Thematic Section - Advances in Analytic Hierarchy Process

AHP in nonlinear scaling: from two-envelope problem to modeling by predictors

Stan Lipovetsky

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Paper aims: Extending the AHP abilities to new areas from explaining the famous Two-Envelope paradox to finding priorities as functions of auxiliary variables is suggested.

Originality: The proposed innovative and advantageous approach permits to find the non-constant priorities via regression modeling for the exponential or Cobb-Douglas production functions.

Research method: Transforming the ratio scale into the additive or logarithmic scales, which correspond to the multiplicative utility function, opens new possibilities in the multiple-criteria decision making.

Main findings: Two-Envelop problem is resolved, priority vectors are presented as functions by auxiliary variables, preferences are predicted and profiled by predictors.

Implications for theory and practice: The suggested techniques open novel possibilities of multiple-criteria decisions helping to researchers and managers to discover useful features of priority behavior due to the demographic, socio-economic, or technical properties of the compared alternatives, and to find optimal solutions for individual customers.


AHP. Two-envelope paradox. Nonlinear scaling. Multiplicative utility. Priority as function. Exponential function. Cobb-Douglas production function.


Abbott, D., Davis, B. R., & Parrondo, J. M. (2010). The two-envelope problem revisited. Fluctuation and Noise Letters, 9(1), 1-8.

Albers, C. J., Kooi, B. P., & Schaafsma, W. (2005). Trying to resolve the two-envelope problem. Synthese, 145(1), 89-109.

Egozcue, M., & Fuentes García, L. (2015). An optimal threshold strategy in the two-envelope problem with partial information. Journal of Applied Probability, 52(1), 298-304.

Ishizaka, A., Tasiou, M., & Martínez, L. (2020). Analytic hierarchy process-fuzzy sorting: An analytic hierarchy process–based method for fuzzy classification in sorting problems. The Journal of the Operational Research Society, 71(6), 928-947.

Keeney, R. L., & Raiffa, H. (1993). Decisions with multiple objectives: preferences and value tradeoffs. New York: Cambridge University Press.

Lee, C. (2013). The Two-envelope Paradox: asymmetric cases. Mind, 122(485), 1-26.

Lipovetsky, S. (2009). Global priority estimation in multiperson decision making. Journal of Optimization Theory and Applications, 140(1), 77-91.

Lipovetsky, S. (2012). Interpretation of Shapley Value regression coefficients as approximation for coefficients derived by elasticity criterion. In Proceedings of the Joint Statistical Meeting of the American Statistical Association (JSM'12) (pp. 3302-3307). San Diego, CA.

Lipovetsky, S. (2019). Express analysis for prioritization: best-worst scaling alteration to System 1. Journal of Management Analytics, 7(1), 12-27.

Lipovetsky, S. (2020a). AHP and Two-Envelope Paradox resolution via nonlinear scaling. In Proceedings of the International Symposium on Analytic Hierarchy Process. Pittsburgh, PA, USA.

Lipovetsky, S. (2020b). Personalized key drivers for individual responses in regression modeling. International Journal of Risk and Contingency Management, 9(3), 15-30.

Lipovetsky, S. (2020c). Priority vector estimation: consistency, compatibility, precision. International Journal of the Analytic Hierarchy Process, 12(3), 577-591.

Lipovetsky, S. (2021). Predictor analysis of group decision making. Stats, 4(1), 108-121.

Lipovetsky, S., & Conklin, M. (2015a). AHP priorities and Markov-Chapman-Kolmogorov Steady-States probabilities. International Journal of the Analytic Hierarchy Process, 7(2), 349-363.

Lipovetsky, S., & Conklin, M. (2015b). Predictor relative importance and matching regression parameters. Journal of Applied Statistics, 42(5), 1017-1031.

Lipovetsky, S., & Tishler, A. (1999). Interval estimation of priorities in the AHP. European Journal of Operational Research, 114(1), 153-164.

Lootsma, F. (1999). Multi-criteria decision analysis via ratio and difference judgement. London: Kluwer Academic Publishers.

Markosian, N. (2011). A simple solution to the Two Envelope problem. Logos & Episteme, 2(3), 347-357.

McDonnell, M. D., Grant, A. J., Land, I., Vellambi, B. N., Abbott, D., & Lever, K. (2011). Gain from the two-envelope problem via information asymmetry: on the suboptimality of randomized switching. Proceedings of the Royal Society of London. Series A, 467(2134), 2825-2851.

Neira-Rodado, D., Ortíz-Barrios, M., De la Hoz-Escorcia, S., Paggetti, C., Noffrini, L., & Fratea, N. (2020). Smart product design process through the implementation of a fuzzy Kano-AHP-DEMATEL-QFD approach. Applied Sciences, 10(5), 1792.

Noto, S., Shiroiwa, T., Kobayashi, M., Murata, T., Ikeda, S., & Fukuda, T. (2020). Development of a multiplicative, multi-attribute utility function and eight single-attribute utility functions for the Health Utilities Index Mark 3 in Japan. Journal of Patient-Reported Outcome, 4(1), 23. PMid:32246218.

Ramos, M. O., Silva, E. M., & Lima-Júnior, F. R. (2020). A fuzzy AHP approach to select suppliers in the Brazilian food supply chain. Production, 30, 1-16.

Saaty, T. L. (1980). The analytic hierarchy process. New York: McGraw-Hill.

Saaty, T. L., & Peniwati, K. (2007). Group decision-making: drawing out and reconciling differences. Pittsburgh, PA: RWS Publications.

Saaty, T. L., & Vargas, L. G. (1984). Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios. Mathematical Modelling, 5(5), 309-324.

Whitaker, R. (2007). Validation examples of the Analytic Hierarchy Process and Analytic Network Process. Mathematical and Computer Modelling, 46(7-8), 840-859.

Yang, J., Vargas, L. G., Jin, X., & Zhou, L. (2020). Quality credit evaluation in the internet company: a system based on the analytic hierarchy process. Journal of Business Economics and Management, 21(2), 344-372.

Yi, B. U. (2013). Conditionals and a Two-envelope Paradox. The Journal of Philosophy, 110(5), 233-257.

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60a414f4a95395288e7d7a63 production Articles
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