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Estimation of Attribute Weights from Preference Comparisons


  • Dan Horsky

    (Graduate School of Management, University of Rochester, Rochester, New York 14627 and Recanati Graduate School of Business, Tel-Aviv University, Tel-Aviv, Israel)

  • M. R. Rao

    (Indian Institute of Management, 33 Langford Road, Bangalore 560 027, India)


The multi-attribute utility model serves as a basis for many marketing decisions such as new product planning and advertising message selection. The estimation of individuals' attribute weights can be performed using several data types and estimation techniques. There is evidence to suggest that the estimates derived from ordinal preference data through linear programming show greater stability and predictive validity. In this paper we address two fundamental issues which have not been addressed in the context of this latter type estimation: the theoretical foundations for estimating cardinal utility functions from ordinal preference data and the properties of the linear programming estimators. First, we establish the theoretical foundations from economics, mathematical psychology, and decision analysis of obtaining a cardinal (interval scaled) multi-attribute function from ordinal data. This leads us to recommend that in addition to the collection of paired preference comparisons, also comparisons of pairs of pairs be collected. We then describe the type of errors which are likely to arise in the measurement stage, and their relationship to the phenomenon of intransitivities. We formulate a linear program, LINPAC, for the estimation of attribute weights from the above preference data. The previously proposed LINMAP procedure is a special case of this formulation when only the information on the paired preferences is utilized. Next, the statistical properties of the estimators, such as uniqueness, unbiasedness, consistency and efficiency, are examined. Then, through a simulation study we examine the rate of convergence of the estimated weights to the true weights as a function of the number of brands. In the simulation study we also examine the conditions under which the estimators outperform equal weights and compare the estimates derived from LINPAC with those derived from LINMAP. Finally, the estimation procedures are examined with actual data while the simulation results, an equal weights model, and a stated weights model serve as benchmarks.

Suggested Citation

  • Dan Horsky & M. R. Rao, 1984. "Estimation of Attribute Weights from Preference Comparisons," Management Science, INFORMS, vol. 30(7), pages 801-822, July.
  • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:7:p:801-822
    DOI: 10.1287/mnsc.30.7.801

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    Cited by:

    1. Oral, Muhittin & Kettani, Ossama & Cinar, Unver, 2001. "Project evaluation and selection in a network of collaboration: A consensual disaggregation multi-criterion approach," European Journal of Operational Research, Elsevier, vol. 130(2), pages 332-346, April.
    2. Oral, Muhittin & Chabchoub, Habib, 1996. "On the methodology of the World Competitiveness Report," European Journal of Operational Research, Elsevier, vol. 90(3), pages 514-535, May.
    3. Vetschera, Rudolf & Weitzl, Wolfgang & Wolfsteiner, Elisabeth, 2014. "Implausible alternatives in eliciting multi-attribute value functions," European Journal of Operational Research, Elsevier, vol. 234(1), pages 221-230.
    4. Hsu-Shih Shih, 2016. "A Mixed-Data Evaluation in Group TOPSIS with Differentiated Decision Power," Group Decision and Negotiation, Springer, vol. 25(3), pages 537-565, May.
    5. Vetschera, Rudolf, 1992. "Estimating preference cones from discrete choices: Computational techniques and experiences," Discussion Papers, Series I 259, University of Konstanz, Department of Economics.
    6. Doumpos, Michael & Zopounidis, Constantin, 2004. "Developing sorting models using preference disaggregation analysis: An experimental investigation," European Journal of Operational Research, Elsevier, vol. 154(3), pages 585-598, May.
    7. András Farkas, 2011. "Budapest Bridges Benchmarking," Proceedings- 9th International Conference on Mangement, Enterprise and Benchmarking (MEB 2011),, Óbuda University, Keleti Faculty of Business and Management.
    8. Chao Fu & Dong-Ling Xu, 2016. "Determining attribute weights to improve solution reliability and its application to selecting leading industries," Annals of Operations Research, Springer, vol. 245(1), pages 401-426, October.
    9. Dan Horsky & Paul Nelson, 2006. "Testing the Statistical Significance of Linear Programming Estimators," Management Science, INFORMS, vol. 52(1), pages 128-135, January.
    10. Lakhal, Salem Y. & H'Mida, Souad & Venkatadri, Uday, 2005. "A market-driven transfer price for distributed products using mathematical programming," European Journal of Operational Research, Elsevier, vol. 162(3), pages 690-699, May.
    11. B. P. S. Murthi & Sumit Sarkar, 2003. "The Role of the Mangement Sciences in Research on Personalization," Review of Marketing Science Working Papers 2-2-1025, Berkeley Electronic Press.
    12. Dong, Yucheng & Liu, Yating & Liang, Haiming & Chiclana, Francisco & Herrera-Viedma, Enrique, 2018. "Strategic weight manipulation in multiple attribute decision making," Omega, Elsevier, vol. 75(C), pages 154-164.
    13. Yang, Guo-liang & Yang, Jian-Bo & Xu, Dong-Ling & Khoveyni, Mohammad, 2017. "A three-stage hybrid approach for weight assignment in MADM," Omega, Elsevier, vol. 71(C), pages 93-105.
    14. Ewa Roszkowska, 2020. "The extention rank ordering criteria weighting methods in fuzzy enviroment," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 2, pages 91-114.
    15. Doumpos, Michael & Zopounidis, Constantin, 2011. "Preference disaggregation and statistical learning for multicriteria decision support: A review," European Journal of Operational Research, Elsevier, vol. 209(3), pages 203-214, March.
    16. Louviere, Jordan & Lings, Ian & Islam, Towhidul & Gudergan, Siegfried & Flynn, Terry, 2013. "An introduction to the application of (case 1) best–worst scaling in marketing research," International Journal of Research in Marketing, Elsevier, vol. 30(3), pages 292-303.


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