Abstract
We review recent work on the accuracy of group judgmental processes as a function of (a) the competences (judgmental accuracies) of individual group members, (b) the group decision procedure, and (c) group size. This work on individual competence and group accuracy represents an important contribution to democratic theory and a useful complement to the usual emphasis in the social choice literature on individual preference and preference aggregation mechanisms. The work reported on is rooted in a tradition which goes back to scholars such as Condorcet, Poisson, and Bayes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Badger, Wade: 1972, ‘Political Individualism, Positional Preferences, and Optimal Decision Rules’, in Richard Niemi and Herbert Weisberg (eds.), Probability Models of Collective Decision-Making, Merrill.
Baker, Keith M.: 1967, ‘Scientism, Elitism, and Liberalism: The Case of Condorcet’, Studies on Voltaire and the Eighteenth Century 55, 129–165.
Baker, Keith M.: 1976, Condorcet: From Natural Philosophy to Social Mathematics, University of Chicago Press, Chicago.
Black, Duncan: 1958, The Theory of Committees and Elections, Cambridge University Press, London.
Condorcet, Nicolas Caritat de: 1785, Essai sur l'Application de l'Analyse a la Probabilite des Decisions Rendues a la Pluralite des Voix, Paris.
Crain, W. M. and Tollison, R. D.: 1977, ‘Legislative Size and Voting Rules’, Journal of Legal Studies 6, 235–240.
Davis, James H.: 1973, ‘Group Decision and Social Interaction: A Theory of Social Decision Schemes’, Psychological Review 80, 97–125.
Duda, R. O. and Hart, P. E.: 1973, Pattern Classification and Scene Analysis, Wiley, New York.
Farquharson, Robin: 1969, The Theory of Voting, Yale University Press, New Haven.
Gelfand, Alan and Solomon, Herbert: 1973, ‘A Study of Poisson's Models for Jury Verdicts in Criminal and Civil Trials’, Journal of American Statistical Association 68, 271–278.
Gelfand, Alan and Solomon, Herbert: 1974, ‘Modelling Jury Verdicts in the American Legal System’, Journal of American Statistical Association 69, 32–37.
Gelfand, Alan and Solomon, Herbert: 1975, ‘Analyzing the Decision-Making Process of the American Jury’, Journal of the American Statistical Association 70, 305–310.
Gelfand, Alan and Solomon, Herbert: 1977, ‘Comparing Juries: An Argument in Favor of Twelve Member Juries’, Jurimetrics 17, 292–313.
Gelfand, Alan and Solomon, Herbert: 1977, ‘An Argument in Favor of Twelve-Member Juries’, in Stuart Nagel (ed.), Modeling the Criminal Justice System, Sage Criminal Justice System Annual 7. Sage Publications, Beverly Hills, California, pp. 205–220.
Gillispie, Charles Coulston: 1972, ‘Probability and Politics: LaPlace, Condorcet, and Turgot’, Proceedings of the American Philosophical Society 116, 1–20.
Grainger, Giles-Gaston de: 1956, La Mathematique Sociale du Marquis de Condorcet, Press Universitaires de France, Paris.
Grofman, Bernard: 1974, ‘A Comment on Black's “Rationality and Cultural Relativism” ’, in Max Black (ed.), Problems of Choice and Decision: Proceedings of a Colloquium Held in Aspen, Colorado, June 24–July 6, 1974, Cornell University Program on Science, Technology, and Society and Aspen Institute for Humanistic Studies: Photo-offset, pp. 161–190.
Grofman, Bernard: 1975a, ‘Mathematics and Politics: Mathematical Reasoning and Optimal Jury Decision Processes. Plus, Reply’, in Max Black (ed.), Problems of Choice and Decision: Proceedings of a Colloquium Held in Aspen, Colorado, June 24–July 6, 1974, Cornell University Program on Science, Technology and Society and Aspen Institute for Humanistic Studies: Photo-offset, pp. 331–337, 544–547.
Grofman, Bernard: 1975b, ‘A Comment on “Democratic Theory: A Preliminary Mathematical Model” ’, Public Choice 21, 100–103.
Grofman, Bernard: 1978, ‘Judgmental Competence of Individuals and Groups in a Dichotomous Choice Situation’, Journal of Mathematical Sociology 6, 47–60.
Grofman, Bernard: 1979, ‘The Case for Majority Jury Verdicts’, Trial Magazine, 23–25, 29, 47–48.
Grofman, Bernard: 1980a, ‘Preliminary Models of Jury Decision-Making’, in Gordon Tullock (ed.), Frontiers of Economics, 3.
Grofman, Bernard: 1980b, ‘Mathematical Modeling of Jury/Juror Decision Making’, in Bruce D. Sales (ed.), Perspectives in Law and Psychology, Volume II: The Jury, Judicial and Trial Processes, Plenum.
Grofman, Bernard, Owen Guillermo, and Feld, Scott: 1982, ‘Average Competence, Individual Competence, and Group Judgmental Accuracy’, Psychological Report, 50, 683–688.
Klevorick, A. K. and Rothschild, M.: 1978, ‘The Jury Decision Process’, Grant proposal to the National Science Foundation.
Klevorick, A. K. and Rothschild, M.: 1979, ‘A Model of the Jury Decision Process’, Journal of Legal Studies, 144–164.
Luce, R. Duncan: 1959, Individual Choice Behaviour, Wiley, New York.
Margolis, Howard: 1976, ‘A Note of Incompetence’, Public Choice 26, 119–129.
Minsky, Marvin and Papert, Seymour: 1971, Perceptrons: An Introduction to Computational Geometry, MIT Press, Cambridge, Mass.
Moore, E. E. and Shannon, C. E.: 1956a, ‘Reliable Circuits Using Less Reliable Relays, I’, Franklin Institute, Philadelphia Journal 262, 191–208.
Moore, E. E. and Shannon, C. E.: 1956b, ‘Reliable Circuits Using Less Reliable Relays, II’, Franklin Institute, Philadelphia Journal 262, 281–297.
Nitzan, Shmuel and Paroush, Jacob: 1980a, Discussion Paper No. 8017, Bar-Ilan University, Israel.
Nitzan, Shmuel and Paroush, Jacob: 1980b, ‘Investment in Human Capital and Social Self Protection under Uncertainty’, International Economic Review 21, 547–557.
Owen, Guillermo, Grofman, Bernard, and Feld, Scott: 1981, ‘The Generalized Condorcet Jury Theorem’, unpublished manuscript.
Penrod, Steven and Hastie, Reid: 1979, ‘Models of Jury Decision-Making: A Critical Review’, Psychological Bulletin 86, 462–492.
Pierce, William: 1961, ‘Improving Reliability of Digital Systems by Redundancy and Adaptation’, unpublished Ph.D. Dissertation, Stanford University.
Poisson, S. D.: 1837, Recherches sur la Probabilite des Jugement en Matiere Criminal et en Matiere Civile: Procedees des Regles Generales du Calcul des Probabilities, Bachelier, Imprimateur Libraire, Paris.
Rae, Douglas W.: 1969, ‘Decision-Rules and Individual Values in Constitution Choice’, American Political Science Review 63, 40–56.
Sattler, Howard E.: 1966, ‘Effect of Group Variability on Pooled Group Decisions’, Psychological Reports 18, 676–678.
Schofield, Norman: 1971, ‘Ethnical Decision Rules for Uncertain Voters’, British Journal of Political Science 2, 193–207.
Schofield, Norman: 1972, ‘Is Majority Rule Special?’ in Richard Niemi and Herbert Weisberg (eds.), Probability Models of Collective Decision-Making, Merrill.
Shapley, L. and Grofman, B.: 1981, ‘Optimizing Group Judgmental Accuracy’, unpublished manuscript.
Steiner, I. D. and Rajaratnam, N.: 1961, ‘A Model for the Comparison of Individual and Group Performance’, Behavioral Science 6, 142–147.
Taylor, Michael: 1969, ‘Proof of a Theorem on Majority Rule’, Behavioral Science 14, 228–231.
Author information
Authors and Affiliations
Additional information
School of Social Sciences, University of California, Irvine.
Department of Economics, University of Iowa, and Visiting Research Scholar, School of Social Sciences, University of California, Irvine.
Department of Sociology, State University of New York at Stony Brook.
Portions of this research were supported by NSF Grant Number SES 80-07915 to Bernard Grofman and Guillermo Owen. An earlier version of this paper (with Lloyd Shapley as a co-author) was presented at the Annual Meeting of the American Political Science Association, Washington, D.C., 1980. We would like to acknowledge the assistance of Professor Thomas Cover, Department of Statistics, Stanford University, in identifying references to earlier proofs of Theorem XIII, and to express our gratitude to the Word Processing Center of the School of Social Sciences, University of California, Irvine, for typing this manuscript with rapidity and cheer, to Sue Pursche for proof-reading it in its several different incarnations, and to Laurel Eaton for bibliographic assistance.
Rights and permissions
About this article
Cite this article
Grofman, B., Owen, G. & Feld, S.L. Thirteen theorems in search of the truth. Theor Decis 15, 261–278 (1983). https://doi.org/10.1007/BF00125672
Issue Date:
DOI: https://doi.org/10.1007/BF00125672