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Random Orderings and Stochastic Theories of Responses (1960)

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Economic Information, Decision, and Prediction

Part of the book series: Theory and Decision Library ((TDLU,volume 7-1))

Abstract

In interpreting human behavior there is a need to substitute ‘stochastic consistency of choices’ for ‘absolute consistency of choices’. The latter is usually assumed in economic theory, but is not well supported by experience. It is, in fact, not assumed in empirical econometrics and psychology.

Research carried out mostly under contracts of the Office of Naval Research with the Cowles Foundations for Economics at Yale University and with Columbia University. The paper was completed while Jacob Marschak was Ford Visiting Research Professor at the Graduate School of Industrial Administration, Carnegie Institute of Technology. We owe much to discussions with D. Davidson, G. Debreu, M. DeGroot, L. Hurwicz, and R. D. Luce.

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Bibliography

  1. Cartwright, D. and Festinger, L., ‘A Quantitative Theory of Decision’, Psychol Rev. 50 (1943) 595–621.

    Article  Google Scholar 

  2. Hotelling, H., ‘Demand Functions with Limited Budgets’, Econometrica 3 (1935) 66–78.

    Article  Google Scholar 

  3. Fechner, G. Th., Elemente der Psychophysik, Breitkopf & Härtel, Leipzig, 1859.

    Google Scholar 

  4. Arrow, K. J., Social Choice and Individual Values, Wiley, New York, 1951.

    Google Scholar 

  5. Debreu, G., ‘Representation of a Preference Ordering by a Numerical Function’, Chap. 11 in R. M. Thrall, C. H. Coombs and R. L. Davis (eds.), Decision Processes, Wiley, New York, 1954.

    Google Scholar 

  6. Wald, A., ‘The Approximate Determination of Indifference Surfaces by Means of Engel Curves, Econometrica 8 (1940) 144–175.

    Article  Google Scholar 

  7. Theil, H. and Neudecker, H., ‘Substitution, Complementarity and the Residual Variation around Engle Curves’, Rev. Econ. Studies 25 (1957) 114–23.

    Google Scholar 

  8. Bernoulli, D., ‘Exposition of a New Theory on the Measurement of Risk’ (translated by Dr. Louise Sommer), Econometrica, 22 (1954) 23–36.

    Article  Google Scholar 

  9. Marshall, A., Principles of Economics, 8th ed. Macmillan, London, 1920.

    Google Scholar 

  10. Mosteller, F. and Nogee, P., ‘An Experimental Measurement of Utility’, J. Polit. Econ. 59 (1951) 371–404.

    Article  Google Scholar 

  11. Guilford, J. P., Psychometric Methods, 2d ed., McGraw-Hill, New York, 1954.

    Google Scholar 

  12. Dahl, R. A., ‘The Concept of Power’, Behav. Sci. 2 (1957) 201–15.

    Article  Google Scholar 

  13. Shapley, L. and Shubik, M., ‘A Method for Evaluating the Distribution of Power in a Committee System’, Amer. Polit. Sci. Rev. 48 (1954) 787–792.

    Article  Google Scholar 

  14. Luce, R. D. and Raiffa, H., Games and Decisions, Wiley, New York, 1957.

    Google Scholar 

  15. Luce, R. D., Individual Choice Behavior, Wiley, New York, 1959.

    Google Scholar 

  16. Thurstone, L. L., ‘A Law of Comparative Judgment’, Psychol. Rev. 34 (1927) 273–286.

    Article  Google Scholar 

  17. Mosteller, F., ‘Remarks on the Method of Paired Comparisons’, Psychometrika 26 (1951) 3–9, 203–206, 207–218.

    Google Scholar 

  18. Block, H. D. and Marschak, J. ‘An Identity in Arithmetic’, Bull Amer. Math. Soc. 65 (1959) 123–124.

    Article  Google Scholar 

  19. Debreu, G., ‘On “An identity in arithmetic”’, Proc. Amer. Math. Soc. 11 (1960) 220–221.

    Google Scholar 

  20. Marschak, J., ‘Binary Choice Constaints on Random Utility Indicators’, Selected Essays, 8.

    Google Scholar 

  21. Block, H. D. and Marschak, J., ‘Random Orderings’, Cowles Foundation Discussion Paper No. 42, Cowles Foundation, New Haven, Conn., 1957 (duplicated).

    Google Scholar 

  22. Georgescu-Roegen, N, ‘Threshold in Choice and the Theory of Demand’, Econometrica 26 (1958) 157–168.

    Article  Google Scholar 

  23. Chipman, J. S. ‘Stochastic Choice and Subjective Probability’, Technical Report No. 2, School of Business Administration, Univ. of Minn., Minneapolis, Minn., 1958 (duplicated).

    Google Scholar 

  24. Debreu, G., ‘Stochastic Choice and Cardinal Utility’, Econometrica 26 (1958) 440–444.

    Article  Google Scholar 

  25. Guilbaud, G. Th., ‘Sur une difficulté de la théorie du risque’, Colloques internationaux du centre national de la recherche scientifique (économétrie) 40 (1953) 19–25.

    Google Scholar 

  26. Tôrnqvist, L., ‘A Model for Stochastic Decision Making’, Cowles Commission Discussion Paper, Economics 2100, Cowles Commission, Chicago, 1954 (duplicated).

    Google Scholar 

  27. Bradley, R. A. and Terry, M. E., ‘Rank Analysis of Incomplete Block Designs, I. The Method of Paired Comparisons’, Biometrika 39 (1952) 324–344.

    Google Scholar 

  28. Ford, L. R., ‘Solution of a Ranking Problem from Binary Comparisons’, Amer. Math. Month. 64 (1957) (Aug. suppl.), 28–33.

    Article  Google Scholar 

  29. Coombs, C., On the Use of Inconsistency of Preferences in Psychological Measurement’, J. Exp. Psychol. 55 (1958) 1–7.

    Article  Google Scholar 

  30. Gulliksen, H., ‘Paired Comparisons and the Logic of Measurement’, Psychol. Rev. 53 (1946) 199–213.

    Article  Google Scholar 

  31. Valavanis-Vail, S., ‘A Stochastic Model for Utilities’, Seminar on the application of mathematics to social sciences, Univ. Michigan, Ann Arbor, 1957 (duplicated).

    Google Scholar 

  32. Edwards, W., ‘Probability Preferences in Gambling’, Amer. J. Psychol. 66 (1955) 349–364.

    Article  Google Scholar 

  33. Papandreou, A. G. (with the collaboration of O. H. Sauerlender, O. H. Brownlee, L. Hurwicz, W. Franklin), ‘A test of a Stochastic Theory of Choice, Univ. Calif. Publ. in Econ. 16 (1957) 1–18.

    Google Scholar 

  34. May, K., ‘Intransitivity, Utility and the Aggregation of Preference Patterns’, Econometrica 22 (1954) 1–13.

    Article  Google Scholar 

  35. Davis, J. M., ‘The Transitivity of Preferences’, Behav. Sci 3 (1958) 26–33.

    Article  Google Scholar 

  36. Davidson, D. and Marschak, J., ‘Experimental Tests of Stochastic Decision Theories’, Selected Essays, 6.

    Google Scholar 

  37. Georgescu-Roegen, N., ‘The Pure Theory of Consumer Behavior’, Quart. J. Econ. 50 (1936) 545–593.

    Article  Google Scholar 

  38. Rosenblatt, D., ‘On Some Stochastic Process Formulations of Individual Preference and Consumer Behavior (abst.)’, Econometrica 24 (1956) 347–348.

    Google Scholar 

  39. Marschak, J., ‘Norms and Habits of Decision Making under Certainty’, Selected Essays, 5.

    Google Scholar 

  40. Kendall, M. G., ‘Further Contributions to the Theory of Paired Comparisons’, Biometrics 11 (1955) 43–67.

    Article  Google Scholar 

  41. Mallows, G. L., ‘Non-Null Ranking Models, I’, Biometrika 44 (1957) 114–130.

    Google Scholar 

  42. Savage, I. R., ‘Contributions to the Theory of Rank Orders’, Ann. Math. Stat. 27 (1956) 590–615; 28 (1957) 968–77.

    Article  Google Scholar 

  43. Lehmann, E. L., ‘Ordered Families of Distributions’, Ann. Math. Stat. 26 (1955) 399–419.

    Article  Google Scholar 

  44. Brunk, H. D., ‘Mathematical Models for Ranking from Paired Comparisons’, Technical Report No. 11, Air Force Office of Scientific Research, Department of Mathematics, University of Missouri, Columbia, Mo., Nov. 1958 (duplicated).

    Google Scholar 

  45. Savage, L. J., The Foundations of Statistics, Wiley, New York, 1954. Revised, Dover, 1972.

    Google Scholar 

  46. Simon, H. A., ‘A Behavioral Model of Rational Choice’, Quart. J. Econ. 69 (1955) 99–118.

    Article  Google Scholar 

  47. Quandt, R. E., ‘A Probabilistic Theory of Consumer Behavior’, Quart. J. Econ. 70 (1956) 507–536.

    Article  Google Scholar 

  48. Neumann, J. von and Morgenstern, O., Theory of Games and Economic Behavior, 2d ed. Princeton Univ. Press, Princeton N.J., 1947.

    Google Scholar 

  49. Herstein, I. N. and Milnor, J., ‘An Axiomatic Approach to Measurable Utility’ Econometrica 21 (1953) 291–297.

    Article  Google Scholar 

  50. Ramsey, F. P., The Foundations of Mathematics and Other Logical Essays, Kegan Paul, London 1931.

    Google Scholar 

  51. Luce, R. D., ‘A Probabilistic Theory of Utility’, Econometrica 26 (1958) 193–224.

    Article  Google Scholar 

  52. Allais, M., ‘Le comportement de l’homme rationnel devant le risque: critique des postulats et axiomes de l’école américaine’, Econometrica 21 (1953) 503–546.

    Article  Google Scholar 

  53. Davidson, D. and Suppes, P. (in collaboration with S. Siegel), Decision Making: An Experimental Approach, Stanford Univ. Press, Stanford, Calif., 1957.

    Google Scholar 

  54. Debreu, G., ‘Cardinal Utility for Even-Chance Mixtures of Pairs of Sure Prospects’, Rev. Econ. Studies 26(1958/9) 174–177.

    Google Scholar 

  55. Jones, L. V., Peryam, D. R., and Thurstone, L. L., ‘Development of a Scale for Measuring Soldiers’ Food Preferences’, Food Research 20 (1955) 512–520.

    Google Scholar 

  56. Thurstone, L. L. and Jones, L., ‘The Rational Origin for Measuring Subjective Values’, J. Amer. Stat. Assoc. 52 (1957) 458–471.

    Article  Google Scholar 

  57. Gulliksen, H., ‘Measurement of Subjective Values’, Psychometrika 21 (1956) 229–244.

    Article  Google Scholar 

  58. Luce, R. D. and Suppes, P., ‘Preference, Utility, and Subjective Probability’, Handbook of Mathematical Psychology, Vol. III, Ch. 19, Wiley, 1965.

    Google Scholar 

  59. Tversky, A., ‘Elimination by Aspects: A Theory of Choice’, Psychological Review 79 (1972) 281–299.

    Article  Google Scholar 

  60. Tversky, A., ‘Intransitivity of Preferences’, Psychological Review 76 (1969) 31–48.

    Article  Google Scholar 

  61. DeGroot, M. H., ‘Optimal Allocation of Observations’, Annals of the Institute of Statistical Mathematics, 18 (1966) 13–28.

    Article  Google Scholar 

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Authors
  1. H. D. Block
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© 1974 D. Reidel Publishing Company, Dordrecht, Holland

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Block, H.D. (1974). Random Orderings and Stochastic Theories of Responses (1960). In: Economic Information, Decision, and Prediction. Theory and Decision Library, vol 7-1. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9276-0_8

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  • DOI: https://doi.org/10.1007/978-94-010-9276-0_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-277-1195-3

  • Online ISBN: 978-94-010-9276-0

  • eBook Packages: Springer Book Archive

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