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Comparison and choice

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Abstract

This paper develops the idea of a choice as a mapping of subsets of a set X into their respective subsets and the idea of the comparison, as a relation between elements of X, that is determined or ‘revealed’ by a choice. It then studies how certain properties of a choice imply or are implied by certain properties, such as acyclicity, quasi-transitivity, pseudo-transitivity and transitivity, of the comparison revealed, finally giving a complete logical diagram of all the implications between these latter properties of the comparison.

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References

  • Ahrens, H. J.: 1974, ‘Multidimensionale Skalierung’, Beltz, Weinheim und Basel.

  • Arrow, K. J.: 1959, ‘Rational Choice Functions and Orderings’, Economica 26, pp. 121–127.

    Google Scholar 

  • Arrow, K. J.: 1963, Social Choice and Individual Values, John Wiley & Sons, New York.

    Google Scholar 

  • Batra, R. N. and Pattanaik, P. K.: 1972, ‘Transitive Multi-Stage Majority Decisions-with Quasi-Transitive Individual Preferences’, Econometrica 40, pp. 1121–1136.

    Google Scholar 

  • Chernoff, H.: 1954, ‘Rational Selection of Decision Functions’, Econometrica 22, pp. 422–443.

    Google Scholar 

  • Chipman, J. S.: 1971, ‘Consumption Theory without Transitive Indifference’, in: Chipman et al. (eds.), pp. 224–253.

  • Chipman, J. S., Hurwicz, L., Richter, M. K., and Sonnenschein, H. F. (eds.): 1971, Preferences, Utility and Demand, Harcourt Brace Jovanovich, New York.

    Google Scholar 

  • Coombs, C. H., Dawes, R. M., and Tversky, A.: 1970, Mathematical Psychology, Prentice Hall, Englewood Cliffs, N.J.

    Google Scholar 

  • Fishburn, P. C.: 1970, ‘Intransitive Indifference in Preference Theory: A Survey’, Operations Research, pp. 207–228.

  • Fishburn, P. C.: 1971, ‘A Comparative Analysis of Group Decision Methods’, Behavioral Science, pp. 538–544.

  • Fishburn, P. C.: 1973, The Theory of Social Choice, Princeton University Press.

  • Fishburn, P. C.: 1973a, ‘Binary Choice Probabilities: on the Varieties of Stochastic Transitivity’, Journal of Mathematical Psychology 10, pp. 327–372.

    Google Scholar 

  • Frey, B. S.: 1974, ‘Entwicklung und Stand der Neuen Politischen Ökonomie’, in: Widmaier (Hrsg.), pp. 30–63.

  • Gäfgen, G.: 1968, Theorie der wirtschaftlichen Entscheidung, Mohr, Tübingen (2. Aufl).

    Google Scholar 

  • Hansson, B.: 1968, ‘Choice Structures and Preference Relations’,Synthese 18, pp. 443–458.

    Google Scholar 

  • Hansson, B.: 1969, ‘Voting and Group Decision Functions’, Synthese 20, pp. 526–537.

    Google Scholar 

  • Hansson, B.: 1973, ‘The Independence Condition in the Theory of Social Choice’, Theory and Decision 4, pp. 25–49.

    Google Scholar 

  • Henderson, J. M. and Quandt, R. E.: 1971, Microeconomic Theory, McGraw-Hill, New York, 2nd ed.

    Google Scholar 

  • Inada, K.: 1970, ‘Majority Rule and Rationality’, Journal of Economic Theory 2, pp. 27–40.

    Google Scholar 

  • Intriligator, M. D. (ed.): 1971, Frontiers of Quantitative Economics, North Holland Publishing Co.

  • Jamison, D. T. and Lau, L. J.: 1973, ‘Semiorders and the Theory of Choice’, Econometrica 41, pp. 901–912.

    Google Scholar 

  • Marschak, Jacob: 1968, ‘Decision-Making: Economic Aspects’, in: Sills (ed.) 4, pp. 42–55.

  • Mas-Colell, A.: 1974, ‘An Equilibrium Existence Theorem without Complete or Transitive Preferences’, Working Paper IP-195, Center for Research in Management Science, University of California, Berkeley.

    Google Scholar 

  • May, K. O.: 1954, ‘Intransitivity, Utility and the Aggregation of Preference Patterns’, Econometrica 22, pp. 1–13.

    Google Scholar 

  • Pattanaik, P. K.: 1970, ‘On Social Choice with Quasitransitive Individual Preferences’, Journal of Economic Theory, vol. 2, pp. 267–275.

    Google Scholar 

  • Pattanaik, P. K.: 1971, Voting and Collective Choice, Cambridge University Press.

  • Plott, C. R.: 1971, ‘Recent Results in the Theory of Voting’, in: Intriligator (ed.), pp. 109–127.

  • Plott, C. R.: 1972, ‘Ethics, Social Choice Theory and the Theory of Economic Policy’, Journal of Mathematical Sociology 2, pp. 181–208.

    Google Scholar 

  • Plott, C. R.: 1973, ‘Path Independence, Rationality, and Social Choice’, Econometrica 41, pp. 1075–1091.

    Google Scholar 

  • Quirk, J., and Saposnik, R., Introduction to General Equilibrium Theory and Welfare Economics, McGraw-Hill, New York, 1968.

    Google Scholar 

  • Radner, R. and Marschak, J.: 1954, ‘Note on Some Proposed Decision Criteria’, in: Thrall-Coombs-Davis, pp. 61–68.

  • Ray, P.: 1973, ‘Independence of Irrelevant Alternatives’, Econometrica 41, pp. 987–991.

    Google Scholar 

  • Richter, M. K.: 1966, ‘Revealed Preference Theory’, Econometrica, pp. 635–645.

  • Richter, M. K.: 1971, ‘Rational Choice’, in: Chipman, et al. (eds.), pp. 29–58.

  • Sen, A. K.: 1969, ‘Quasi-Transitivity, Rational Choice and Collective Decisions’, Review of Economic Studies, pp. 381–293.

  • Sen, A. K.: 1970, Collective Choice and Social Welfare, Holden Day, San Francisco, and Oliver & Boyd, Edinburgh and London.

    Google Scholar 

  • Sen, A. K.: 1971, ‘Choice Functions and Revealed Preferences’, Review of Economic Studies, pp. 307–317.

  • Sen, A. K. and Pattanaik, D. K.: 1969, ‘Necessary and Sufficient Conditions for Rational Choice under Majority Decision’, Journal of Economic Theory, pp. 178–202.

  • Sertel, M. R.: 1976, ‘Choice by Binary Comparison is Semi-Independent of Path’, IIM Preprint Series, I/76-9, Berlin, (forthcoming in Bogazici University Journal).

  • Sertel, M. R. and Van der Bellen, A.: 1976, ‘The Algebraic Structure of Sequential Choice’, IIM Preprint Series, I/76-3, Berlin.

  • Sertel, M. R. and Van der Bellen, A.: 1979, ‘Synopses in the Theory of Choice’, Econometrica 47, pp. 1367–1389.

    Google Scholar 

  • Sertel, M. R. and Van der Bellen, A.: 1980a, ‘Computations in Choice Groupoids’, Aequationes Mathematicae 20, pp. 129–132.

    Google Scholar 

  • Sertel, M. R. and Van der Bellen, A.: 1980b, ‘On the Routewise Application of Choice’, Journal of Economic Theory 22, pp. 423–438.

    Google Scholar 

  • Sills, D. L. (ed.): 1968, International Encyclopedia of the Social Sciences, Macmillan & Free Press.

  • Sonnenschein, H. F.' 1971, ‘Demand Theory without Transitive Preferences, with Applications to the Theory of Competitive Equilibrium’, in Chipman et al. (eds.), pp. 215–223.

  • Thrall, R. M., Coombs, C. H., and Davis, R. L.: 1954, Decision Processes, Wiley & Sons, New York.

    Google Scholar 

  • Tullock, G.: 1964, ‘The Irrationality of Intransitivity’, Oxford Economic Papers, pp. 401–406.

  • Tversky, A.: 1969, ‘Intransitivity of Preferences’, Psychological Review 76, pp. 31–48.

    Google Scholar 

  • Van der Bellen, A.: 1976, Mathematische Auswahlfunktionen und gesellschaftliche Entscheidungen. Birkhäuser Verlag, Basel & Stuttgart.

    Google Scholar 

  • Weinstein, A. A.: 1968, ‘Individual Preference Intransitivity’, Southern Economic Journal, pp. 335–343.

  • Widmaier, H. P. (Hrsg.): 1974, Politische Ökonomie des Wohlfahrtsstaates, Anthenäum Fischer TB, Frankfurt.

    Google Scholar 

  • Wilson, R.: 1970, ‘The Finer Structure of Revealed Preference’, Journal of Economic Theory 2, pp. 348–353.

    Google Scholar 

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Authors and Affiliations

  1. Bogazici University, Turkey

    M. R. Sertel & A. V. D. Bellen

  2. Vienna University, Austria

    M. R. Sertel & A. V. D. Bellen

Authors
  1. M. R. Sertel
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  2. A. V. D. Bellen
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Sertel, M.R., Bellen, A.V.D. Comparison and choice. Theor Decis 14, 35–50 (1982). https://doi.org/10.1007/BF00135143

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