An update on combinatorial method for aggregation of expert judgments in AHP

Abstract

Paper aims

the paper aims to demonstrate the advantages of several modifications of combinatorial method of expert judgment aggregation in AHP. Modifications are based on 1) weighting of spanning trees; 2) sorting of spanning trees by graph diameter during aggregation.

Originality

Both the method and its modifications are developed and improved by the authors. We propose to 1) weight spanning trees, based on quality of respective expert estimates, and 2) sort them by diameter in order to reduce the impact of expert errors and the method’s computational complexity.

Research method

we focus on theoretical and empirical studies of several modifications of combinatorial method of aggregation of expert judgments within AHP.

Main findings

modified combinatorial method has several conceptual advantages over ordinary method. It is also less sensitive to perturbations of initial data. Additionally, selection of spanning trees with smaller diameters allows us to reduce computational complexity of the method and minimize the impact of expert errors.

Implications for theory and practice

Combinatorial method is a universal instrument of expert judgment aggregation, applicable to additive/multiplicative, complete/incomplete, individual/group pair-wise comparisons, provided in different scales. It is used in the original strategic planning technology, which has recently found several important applications.

Keywords
Pair-wise comparison; Consistency; Compatibility; Spanning tree graph diameter; Prüfer sequence