise comparisons

Abstract

Pairwise comparisons are a well-known method for the representation of the subjective preferences of a decision maker. Evaluating their inconsistency has been a widely studied and discussed topic and several indices have been proposed in the literature to perform this task. Since an acceptable level of consistency is closely related with the reliability of preferences, a suitable choice of an inconsistency index is a crucial phase in decision making processes. The use of different methods for measuring consistency must be carefully evaluated, as it can affect the decision outcome in practical applications. In this paper, we present five axioms aimed at characterizing inconsistency indices. In addition, we prove that some of the indices proposed in the literature satisfy these axioms, while others do not, and therefore, in our view, they may fail to correctly evaluate inconsistency.

25 pages, 3 figures

Cited by in corpus (22)

• On Axiomatization of Inconsistency Indicators for Pairwise Comparisons
• Studying a set of properties of inconsistency indices for pairwise comparisons
• A characterization of the Logarithmic Least Squares Method
• New results on inconsistency indices and their relationship with the quality of priority vector estimation
• Boundary properties of the inconsistency of pairwise comparisons in group decisions
• A general unified framework for interval pairwise comparison matrices
• On reducing inconsistency of pairwise comparison matrices below an acceptance threshold
• Characterization of an inconsistency ranking for pairwise comparison matrices
• Inconsistency indices for incomplete pairwise comparisons matrices
• Towards quantification of incompleteness in the pairwise comparisons method
• Axiomatizations of inconsistency indices for triads
• On the monotonicity of the eigenvector method
• Characterization of the row geometric mean ranking with a group consensus axiom
• Efficiency analysis of double perturbed pairwise comparison matrices
• Efficiency analysis of simple perturbed pairwise comparison matrices
• Entropy production rate as a criterion for inconsistency in decision theory
• Heuristic rating estimation - geometric approach
• Deriving Priorities From Inconsistent PCM using the Network Algorithms
• Notes on the existence of solutions in the pairwise comparisons method using the Heuristic Rating Estimation approach
• Satisfaction of the Condition of Order Preservation: A Simulation Study
• On Mathematical structures on pairwise comparisons matrices with coefficients in a group arising from quantum gravity
• Detection of decision-making manipulation in the pairwise comparisons method