Advertisement

Random Orderings and Stochastic Theories of Responses (1960)

  • H. D. Block
Chapter
Part of the Theory and Decision Library book series (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.

Keywords

Subjective Probability Binary Choice Random Utility Stochastic Theory Basic Observation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [1]
    Cartwright, D. and Festinger, L., ‘A Quantitative Theory of Decision’, Psychol Rev. 50 (1943) 595–621.CrossRefGoogle Scholar
  2. [2]
    Hotelling, H., ‘Demand Functions with Limited Budgets’, Econometrica 3 (1935) 66–78.CrossRefGoogle Scholar
  3. [3]
    Fechner, G. Th., Elemente der Psychophysik, Breitkopf & Härtel, Leipzig, 1859.Google Scholar
  4. [4]
    Arrow, K. J., Social Choice and Individual Values, Wiley, New York, 1951.Google Scholar
  5. [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. [6]
    Wald, A., ‘The Approximate Determination of Indifference Surfaces by Means of Engel Curves, Econometrica 8 (1940) 144–175.CrossRefGoogle Scholar
  7. [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. [8]
    Bernoulli, D., ‘Exposition of a New Theory on the Measurement of Risk’ (translated by Dr. Louise Sommer), Econometrica, 22 (1954) 23–36.CrossRefGoogle Scholar
  9. [9]
    Marshall, A., Principles of Economics, 8th ed. Macmillan, London, 1920.Google Scholar
  10. [10]
    Mosteller, F. and Nogee, P., ‘An Experimental Measurement of Utility’, J. Polit. Econ. 59 (1951) 371–404.CrossRefGoogle Scholar
  11. [11]
    Guilford, J. P., Psychometric Methods, 2d ed., McGraw-Hill, New York, 1954.Google Scholar
  12. [12]
    Dahl, R. A., ‘The Concept of Power’, Behav. Sci. 2 (1957) 201–15.CrossRefGoogle Scholar
  13. [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.CrossRefGoogle Scholar
  14. [14]
    Luce, R. D. and Raiffa, H., Games and Decisions, Wiley, New York, 1957.Google Scholar
  15. [15]
    Luce, R. D., Individual Choice Behavior, Wiley, New York, 1959.Google Scholar
  16. [16]
    Thurstone, L. L., ‘A Law of Comparative Judgment’, Psychol. Rev. 34 (1927) 273–286.CrossRefGoogle Scholar
  17. [17]
    Mosteller, F., ‘Remarks on the Method of Paired Comparisons’, Psychometrika 26 (1951) 3–9, 203–206, 207–218.Google Scholar
  18. [18]
    Block, H. D. and Marschak, J. ‘An Identity in Arithmetic’, Bull Amer. Math. Soc. 65 (1959) 123–124.CrossRefGoogle Scholar
  19. [19]
    Debreu, G., ‘On “An identity in arithmetic”’, Proc. Amer. Math. Soc. 11 (1960) 220–221.Google Scholar
  20. [20]
    Marschak, J., ‘Binary Choice Constaints on Random Utility Indicators’, Selected Essays, 8.Google Scholar
  21. [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. [22]
    Georgescu-Roegen, N, ‘Threshold in Choice and the Theory of Demand’, Econometrica 26 (1958) 157–168.CrossRefGoogle Scholar
  23. [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. [24]
    Debreu, G., ‘Stochastic Choice and Cardinal Utility’, Econometrica 26 (1958) 440–444.CrossRefGoogle Scholar
  25. [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. [26]
    Tôrnqvist, L., ‘A Model for Stochastic Decision Making’, Cowles Commission Discussion Paper, Economics 2100, Cowles Commission, Chicago, 1954 (duplicated).Google Scholar
  27. [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. [28]
    Ford, L. R., ‘Solution of a Ranking Problem from Binary Comparisons’, Amer. Math. Month. 64 (1957) (Aug. suppl.), 28–33.CrossRefGoogle Scholar
  29. [29]
    Coombs, C., On the Use of Inconsistency of Preferences in Psychological Measurement’, J. Exp. Psychol. 55 (1958) 1–7.CrossRefGoogle Scholar
  30. [30]
    Gulliksen, H., ‘Paired Comparisons and the Logic of Measurement’, Psychol. Rev. 53 (1946) 199–213.CrossRefGoogle Scholar
  31. [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. [32]
    Edwards, W., ‘Probability Preferences in Gambling’, Amer. J. Psychol. 66 (1955) 349–364.CrossRefGoogle Scholar
  33. [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. [34]
    May, K., ‘Intransitivity, Utility and the Aggregation of Preference Patterns’, Econometrica 22 (1954) 1–13.CrossRefGoogle Scholar
  35. [35]
    Davis, J. M., ‘The Transitivity of Preferences’, Behav. Sci 3 (1958) 26–33.CrossRefGoogle Scholar
  36. [36]
    Davidson, D. and Marschak, J., ‘Experimental Tests of Stochastic Decision Theories’, Selected Essays, 6.Google Scholar
  37. [37]
    Georgescu-Roegen, N., ‘The Pure Theory of Consumer Behavior’, Quart. J. Econ. 50 (1936) 545–593.CrossRefGoogle Scholar
  38. [38]
    Rosenblatt, D., ‘On Some Stochastic Process Formulations of Individual Preference and Consumer Behavior (abst.)’, Econometrica 24 (1956) 347–348.Google Scholar
  39. [39]
    Marschak, J., ‘Norms and Habits of Decision Making under Certainty’, Selected Essays, 5.Google Scholar
  40. [40]
    Kendall, M. G., ‘Further Contributions to the Theory of Paired Comparisons’, Biometrics 11 (1955) 43–67.CrossRefGoogle Scholar
  41. [41]
    Mallows, G. L., ‘Non-Null Ranking Models, I’, Biometrika 44 (1957) 114–130.Google Scholar
  42. [42]
    Savage, I. R., ‘Contributions to the Theory of Rank Orders’, Ann. Math. Stat. 27 (1956) 590–615; 28 (1957) 968–77.CrossRefGoogle Scholar
  43. [43]
    Lehmann, E. L., ‘Ordered Families of Distributions’, Ann. Math. Stat. 26 (1955) 399–419.CrossRefGoogle Scholar
  44. [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. [45]
    Savage, L. J., The Foundations of Statistics, Wiley, New York, 1954. Revised, Dover, 1972.Google Scholar
  46. [46]
    Simon, H. A., ‘A Behavioral Model of Rational Choice’, Quart. J. Econ. 69 (1955) 99–118.CrossRefGoogle Scholar
  47. [47]
    Quandt, R. E., ‘A Probabilistic Theory of Consumer Behavior’, Quart. J. Econ. 70 (1956) 507–536.CrossRefGoogle Scholar
  48. [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. [49]
    Herstein, I. N. and Milnor, J., ‘An Axiomatic Approach to Measurable Utility’ Econometrica 21 (1953) 291–297.CrossRefGoogle Scholar
  50. [50]
    Ramsey, F. P., The Foundations of Mathematics and Other Logical Essays, Kegan Paul, London 1931.Google Scholar
  51. [51]
    Luce, R. D., ‘A Probabilistic Theory of Utility’, Econometrica 26 (1958) 193–224.CrossRefGoogle Scholar
  52. [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.CrossRefGoogle Scholar
  53. [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. [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. [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. [56]
    Thurstone, L. L. and Jones, L., ‘The Rational Origin for Measuring Subjective Values’, J. Amer. Stat. Assoc. 52 (1957) 458–471.CrossRefGoogle Scholar
  57. [57]
    Gulliksen, H., ‘Measurement of Subjective Values’, Psychometrika 21 (1956) 229–244.CrossRefGoogle Scholar
  58. [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. [59]
    Tversky, A., ‘Elimination by Aspects: A Theory of Choice’, Psychological Review 79 (1972) 281–299.CrossRefGoogle Scholar
  60. [60]
    Tversky, A., ‘Intransitivity of Preferences’, Psychological Review 76 (1969) 31–48.CrossRefGoogle Scholar
  61. [61]
    DeGroot, M. H., ‘Optimal Allocation of Observations’, Annals of the Institute of Statistical Mathematics, 18 (1966) 13–28.CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1974

Authors and Affiliations

  • H. D. Block

There are no affiliations available

Personalised recommendations