Random Behavior in Numerical Analysis, Decision Theory, and Macrosystems: Some Impossibility Theorems
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.
KeywordsNash Cond Iterative Dynamic
Unable to display preview. Download preview PDF.
- 1.Collet, P. and J. P. Eckmann, Iterated Maps of the Interval as Dynamical Systems, Birkhauser, Boston, 1980.Google Scholar
- 2.Preston, C., Iterates of Maps on an Interval Lecture Notes in Mathematics Series, no. 999, Springer-Verlag, New York, 1983.Google Scholar
- 3.Saari, D. G., Iterative price mechanisms, to appear in Econometrica.Google Scholar
- 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
- 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.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
- 11.Arrow, K., Social Choice and Individual Values, Crowles Foundation for Research in Economics, Monograph 12, 1963.Google Scholar
- 13.Wagner, C., Simpson’s paradox in real life, The American Statistician 36 (1982), 46–48.Google Scholar
- 15.Saari, D. G., Mathematical Economics and Dynamical Systems, to be published in a vol. ed by H. Weinberger and H Sonnenschein.Google Scholar