Abstract
This paper deals with various connections that are found to exist between statistical estimation methods for decision-making and rules of group choice in the social choice area. Initially the aggregation of individual opinions is formulated as a pattern recognition problem; firstly it is shown that individual preferences lead to a natural representation in terms of binary patterns. Then we proceed to show how the search for a group preference pattern can be conducted by classifying the input preference patterns into various ‘pattern classes’ and using the resulting classification boundaries to define the area of mutual agreement over some of the available alternatives. This leads to a decision-theoretic problem which consists in defining a decision rule (for classification) that is least likely to lead to misrecognition of arbitrary preference patterns. A maximum likelihood solution is obtained and compared with some well-known rules of group decision-making. Other solutions are also possible, on the basis of different optimality criteria, and their social choice interpretation is suggested. Finally, a method using Coleman's linear model for attributes is applied to yield group decision rules by feature weighting of election issues.
Similar content being viewed by others
Bibliography
Arrow, K. J., Social Choice and Individual Values, 2nd ed. J. Wiley and Sons, New York, 1962.
Blin, J. M., Patterns and Configurations in Economic Science, D. Reidel Publishing Co., Dordrecht, Holland/Cambridge, Mass., 1973.
Blin, J. M., ‘Majority Voting Rules as Behavior Towards Risk’, Working Paper #103-72, Northwestern University, G.S.M., 1972.
Blin, J. M., ‘A General Formulation of the Multiattribute Decision Problem: Concepts and Solution Algorithms’, Working Paper #102-72, Northwestern University, G.S.M., 1972.
Blin, J. M., Fu, K. S., Whinston, A. B., ‘Application of Pattern Recognition to Some Problems in Economies’, in Balakrishnan (ed.), Techniques of Optimization, Academic Press, 1972.
Coleman, J. S., Introduction to Mathematical Sociology, Collier-MacMillan, New York, 1964.
David, H. A., The Method of Paired Comparisons, Griffin & Co., London 1969.
Feldman, J., ‘A Study of Coleman's Linear Model for Attributes’, Quality & Quantity 5 (1970) 255.
Fu, K. S., Sequential Methods in Pattern Recognition and Machine Learning, Academic Press, New York, 1968.
Guilbaud, G. T., ‘Les Théories de l'intérêt général et le problème logique de l'agrégation’, Economie Appliquée (1952) 501–584.
Kendall, M. G. and Stuart, A., The Advanced Theory of Statistics (3 vols.) Griffin & Co., London, 1954.
Malinvaud, E., ‘L'agrégation dans les modèles économiques’, Cahiers du C.N.R.S, Paris, 1956.
Moon, J. W. and Pullman, N. J., ‘On Generalized Tournament Matrices’, SIAM Review 12 (1970) 384–399.
Roy, B., ‘Sur quelques propriétés des graphes fortement connexes’, Compte Rendus de l'Académie des Sciences, Paris 247 (1958) 399–401.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Blin, JM. Preference aggregation and statistical estimation. Theor Decis 4, 65–84 (1973). https://doi.org/10.1007/BF00133399
Issue Date:
DOI: https://doi.org/10.1007/BF00133399