Skip to main content

Part of the book series: Theory and Decision Library ((TDLU,volume 16))

Abstract

The purpose of this paper is to review models and methods for aggregating opinions. By the word “opinion” is meant the expression of a person’s belief concerning the outcome of an uncertain event, either in the form of a point estimate or a probability distribution1. For example, consider a group of businessmen meeting to decide upon a sales forecast, the evolution of certain share prices or an uncertain economic variable (e. g. U.K. oil revenues in 1984). Given the prevalence of such forecasting activity in many fields, the importance of this topic hardly needs emphasizing.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Asch, SE . Effects of group pressure upon the modification and distortion of judgments., In H.Guetzkow (Ed.),, Groups, leadership and men. Pittsburgh: Carnegie Press, 1951

    Google Scholar 

  • Barnlund, D.C. A comparative study of individual, majority, and group judgment., Journal of Abnormal Social Psychology, 1959, 58, 55–60.

    Article  Google Scholar 

  • Belovicz, M.W., & Finch, F.E. A critical analysis of the “risky shift” phenomenon., Organizational Behavior and Human Performance, 1971, 6, 150–168.

    Article  Google Scholar 

  • Brown, R.W. Social psychology, New York: Free Press, 1965.

    Google Scholar 

  • Brown, T.A. An experiment in probabilistic forecasting (R-944-ARPA)., Santa Monica, California: Rand Corporation, July 1973.

    Google Scholar 

  • Carroll, J.D., & Chang, J-J. Analysis of individual differences on multidimensional scaling via an n-way generalization of “Eckart- Young” decomposition., Psychometrika, 1970, 35, 283–319.

    Article  Google Scholar 

  • Clark, R.D. III. Group induced shift toward risk: A critical appraisal. Psychological Bulletin, 1971, 76, 251–270.

    Article  Google Scholar 

  • Cochran, W.G. Sampling techniques (2nd edition)., New York: Wiley, 1963.

    Google Scholar 

  • Condorcet, Marquis de. Essai sur l’application de l’analyse a la probability des decisions rendues a la pluralite des voix. Paris, 1785

    Google Scholar 

  • Dalkey, N.C. The Delphi method: An experimental study of group opinion (RM-5888-PR). Santa Monica, California: Rand Corporation, June 1969.

    Google Scholar 

  • Daley, N.C., Brown, B., & Cochran, S. The Delphi method, III. Use of self ratings to improve group estimates (RM-6115-PR). Santa Monica, California: Rand Corporation, November 1969.

    Google Scholar 

  • Dalkey, N.C., & Helmer, O., An experimental application of the Delphi method to the use of experts., Management Science, 1963, 9, 458–467.

    Article  Google Scholar 

  • Davis, J.H,. Group performance, Reading, Mass.: Addison-Wesley, 1969.

    Google Scholar 

  • Davis, J.H. Group decision and social interaction: A theory of social decision schemes. Psychological Review, 1973, 80, 97–125.

    Article  Google Scholar 

  • Dawes, R.M. An inequality concerning correlation of composites vs. composites of correlations., Oregon Research Institute Methodological Note, 1970, 1 (1).

    Google Scholar 

  • Dawes, R.M., & Corrigan, B. Linear models in decision making., Psychological Bulletin, 1974, 81 95–106.

    Article  Google Scholar 

  • de Finetti, B. Does it make sense to speak of “good probability appraisers?” In I.J.Good (Ed.), The scientist speculates - An anthology of partly-baked ideas. London: Heineman, 1962.

    Google Scholar 

  • de Finetti, B. Theory of Probability (Vol. 1 ). New York: Wiley, 1974.

    Google Scholar 

  • De Groot, M.H. Reaching a consensus. Journal of the American Statistical Association, 1974, 69, 118–121.

    Article  Google Scholar 

  • Deutsch, M., & Gerard, H.B., A study of normative and informational social influences upon individual judgment., Journal of Abnormal and Social Psychology, 1955, 51, 629–636.

    Article  Google Scholar 

  • Einhorn, H.J. Expert judgment: Some necessary conditions and an example. Journal of Applied Psychology, 1974, 59, 562–571.

    Article  Google Scholar 

  • Einhorn, H.J., & Hogarth, R.M. Unit weighting schemes for decision making. Organizational Behavior and Human Performance, 1975, 13, 171–192.

    Article  Google Scholar 

  • Einhorn, H.J., Hogarth, R.M., & Klempner, E. Quality of group judgment, Unpublished manuscript, University of Chicago, 1975.

    Google Scholar 

  • Eisenberg, E., & Gale, D. Consensus of subjective probabilities: The parimutuel method. Annals of Mathematical Statistics, 1959, 30, 165–168.

    Article  Google Scholar 

  • Eysenck, H.J. The validity of judgments as a function of the number of judges., Journal of Experimental Psychology, 1939, 25, 650–654.

    Article  Google Scholar 

  • Fishburn, PC . A comparative analysis of group decision methods., Behavioral Science, 1971, 538–544

    Google Scholar 

  • Fishburn, P.C. Voter concordance, simple majorities, and group decision methods., Behavioral Science, 1973, 18, 364–376.

    Article  Google Scholar 

  • Fishburn, P.C. Single-peaked preferences and probabilities of cyclical majorities., Behavioral Science, 1974, 19, 21–27. (a)

    Google Scholar 

  • Fishburn, P.C. Simple voting systems and majority rule. Behavioral Science, 19, 166–176. (b)

    Google Scholar 

  • Fishburn, P.C. Aspects of one-stage voting rules., Management Science, 1974, 31, 422–427. (c)

    Google Scholar 

  • Ghiselli, E.E. Theory of psychological measurement. New York: McGraw- Hill, 1964.

    Google Scholar 

  • Goldberg, L.R. Man versus model of man: A rationale, plus some evidence, for a method of improving on clinical inferences. Psychological Bulletin, 1970, 73, 422–432.

    Article  Google Scholar 

  • Goodman, B.C. Action selection and likelihood ratio estimation by individuals and groups., Organizational Behavior and Human Performance, 1972, 7, 121–141.

    Article  Google Scholar 

  • Gordon, K.H. Group judgments in the field of lifted weights., Journal of Experimental Psychology, 1924, 3, 398–400.

    Article  Google Scholar 

  • Gough, R.C. The effect of group format on aggregate subjective probability distributions, Paper presented at the Fourth Research Conference on Subjective Probability, Utility and Decision Making, Rome, September 1973.

    Google Scholar 

  • Gulliksen, H. Theory of mental tests. New York: Wiley, 1950.

    Book  Google Scholar 

  • Gustafson, D.H., Shukla, R.K., Delbecq, A., & Walster, G.W. A comparative study of differences in subjective likelihood estimates made by individuals, interacting groups, Delphi groups, and nominal groups., Organizational Behavior and Human Performance, 1973, 9, 280–291.

    Article  Google Scholar 

  • Hackman, J.R., & Kaplan, R. E. Interventions into group process: An approach to improving the effectiveness of groups. Decision Sciences, 1974, 5, 459–480.

    Article  Google Scholar 

  • Hoffman, L.R. Group problem solving., In L.Berkowitz (Ed.),, Advances in experimental social psychology (Vol. 2 ). New York: Academic Press, 1965.

    Google Scholar 

  • Hoffman, L.R., & Maier, N.R.F. Valence in the adoption of solutions by problem-solving groups: Concept, method and results. Journal of Abnormal and Social Psychology, 1964, 69, 264–271.

    Article  Google Scholar 

  • Hoffman, L.R., & Maier, N.R.F. Valence in the adoption of solutions by problem-solving groups: II. Quality and Acceptance as goals of leaders and members., Journal of Personality and Social Psychology, 1967, 6, 175–182.

    Article  Google Scholar 

  • Hogarth, R.M. On the aggregation of opinion, Unpublished manuscript, INSEAD, Fontainebleau, France, 1974.

    Google Scholar 

  • Hogarth, R.M. Cognitive processes and the assessment of subjective probability distributions., Journal of the American Statistical Association, 1975, 70, 271–289.

    Article  Google Scholar 

  • Kelley, H.H., & Thibaut, J.W. Group problem solving., In G.Lindzey & E.Aronson (Eds.), Handbook of Social Psychology (Vol. 4 ). Reading, Mass.: Addison-Wesley, 1968.

    Google Scholar 

  • Kish, L. Survey sampling. New York: Wiley, 1965.

    Google Scholar 

  • Klugman, S.F. Group and individual judgments for anticipated events., Journal of Social Psychology, 1947, 26, 21–33.

    Article  Google Scholar 

  • Knight, H.C. A comparison of the reliability of group and individual judgments, Unpublished master’s thesis, Columbia University, 1921.

    Google Scholar 

  • Lorge, I., Fox, D., Davitz, J., & Brenner, M. A survey of studies contrasting the quality of group performance and individual performance., Psychological Bulletin, 1958, 55, 337–372.

    Article  Google Scholar 

  • Lorge, I., & Solomon, H., Two models of group behavior in the solution of eureka-type problems., Psychometrika, 1955, 20, 139–148.

    Article  Google Scholar 

  • Mackenzie, K.D. An analysis of risky shift experiments., Organizational Behavior and Human Performance, 1971, 6, 283–303.

    Article  Google Scholar 

  • Maier, N.R.F. Assets and liabilities in group problem solving: The need for an integrative function. Psychological Review, 1967, 74, 239–249.

    Article  Google Scholar 

  • Maier, N.R.F., Problem solving and creativity in individuals and groups, Belmont, California: Wadsworth, 1970.

    Google Scholar 

  • Morris, P.A., Bayesian expert resolution. Unpublished doctoral dissertation, Department of Engineering Economic Systems, Stanford University, 1971

    Google Scholar 

  • Morris, P.A., Decision analysis expert use. Management Science, 1974, 20, 1233–1241.

    Article  Google Scholar 

  • Morris, P.A., Modeling experts, Unpublished manuscript, February 1975.

    Google Scholar 

  • Press, S.J., & Harman, A.J., Methodology for subjective assessment of technological advancement (R-1375)., Santa Monica, California: Rand Corporation, April 1975.

    Google Scholar 

  • Preston, M.G. Note on the reliability and validity of the group judgment. Journal of Experimental Psychology, 1938, 22, 462–471.

    Article  Google Scholar 

  • Raiffa, H. Decision analysis: Introductory lectures on choices under uncertainy. Reading, Mass.: Addison-Wesley, 1968.

    Google Scholar 

  • Roberts, H.V. Probabilistic prediction., Journal of the American Statistical Association, 1965, 60, 50–62.

    Article  Google Scholar 

  • Rotter, J.B. Generalized expectancies for internal versus external control of reinforcement. Psychological Monographs, 1966, 80 (Whole No. 609), 1–28.

    Google Scholar 

  • Sackman, H. Delphi assessment: Expert opinion, forecasting, and group process (R-1283-PR). Santa Monica, California: Rand Corporation, April 1974.

    Google Scholar 

  • Sanders, F., On subjective probability forecasting., Journal of Applied Meteorology, 1963, 2, 191–201.

    Article  Google Scholar 

  • Sanders, F. Skill in forecasting daily temperature and precipitation: Some experimental results. Bulletin of the American Meteorological Society, 1973, 54, 1171–1179.

    Article  Google Scholar 

  • Savage, L.J. The foundations of statistics, New York: Wiley, 1954.

    Google Scholar 

  • Savage, L.J. Elicitation of personal probabilities and expectations. Journal of the American Statistical Association, 1971, 66, 783–801.

    Article  Google Scholar 

  • Sommer, R. Small group ecology., Psychological Bulletin, 1967, 67, 145–152.

    Article  Google Scholar 

  • Spetzler, C.S., & Staél von Holstein, C.-A.S. Probability encoding in decision analysis., Management Science, 1975, 22, 340–358.

    Article  Google Scholar 

  • Staél von Hoistein, C.-A.S. Assessment and evaluation of subjective probability distributions. Stockholm: The Economic Research Institute at the Stockholm School of Economics, 1970.

    Google Scholar 

  • Steiner, I.D. Models for inferring relationships between group size and potential group productivity., Behavioral Science, 1966, 11, 273–283.

    Article  Google Scholar 

  • Steiner, I.D., & Rajaratnam, N., A model for the comparison of individual and group performance scores., Behavioral Science, 1961, 6, 142–147.

    Article  Google Scholar 

  • Stone, M. The opinion pool., Annals of Mathematical Statistics, 1961, 32, 1339–1342.

    Article  Google Scholar 

  • Stroop, J.B. Is the judgment of the group better than that of the average member of the group? Journal of Experimental Psychology, 1932, 15, 550–560.

    Article  Google Scholar 

  • Thomas, E.J., & Fink, C.F., Effects of group size. Psychological Bulletin, 1963, 60, 371–384.

    Article  Google Scholar 

  • Thorndike, R.L. The effect of discussion upon the correctness of group decisions, when the factor of majority influence is allowed for. Journal of Social Psycholgy, 1938, 9, 343–363.

    Article  Google Scholar 

  • Toda, M. Information receiving behavior of man., Psychological Review, 1956, 63, 204–212

    Article  Google Scholar 

  • Torrance, E.P. Some consequences of power differences on decision making in permanent and temporary three-man groups., In A.P.Hare, E.F.Borgatta, & R.F.Bales (Eds.), Small groups: Studies in social interaction. New York: Knopf, 1955.

    Google Scholar 

  • Triandis, H.C. Cognitive similarity and communication in a dyad., Human Relations, 1960, 13, 175–183. (a)

    Google Scholar 

  • Triandis, H.C. Some determinants of interpersonal communication., Human Relations, 1960, 13, 279–287. (b)

    Google Scholar 

  • Vroom, V.H., Grant, L.D., & Cotton, T.S., The consequences of social interaction in group problem solving., Organizational Behavior and Human Performance, 1969, 4, 77–95.

    Article  Google Scholar 

  • Vroom, V.H., & Jago, A.G. Decision making as a social process: Normative and descriptive models of leader behavior. Decision Sciences, 1974, 5, 7430–769

    Article  Google Scholar 

  • Vroom, V.H., & Yetton, P.W. Leadership and decision making., Pittsburgh: University of Pittsburgh Press, 1973.

    Google Scholar 

  • Wilson, R. The theory of syndicates., Econometrica, 1968, 36, 119–132.

    Article  Google Scholar 

  • Winkler, R.L., The consensus of subjective probability distributions., Management Science, 1968, 15, B-61-75.

    Google Scholar 

  • Winkler, R.L., Scoring rules and the evaluation of probability assessors., Journal of the American Statistical Association, 1969, 64, 1073–1078.

    Article  Google Scholar 

  • Winkler, R.L. Probabilistic prediction: Some experimental results. 66, 675–685.

    Article  Google Scholar 

  • Winkler, R.L., & Cummings, L.L., On the choice of a consensus distribution in Bayesian analysis., Organizational Behavior and Human Performance, 1972, 7, 63–76.

    Article  Google Scholar 

  • Winkler, R.L., & Murphy, A.H., “Good” probability assessors., Journal of Applied Meteorology, 1968, 7, 751–758.

    Article  Google Scholar 

  • Winkler, R.L., & Murphy, A.H. Experiments in the laboratory and the real world., Organizational Behavior and Human Performance, 1973, 10, 252–270.

    Article  Google Scholar 

  • Zajonc, R.B. A note on group judgments and group size., Human Relations, 1962, 15, 177–180.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1977 D. Reidel Publishing Company, Dordrecht-Holland

About this chapter

Cite this chapter

Hogarth, R.M. (1977). Methods for Aggregating Opinions. In: Jungermann, H., De Zeeuw, G. (eds) Decision Making and Change in Human Affairs. Theory and Decision Library, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1276-8_16

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-1276-8_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1278-2

  • Online ISBN: 978-94-010-1276-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics