An experiment on the consistency of aggregated comparison matrices in AHP

Rhonda Aull-Hyde, Sevgi Erdogan, Joshua M. Duke

Research output: Contribution to journalArticlepeer-review

93 Scopus citations


The analytic hierarchy process can be used for group decision making by aggregating individual judgments or individual priorities. The most commonly used aggregation methods are the geometric mean method and the weighted arithmetic mean method. While it is known that the weighted geometric mean comparison matrix is of acceptable consistency if all individual comparison matrices are of acceptable consistency, this paper addresses the following question: Under what conditions would an aggregated geometric mean comparison matrix be of acceptable consistency if some (or all) of the individual comparison matrices are not of acceptable consistency? Using Monte Carlo simulation, results indicate that given a sufficiently large group size, consistency of the aggregate comparison matrix is guaranteed, regardless of the consistency measures of the individual comparison matrices, if the geometric mean is used to aggregate. This result implies that consistency at the aggregate level is a non-issue in group decision making when group size exceeds a threshold value and the geometric mean is used to aggregate individual judgments. This paper determines threshold values for various dimensions of the aggregated comparison matrix.

Original languageEnglish (US)
Pages (from-to)290-295
Number of pages6
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - May 16 2006
Externally publishedYes


  • Analytic hierarchy process
  • Group decisions
  • Simulation

ASJC Scopus subject areas

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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