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

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  • Donald Saari
  • Jill Newenhizen

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 Kluwer Academic Publishers 1988

Suggested Citation

  • Donald Saari & Jill Newenhizen, 1988. "The problem of indeterminacy in approval, multiple, and truncated voting systems," Public Choice, Springer, vol. 59(2), pages 101-120, November.
    • Handle: RePEc:kap:pubcho:v:59:y:1988:i:2:p:101-120
    DOI: 10.1007/BF00054447
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    References listed on IDEAS

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    1. Saari, Donald G., 1987. "The source of some paradoxes from social choice and probability," Journal of Economic Theory, Elsevier, vol. 41(1), pages 1-22, February.
    2. Peter Fishburn & Steven Brams, 1984. "Manipulability of voting by sincere truncation of preferences," Public Choice, Springer, vol. 44(3), pages 397-410, January.
    3. Niemi, Richard G., 1984. "The Problem of Strategic Behavior under Approval Voting," American Political Science Review, Cambridge University Press, vol. 78(4), pages 952-958, December.
    4. Donald G. Saari, 1985. "The Optimal Ranking Method is the Borda Count," Discussion Papers 638, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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