Social Choice and Welfare

, Volume 1, Issue 2, pp 149–158 | Cite as

Heights of representative systems: A proof of Fishburn's conjecture

  • H. Keiding


Representative systems with n-voters are hierarchical choice functions from {-1, 0, 1} n to {-1, 0, 1} constructed as iterations of weighted majority voting. The height of a representative system is the minimal number of iterations necessary for this construction.

In the paper we give an upper bound for μ(n), the maximal height of any n-voter representative system, and show that \(\frac{{\mu (n)}}{n}\) goes to zero as n goes to infinity, thus proving a conjecture made by Fishburn. Technically, the results are obtained by transferring the problem to the context of proper simple games, which have a similar hierarchical structure, and using known results on heights of simple games.


Economic Theory Hierarchical Structure Maximal Height Majority Vote Choice Function 
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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • H. Keiding
    • 1
  1. 1.Institute of EconomicsUniversity of CopenhagenCopenhagenDenmark

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