Skip to main content
SpringerLink
Log in

Revealed stochastic preference: a synthesis

  • Conference paper
Rationality and Equilibrium

Part of the book series: Studies in Economic Theory ((ECON.THEORY,volume 26))

Summary

The problem of revealed stochastic preference is whether probability distributions of observed choices in a population for various choice situations are consistent with a hypothesis of maximization of preference preorders by members of the population. This is a population analog of the classical revealed preference problem in economic consumer theory. This paper synthesizes the solutions to this problem that have been obtained by Marcel K. Richter and the author, and by J. C. Falmagne, in the case of finite sets of alternatives, and utilizes unpublished research of Richter and the author to give results for the non-finite choice sets encountered in economic consumer theory.

The preparation of this paper was supported by the E. Morris Cox endowment at the University of California, Berkeley. I am indebted to Robert Anderson, Salvador Barbara, Werner Hildenbrand, Rosa L. Matzkin, and Aviv Nevo for useful suggestions and comments. I am especially indebted to Marcel K. Richter, who was the source of many of the ideas and arguments contained in this paper.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bandyopadhyay, T., Dasgupta, I., Pattanaik, P.: Stochastic revealed preference and the theory of demand. Journal of Economic Theory 84, 95–110 (1999)

    Article  Google Scholar 

  • Barbera, S., Pattanaik, P.: Falmagne and the rationalizability of stochastic choices in terms of random orderings. Econometrica 54, 707–716 (1986)

    MathSciNet  Google Scholar 

  • Barbara, S.: Rationalizable stochastic choice over restricted domains. In: Chipman, J., McFadden, D., Richter, K. (eds.) Preferences, uncertainty, and rationality, pp. 203–217. Boulder: Westview Press 1991

    Google Scholar 

  • Block, H., Marschak, J.: Random orderings and stochastic theories of response. In: Olkin, I., et al (eds.) Contributions to probability and statistics, pp. 97–132. Stanford: Stanford University Press 1960

    Google Scholar 

  • Brown, D., Matzkin, R.: Testable Restrictions on the equilibrium manifold. Econometrica 64, 1249–1262 (1996)

    Google Scholar 

  • Cohen, M.: Random utility systems — the infinite case. Journal of Mathematical Psychology 22, 1–23 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  • Cohen, M., Falmagne, J.: Random utility representation of binary choice probabilities: a new class of necessary conditions. Journal of Mathematical Psychology 34, 88–94 (1990)

    Article  MathSciNet  Google Scholar 

  • Debreu, G.: Preference functions on a measure space of economic agents. Econometrica 35, 111–122 (1967)

    MATH  MathSciNet  Google Scholar 

  • Dunford, N., Schwartz, J.: Linear operators. New York: Interscience 1964

    Google Scholar 

  • Falmagne, J.: A representation theorem for finite random scale systems. Journal of Mathematical Psychology 18, 52–72 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  • Fishburn, P.: Choice probabilities and choice functions. Jounal of Mathematical Psychology 10, 327–352 (1978)

    MathSciNet  Google Scholar 

  • Fishburn, P., Falmagne, J.: Binary choice probabilities and rankings. Economic Letters 31, 113–117 (1989)

    Article  MathSciNet  Google Scholar 

  • Fishburn, P.: Induced binary probabilities and the linear ordering polytope: a status report. Mathematical Social Sciences 23, 67–80 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  • Fishburn, P.: Stochastic utility. In: Barbara, S., Hammond, P., Seidl, C. (eds.) Handbook of utiltiy theory, pp. 273–320. Boston: Kluwer 1998

    Google Scholar 

  • Freedman, D., Purves, R.: Bayes method for bookies. Annals of Mathematical Statistics 40, 117–1186 (1969)

    MathSciNet  Google Scholar 

  • Halldin, C.: The choice axiom, revealed preference, and the theory of demand. Theory and Decision 5, 139–160 (1974)

    Article  MATH  Google Scholar 

  • Hildenbrand, W.: Random preferences and equilibrium analysis. Journal of Economic Theory 3, 414–429 (1971)

    Article  MathSciNet  Google Scholar 

  • Hildenbrand, W.: Core and equilibrium of a large economy. Princeton, NJ: Princeton University Press 1974

    Google Scholar 

  • Houthakker, H.: Revealed preference and the utility function. Economica 17, 159–174 (1950)

    MathSciNet  Google Scholar 

  • Karlin, S.: Mathematical methods and theory in games, programming, and economics, pp. 265–273. New York: Addison-Wesley 1959

    Google Scholar 

  • Luce, D.: Individual choice behavior. New York: Wiley 1959

    Google Scholar 

  • Luce, D., Suppes, P.: Preferences, utility, and subjective probability. In: Luce, D., et al (eds.) Handbook of mathematical psychology, Vol. III, pp. 249–410. New York: Wiley 1965

    Google Scholar 

  • Manski, C.: The structure of random utility models. Theory and Decision 8, 229–254 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  • Marschak, J.: Binary-choice constrains on random utility indicators. In: Arrow, K., Karlin, S., Suppes, P. (eds.) Mathematical methods in the social sciences, pp. 312–329. Stanford: Stanford University Press 1960

    Google Scholar 

  • Matzkin, R.: Nonparametric and distribution-free estimation of the binary threshold crossing and the binary choice models. Econometrica 60, 239–270 (1992)

    MATH  MathSciNet  Google Scholar 

  • McCausland, W.: A theory of random consumer demand. Working paper (2002)

    Google Scholar 

  • McFadden, D., Richter, M.K.: On the extension of a set function on a set of events to a probability on the generated Boolean σ-algebra. University of California, Berkeley, Working paper (1971)

    Google Scholar 

  • McFadden, D.: Estimation and testing of models of individual choice behavior from data on a population of subjects. University of California, Berkeley, Working paper (1973)

    Google Scholar 

  • McFadden, D.: Conditional logit analysis of qualitative choice behavior. In: Zarembka, P. (ed.) Frontiers of econometrics, pp. 105–142. New York: Academic Press 1974

    Google Scholar 

  • McFadden, D.: Tchebyscheff bounds for the space of agent characteristics. Journal of Mathematical Economics 2, 225–242 (1975)

    MATH  MathSciNet  Google Scholar 

  • McFadden, D.: A note on the computability of the strong axiom of revealed preference. Journal of Mathematical Economics 6, 15–16 (1979)

    Article  MATH  Google Scholar 

  • McFadden, D., Richter, K. Stochastic rationality and revealed stochastic preference. In Chipman, J., McFadden, D., Richter, K. (eds.) Preferences, uncertainty, and rationality, pp. 161–186. Boulder: Westview Press 1991

    Google Scholar 

  • McFadden, D.: Economic choices. American Economic Review 91, 351–378 (2001)

    Google Scholar 

  • McLennan, A.: Binary stochastic choice. in: Chipman, J., McFadden, d., Richter, K. (eds.) Preferences, uncertainty, and rationality, pp. 187–202. Boulder: Westview Press 1991

    Google Scholar 

  • Neveu, J.: Mathematical foundations of the calculus of probability. San Francisco: Holden-Day 1965

    Google Scholar 

  • Richter, K.: Revealed preference theory. Econometrica 34, 635–645 (1966)

    MATH  Google Scholar 

  • Richter, K.: Rational choice. In: Chipman, J., et al (eds.) Preferences, utility and demand, pp. 29–58. New York: Harcourt-Brace 1971

    Google Scholar 

  • Samuelson, P.: A note on the pure theory of consumer behavior. Economica 5, 51–71 and 353–354 (1938)

    Google Scholar 

  • Thurstone, L.: A law of comparative judgment. Psychological Review 34, 273–286 (1927)

    Google Scholar 

  • Varian, H.: The nonparametric approach to demand analysis. Econometrica 50, 945–974 (1982)

    MATH  MathSciNet  Google Scholar 

  • Varian, H.: Nonparametric tests of consumer behavior. Review of Economic Studies 50, 99–110 (1983)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, University of California, Berkeley, CA, 94720-3880, USA

    Daniel L. McFadden

Authors
  1. Daniel L. McFadden
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Krannert School of Management Department of Economics, Purdue University, West Lafayette, IN, 47907-2076, USA

    Charalambos D. Aliprantis  & James C. Moore  & 

  2. Department of Economics, Northwestern University, Evanston, IL, 60208, USA

    Rosa L. Matzkin

  3. Department of Economics, University of California, Berkeley, CA, 94720-3880, USA

    Daniel L. McFadden

  4. Department of Economics, University of Illinois, Champaign, IL, 61820, USA

    Nicholas C. Yannelis

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

McFadden, D.L. (2006). Revealed stochastic preference: a synthesis. In: Aliprantis, C.D., Matzkin, R.L., McFadden, D.L., Moore, J.C., Yannelis, N.C. (eds) Rationality and Equilibrium. Studies in Economic Theory, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29578-X_1

Download citation

  • DOI: https://doi.org/10.1007/3-540-29578-X_1

  • Received:

  • Revised:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29577-8

  • Online ISBN: 978-3-540-29578-5

  • eBook Packages: Business and EconomicsEconomics and Finance (R0)

Publish with us

Policies and ethics

Search

Navigation