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


  • Donald Saari
  • Jill Newenhizen


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

    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. repec:cup:apsrev:v:78:y:1984:i:04:p:952-958_25 is not listed on IDEAS
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    Cited by:

    1. Pierre Dehez & Victor Ginsburgh, 2018. "Approval Voting and Shapley Ranking," Working Papers ECARES 2018-09, ULB -- Universite Libre de Bruxelles.
    2. Bouton, Laurent & Castanheira, Micael & Llorente-Saguer, Aniol, 2016. "Divided majority and information aggregation: Theory and experiment," Journal of Public Economics, Elsevier, vol. 134(C), pages 114-128.
    3. repec:eee:gamebe:v:106:y:2017:i:c:p:227-238 is not listed on IDEAS
    4. Arnaud Dellis & Mandar Oak, 2016. "Multiple votes, multiple candidacies and polarization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 1-38, January.
    5. Enriqueta Aragones & Micael Castanheira, 2010. "approval voting," The New Palgrave Dictionary of Economics, Palgrave Macmillan.
    6. Eric Kamwa, 2019. "The Condorcet Efficiency of the Preference Approval Voting and the Probability of Selecting the Condorcet Loser," Post-Print hal-01786121, HAL.
    7. Kangas, Annika & Laukkanen, Sanna & Kangas, Jyrki, 2006. "Social choice theory and its applications in sustainable forest management--a review," Forest Policy and Economics, Elsevier, vol. 9(1), pages 77-92, November.
    8. repec:spr:sochwe:v:49:y:2017:i:1:d:10.1007_s00355-017-1052-x is not listed on IDEAS
    9. Michel Regenwetter & Bernard Grofman, 1998. "Approval Voting, Borda Winners, and Condorcet Winners: Evidence from Seven Elections," Management Science, INFORMS, vol. 44(4), pages 520-533, April.
    10. repec:spr:homoec:v:35:y:2018:i:1:d:10.1007_s41412-018-0069-4 is not listed on IDEAS
    11. Eric Kamwa, 2018. "On the Condorcet Efficiency of the Preference Approval Voting and the Probability of Selecting the Condorcet Loser," Working Papers hal-01786121, HAL.
    12. Donald Saari & Jill Newenhizen, 1988. "Is approval voting an ‘unmitigated evil’?: A response to Brams, Fishburn, and Merrill," Public Choice, Springer, vol. 59(2), pages 133-147, November.

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