Price Dynamics, Social Choice, Voting Methods, Probability and Chaos

Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 244)


An intriguing aspect of the mathematical social sciences is the discovery that so many things can go wrong! Mathematical models are developed to clarify, sharpen, and advance arguments originally put forth in a verbal form. Often these verbal arguments persuasively leave us with a sense of security and of orderliness; then often the mathematical formulation shatters this stability. (This is because the mathematics may uncover subtle combinatorics or hidden second and higher level interaction effects.) Perhaps the most dramatic illustration of this comes from the social choice literature with the well-known Arrow Impossibility Theorem [1]). In economics, the stability of the price adjustment model of tatonnement was threatened by Scarf’s example [2] where he showed that the tatonnement market forces of supply and demand could push the prices away from any equilibrium. Any remaining faith in this price story was destroyed by the work of Sonnenschein and others [3] which disclosed, as a corollary, that almost any type of price trajectory could occur.


Social Choice Condorcet Winner Approval Vote Vote Method Ordinal Ranking 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Arrow, K., Social Choice and Individual Values, Cowles Foundation for Research in Economics, Monograph 12, Yale University, New Haven, 1953.Google Scholar
  2. 2.
    Scarf, H., Some examples of global instabilities of the competitive equilibrium, International Econ. Review, 1 (1960), 157–172.Google Scholar
  3. 3.
    Shafer, W. and H. Sonnenschein, Market demand and excess demand function, Chp. 14 in Handbook of Mathematical Economics, 2, edited by K. Arrow and M. D. Intriligator, North Holland, Amsterdam, 1982.Google Scholar
  4. 4.
    Benhabib, J. and K. Nishimura, Competitive equilibrium cycles, NYU preprint, 1983.Google Scholar
  5. 5.
    Grandmont, J. M., On endogeneous competitive business cycles, CEPREMAP Discussion paper no. 8316, Sept. 1983.Google Scholar
  6. 6.
    Bewley, T., A talk given at a conference on price dynamics at the University of Minnesota, Oct. 1983.Google Scholar
  7. 7..
    Saari, D. G., Dynamical systems and mathematical economics, to appear in a book ed. by H. Sonnenschein and H. Weinberger, Springer Verlag series.Google Scholar
  8. 8.
    Saari, D. G., and J. Urenko, Newton’s method, circle maps, and chaotic motion, Amer. Math. Monthly, 91 (1984), 3–17.CrossRefGoogle Scholar
  9. 9.
    Barna, B., Uber die divergenzpunkte des Newtonschen Verfahrens zur Bestimmung von Wurzein algebraischer Gleichungen 3, Publicationes Mathematicae, Debrecen, 8 (1961), 193–207.Google Scholar
  10. 10.
    Martin, C. and R. Hurley, Newton’s algorithm and chaotic dynamical systems, SIAM Jour of Math Anal. 1984.Google Scholar
  11. 11..
    Urenko, J., The improbability of chaos in Newtons method, To appear in Jour of Math Anal and Appl.Google Scholar
  12. 12.
    Saari, D. G., Iterative price dynamics, to appear in Econometrica. (NU preprint, October 1983.)Google Scholar
  13. 13.
    Fishburn, P., The Theory of Social Choice, Princeton University Press, Princeton, 1973.Google Scholar
  14. 14.
    Fishburn, P., Inverted orders for monotone scoring rules, Discrete Applied Mathematics, 3 (1981), 27–36.CrossRefGoogle Scholar
  15. 15.
    Saari, D. G., Inconsistencies of weighted voting systems, Math of OR, 7 (1982), 479–490.Google Scholar
  16. 16.
    Saari, D. G., The ultimate of chaos resulting from weighted voting systems, Advances in Applied Mathematics 5(1984), 286–308.CrossRefGoogle Scholar
  17. 17.
    Saari, D. G., The source of some paradoxes from social choice and probability, NU Center for Mathematical Studies in Economics, Discussion paper no. 609, June, 1984.Google Scholar
  18. 18.
    Brams, and Fishburn, Approval Voting, Birkhauser, Boston, 1982.Google Scholar
  19. 19.
    Steinhaus, H. and S. Tribula, On a paradox in applied probability, Bull Acad Polo Sci, 7 (1959), 67–69.Google Scholar
  20. 20.
    Blyth, C., On Simpson’s paradox and the sure-thing principle, Jour of Amer Statistical Assoc, 67 (1972), 364–366.CrossRefGoogle Scholar
  21. 21.
    Wagner, C., Simpson’s paradox in real life, The American Statistician, 36 (1982), 46–48.Google Scholar
  22. 22.
    Bickel, P. J., Hammel, E. A., and J. W. O’Connell, Sex bias in graduate admissions: data from Berkely, Science, 187, 398–404.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA

Personalised recommendations