Public Choice

, Volume 59, Issue 2, pp 101–120

The problem of indeterminacy in approval, multiple, and truncated voting systems

  • Donald G. Saari
  • Jill Van Newenhizen
Article

DOI: 10.1007/BF00054447

Cite this article as:
Saari, D.G. & Van Newenhizen, J. Public Choice (1988) 59: 101. doi:10.1007/BF00054447

Abstract

It is well known that a plurality election need not reflect the true sentiments of the electorate. Some of the proposed reform procedures, such as approval and cumulative voting, share the characteristics that there are several ways to tally each voter's preferences. Voting systems that permit truncated ballots share this feature. It is shown that the election results for any such procedure can be highly indeterminate; all possible election results can occur with the same choice of sincere voters. This conclusion of indeterminacy holds even when measures of voters' sentiments, such as the existence of a Condorcet winner or even much stronger measures, indicate there is considerable agreement among the voters. Then, multiple systems are compared with all standard tallying procedures. For instance, a corollary asserts it is probable for the plurality voting method to elect the Condorcet winner while approval voting has an indeterminate outcome.

Copyright information

© Kluwer Academic Publishers 1988

Authors and Affiliations

  • Donald G. Saari
    • 1
  • Jill Van Newenhizen
    • 1
  1. 1.Department of MathematicsNorthwestern UniversityEvanston