Annals of Operations Research

, Volume 23, Issue 1, pp 103–137 | Cite as

Consistency of decision processes

  • Donald G. Saari


If a statistical or a voting decision procedure is used by several subpopulations and if each reaches an identical conclusion, then one might expect this conclusion to be the outcome for the full group. It is shown that this property fails to hold for large classes of decision procedures. The geometric reasons why the consistency does not hold are described. A general theorem is given to characterize the procedures that satisfy this property of “weak consistency”.


Decision Process Large Classis Decision Procedure General Theorem Full Group 
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]
    E. Andreev, W. Lutz and S. Scherbov, Averaging life expectancy, IIASA Working Paper WP-89-35, Laxenburg (1989).Google Scholar
  2. [2]
    S. Barbera, Majority and positional voting in a probabilistic framework, Rev. Econ. Studies 46(1979)379–389.Google Scholar
  3. [3]
    D. Black,The Theory of Committees and Elections (Cambridge University Press, 1958).Google Scholar
  4. [4]
    S. Brams and P. Fishburn, Paradoxes of preferential voting, Math. Mag. 56(1983)207–214.Google Scholar
  5. [5]
    A. Caplin and B. Nalebuff, On 64% majority rule, Econometrica 54(1986)787–814.Google Scholar
  6. [6]
    J. Cohen, An uncertainty principle in demography and the unisex issue, Amer. Statis. 40(1986)32–39.Google Scholar
  7. [7]
    P. Fishburn and W. Gehrlein, Borda's rule, positional voting, and Condorcet's simple majority principle, Public Choice (1976)79–88.Google Scholar
  8. [8]
    I.J. Good and Y. Mittal, The amalgamation and geometry of two by two contingency tables, Ann. Statis. 15(1987)694–711.Google Scholar
  9. [9]
    H. Moulin, Condorcet's principle implies the no show paradox, J. Econ. Theory 45(1988)53–64.Google Scholar
  10. [10]
    H. Nurmi,Comparing Voting Systems (Reidel, Boston, 1987).Google Scholar
  11. [11]
    K. Pearson, Theory of genetic selection, Philos. Trans. Roy. Soc. London, Ser. A 192(1899)260–278.Google Scholar
  12. [12]
    D.G. Saari, Symmetry, voting, and social choice, The Mathematical Intelligencer 10(1988)32–42.Google Scholar
  13. [13]
    D.G. Saari, The source of some paradoxes from social choice and probability, J. Econ. Theory. 41(1987)1–22.Google Scholar
  14. [14]
    D.G. Saari, A dictionary for voting paradoxes, J. Econ. Theory 48(1989)443–475.Google Scholar
  15. [15]
    D.G. Saari, The Borda dictionary, NU Center for Mathematical Economics Discussion Paper No. 821 (1989).Google Scholar
  16. [16]
    D.G. Saari, Relationship admitting families of candidates, NU Center for Mathematical Economics Discussion Paper No. 823 (1989).Google Scholar
  17. [17]
    J.H. Smith, Aggregation of preferences with variable electorate, Econometrica 41(1973)1027–1041.Google Scholar
  18. [18]
    J.W. Vaupel and A.L. Yashin, Heterogeneity's ruses: Some surprising effects on selection in population dynamics, Amer. Statist. 36(1985)46–48.Google Scholar
  19. [19]
    H.P. Young, Social choice scoring functions, SIAM J. Appl. Math. 28(1975)824–838.Google Scholar
  20. [20]
    G.U. Yule, Notes on the theory of attributes in statistics, Biometrika 2(1903)121–134.Google Scholar

Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1990

Authors and Affiliations

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

Personalised recommendations