An experiment on the consistency of aggregated comparison matrices in AHP |
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| Institution: | 1. Operations Research Program, 226 Townsend Hall, University of Delaware, Newark, DE 19716, USA;2. Department of Civil and Environmental Engineering, University of Maryland, College Park, 1173 Glenn L.Martin Hall, College Park, MD 20742-3021, USA;3. Department of Food and Resource Economics, 205 Townsend Hall, University of Delaware, Newark, DE 19716, USA;1. Vrije Universiteit Brussel, Mobility, Logistics and Automotive Research Centre (MOBI), Department Business Technology and Operations (BUTO), Pleinlaan 2, Brussels 1050, Belgium;2. Utrecht University, Faculty of Geosciences, PO Box 80115, 3508 TC Utrecht, The Netherlands;1. Urban Studies and Planning Program, School of Architecture, Planning and Preservation, National Center for Smart Growth Research and Education, University of Maryland, College Park, MD, 20742, USA;2. School of Architecture, Planning and Preservation, National Center for Smart Growth Research and Education, University of Maryland, College Park, MD, 20742, USA;3. Faculty Research Scientist, University of Maryland, College Park, USA;1. School of Business Administration, Southwestern University of Finance and Economics, Chengdu 611130, China;2. School of Economics and Management, University of Electronic Science and Technology of China, Chengdu 611731, China;1. Department of Mechanical Engineering, Government Engineering College, Nilokheri, Haryana, India;2. Centre for Engineering Operations Management, Department of Technology and Innovation, University of Southern Denmark, Odense, Denmark;3. Department of Mechanical Engineering Graphic Era University, Dehradun 248002, Uttarakhand, India;4. Department of Management Studies, Indian Institute of Technology, Roorkee 247667, Uttarakhand, India;1. Br. Andrew Gonzalez FSC College of Education, De La Salle University, 2401 Taft Avenue, Manila 1004, Philippines;2. Gokongwei College of Engineering, De La Salle University, 2401 Taft Avenue, Manila 1004, Philippines;3. School of Economics, De La Salle University Manila, 2401 Taft Avenue, Manila 1004, Philippines |
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| Abstract: | 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. |
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