Random Behavior in Numerical Analysis, Decision Theory, and Macrosystems: Some Impossibility Theorems

  • Donald G. Saari
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 257)

Abstract

For many topics, including decision analysis, policy making, and the normative study of certain macrosystems, tools of analysis are applied to determine the essence or the state of a problem. The one commonality among these tools is that we want them to be “reliable”. For certain standard tools, it is shown that this goal of reliability may be impossible to attain. For some of these impossibility statements, alternative approaches are suggested.

Keywords

Nash Cond Iterative Dynamic 

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References

  1. 1.
    Collet, P. and J. P. Eckmann, Iterated Maps of the Interval as Dynamical Systems, Birkhauser, Boston, 1980.Google Scholar
  2. 2.
    Preston, C., Iterates of Maps on an Interval Lecture Notes in Mathematics Series, no. 999, Springer-Verlag, New York, 1983.Google Scholar
  3. 3.
    Saari, D. G., Iterative price mechanisms, to appear in Econometrica.Google Scholar
  4. 4.
    Barna, B., Uber die divergenzpunkte des Newtonschen verfahrens zur bestimmung von wurzeln algebraischer gleichungen II, Publicationes Mathematicae Debrecen 4,(1956) 384–397; and III, same journal, 8 (1961), 193–207.Google Scholar
  5. 5.
    Saari, D. G., and J. B. Urenko, Newton’s method, circle maps, and chaotic motion, American Mathematical Monthly, 91 (1984), 3–17.CrossRefGoogle Scholar
  6. 6.
    Martin, C., and R Hurley, Newton’s algorithm and chaotic dynamical systems, SIAM Journal on Math Anal. 15 (1984), 238–252.CrossRefGoogle Scholar
  7. 7.
    Surale, S., The fundamental theorem of algebra and complexity theory, Bull Amer. Math Soc., 4 (1981), 1–37.CrossRefGoogle Scholar
  8. 8.
    Shafer, W., and H. Sonnenschein, Market demand and excess demand functions, in Handbook of Mathematical Economics, vol 2, pp 671–693, ed by K Arrow and M Intriligator, North Holland, 1982.Google Scholar
  9. 9.
    Saari, D. G., The source of some paradoxes from social choice and probabiliity, Center for Mathematical Studies in Economics Discussion paper no. 609, May, 1984.Google Scholar
  10. 10.
    Saari, D. G., The ultimate of chaos resulting from weighted voting systems, Advances in Applied Math, 5 (1984), 286–308.CrossRefGoogle Scholar
  11. 11.
    Arrow, K., Social Choice and Individual Values, Crowles Foundation for Research in Economics, Monograph 12, 1963.Google Scholar
  12. 12.
    Blyth, C., On Simpson’s paradox and the sure-thing principle, Jour. of Amer. Stat. Assoc., 67 (1972), 364–366.CrossRefGoogle Scholar
  13. 13.
    Wagner, C., Simpson’s paradox in real life, The American Statistician 36 (1982), 46–48.Google Scholar
  14. 14.
    Bickel, P. J., Hammel, E. A., and J. W. O’Connel, Sex bias in graduate admissions: data from Berkeley, Science, 187 (1975), 398–404.CrossRefGoogle Scholar
  15. 15.
    Saari, D. G., Mathematical Economics and Dynamical Systems, to be published in a vol. ed by H. Weinberger and H Sonnenschein.Google Scholar
  16. 16.
    Saari, D. G., A method for constructing message systems for smooth performance functions, Jour. of Econ. Theory, 33 (1984), 249–274.CrossRefGoogle Scholar

Copyright information

© International Institute for Applied Systems Analysis, Laxenburg/Austria 1985

Authors and Affiliations

  • Donald G. Saari
    • 1
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA

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