Abstract
The method to be considered was proposed bt Legrer[1] and attracted great interest in discussions during the Conference. In the present note we shall be concerned with mathematical aspects of the method, rather than applications, the reason being as follows.
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Bibliography
Forthcoming papers by K. Lehrer are as follows. When rational disagreement is impossible. (To appear in Nous.) Social consensus and rational agnoiology. (To appear in Synthese.) Rationality in science and society: a consensual theory. (To appear in Proceedings of Third International Conference, Oxford University.) I want to thank Prof. Lehrer for sending me the manuscripts of these three papers.
We mention the following relevant books which also contain references to original literature.
Bartos, O. J., Simple Models of Group Behavior, Columbia University Press, New York, 1967.
Chung, K. L., Markov Chains With Stationary Transition Probabilities. 2nd edn. Springer, New York, 1967.
Doob, J. L., Stochastic Processes, Wiley, New York, 1953.
Dynkin, E. B., Die Grundlagen der Theorie der Markoffschen Prozesse. Springer, Berlin, 1961.
Dynkin, E. BMarkov Processes, Springer, Berlin, 1965.
Dynkin, E. B., and Juschkewitsch, A. A., Sätze und Aufgaben liber Markoffsche Prozesse, Springer, Berlin, 1969.
Feller, W., An Introduction to Probability Theory and Its Applications, Vol. I, 2nd edn., Wiley, New York, 1957.
Ito, K. and McKean, H. P., Diffusion Processes and Their Sample Paths, Springer, Berlin, 1965.
Karlin, S.M First Course in Stochastic Processes, Academic Press, New York, 1966.
Kemeny, J. G. and Snell, J. L., Finite Markov Chains, Van Nostrand, Princeton, N.J., 1960.
Loève, M., Probability Theory, 3rd edn, Van Nostrand Reinhold, New York, 1963.
Spitzer, F., Principles of Random Walk, Van Nostrand, Princeton, N.J., 1964.
This is a famous theorem in the theory of real matrices with positive elements. For a proof of the theorem and its extension by G. Frobenius, see Gantmacher, F. R., The Theory of Matrices, Vol. 2, p. 53, Chelsea, New York, 1959.
See Kreyszig, E., Advanced Engineering Mathematics, 3rd edn, Wiley, New York, 1972, where the Gauss algorithm is discussed on p. 672 and iteration methods on pp. 675–678.
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© 1978 D. Reidel Publishing Company, Dordrecht, Holland
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Kreyszig, E. (1978). On a Decision Theoretic Method for Social Decision. In: Hooker, C.A., Leach, J.J., >McClennen, E.F. (eds) Foundations and Applications of Decision Theory. The University of Western Ontario Series in Philosophy of Science, vol 13a. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9789-9_11
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