Group Decision and Negotiation

, Volume 22, Issue 3, pp 519–540 | Cite as

On the Use of Paired Comparisons to Construct Group Preference Scales for Decision Making

  • Kung-E. ChengEmail author
  • James A. McHugh
  • Fadi P. Deek


Polling opinion is a common group activity. Scaling tools can be used to provide a more precise presentation of opinions than traditional polling/voting. The interval scale of items constructed by scaling tools can aid participants in finding the current disposition of a group. We consider Thurstone’s law of comparative judgment as well as a weighted digraph ranking system for building group scales from pairwise comparisons. Assumptions for computing scales are reviewed together with issues and limitations of applying these scaling methods in groups. Results from a classic experiment and simulations by both methods are compared. We also made recommendations on choosing scaling method based on theoretic and practical consideration.


Group decision Polling Scaling Paired comparison Law of comparative judgment Weighted digraph 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bang-Jensen J, Gutin G (2000) Digraphs: theory, algorithms and applications. Springer, LondonGoogle Scholar
  2. Belton V, Stewart TJ (2002) Multiple criteria decision analysis: an integrated approach. Kluwer Academic Publishers, DordrechtCrossRefGoogle Scholar
  3. Bradley RA, Terry ME (1952) Rank analysis of incomplete block designs, I. The method of paired comparisons. Biometrika 39(3/4): 324–345CrossRefGoogle Scholar
  4. Cheng K-E, Deek FP (2007) A framework for studying voting in group support systems. Paper presented at the 40th Hawaii international conference on system sciences, Waikaloa, HI, 3–6 Jan 2007Google Scholar
  5. Dawes RM (1994) Psychological measurement. Psychol Rev 101(2): 278–281CrossRefGoogle Scholar
  6. Easley RF, Mackay DB (1995) Supporting complex group decisions—a probabilistic multidimensional-scaling approach. Math Comput Model 21(12): 25–33CrossRefGoogle Scholar
  7. Engeldrum PG (2000) Psychometric scaling: a toolkit for imaging systems development. Imcotek Press, WinchesterGoogle Scholar
  8. Harary F, Moser L (1966) The theory of round robin tournaments. Am Math Mon 7(3): 231–246CrossRefGoogle Scholar
  9. Li Z, Cheng K, Wang Y, Hiltz SR, Turoff M (2001) Thurstone’s law of comparative judgment for group support. In: Strong D, Straub D, DeGross JI (eds) The seventh Americas conference on information systems, Boston, MA. Association for Information Systems, pp 241–244, 2–5 Aug 2001Google Scholar
  10. Luce RD (1959) Individual choice behaviours: a theoretical analysis. Wiley, New YorkGoogle Scholar
  11. Luce RD (1994) Thurstone and sensory scaling—then and now. Psychol Rev 101(2): 271–277CrossRefGoogle Scholar
  12. Maydeu-Olivares A (2003) On Thurstone’s model for paired comparisons and ranking data. In: Yanai H, Okada A, Shigematu K, Kano Y, Meulman JJ (eds) New developments in psychometrics. Springer, Tokyo, pp 519–526Google Scholar
  13. McHugh JA (1989) Algorithmic graph theory. Prentice-Hall, New YorkGoogle Scholar
  14. Ore Ø, Wilson RJ (1990) Graphs and their uses. New Mathematical Library. The Mathematical Association of America, Washington, DCGoogle Scholar
  15. Richard E (1999) Tools of governance. In: Hague BN, Loader B (eds) Digital democracy: discourse and decision making in the information age. Routledge, LondonGoogle Scholar
  16. Rubinstein A (1980) Ranking the participants in a tournament. J Soc Ind Appl Math 38(1): 108–111CrossRefGoogle Scholar
  17. Takane Y (1987) Analysis of covariance structures and probabilistic binary choice data. Commun Cogn 20(1): 45–62Google Scholar
  18. Thurstone LL (1927a) A law of comparative judgment. Psychol Rev 34: 273–287CrossRefGoogle Scholar
  19. Thurstone LL (1927b) The method of paired comparisons for social values. J Abnorm Soc Psychol 21: 384–400CrossRefGoogle Scholar
  20. Thurstone LL (1927c) Psychophysical analysis. Am J Psychol 38: 368–389CrossRefGoogle Scholar
  21. Thurstone LL (1928) An experimental study of national preferences. J Gen Psychol 1: 405–425CrossRefGoogle Scholar
  22. Thurstone LL (1928) The measurement of opinions. J Abnorm Soc Psychol 22: 415–430CrossRefGoogle Scholar
  23. Thurstone LL (1931) Rank order as a psychophysical method. J Exp Psychol 14: 187–201CrossRefGoogle Scholar
  24. Thurstone LL (1959) The measurement of values. University of Chicago Press, ChicagoGoogle Scholar
  25. Torgerson WS (1958) Theory and methods of scaling. Wiley, New YorkGoogle Scholar
  26. Tsukida K, Gupta MR (2011) How to analyze paired comparison data. UWEE technical report number UWEETR-2011-0004, Department of Electrical Engineering, University of Washington, Seattle, WAGoogle Scholar
  27. Turoff M, Hiltz SR, Cho H, Li Z, Wang Y (2002) Social decision support systems (SDSS). Paper presented at the 35th Hawaii international conference on system sciences, Waikoloa, Hawaii, 7–10 Jan 2002Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Kung-E. Cheng
    • 1
    Email author
  • James A. McHugh
    • 2
  • Fadi P. Deek
    • 3
  1. 1.National Center for Transportation and Industrial ProductivityNew Jersey Institute of TechnologyNewarkUSA
  2. 2.Computer Science Department, College of Computing SciencesNew Jersey Institute of TechnologyNewarkUSA
  3. 3.College of Science and Liberal ArtsNew Jersey Institute of TechnologyNewarkUSA

Personalised recommendations