IDEAS home Printed from https://ideas.repec.org/a/kap/pubcho/v59y1988i2p101-120.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/BF00054447
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/BF00054447?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Peter Fishburn & Steven Brams, 1984. "Manipulability of voting by sincere truncation of preferences," Public Choice, Springer, vol. 44(3), pages 397-410, January.
    2. 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.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Núñez, Matías & Sanver, M. Remzi, 2017. "Revisiting the connection between the no-show paradox and monotonicity," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 9-17.
    3. Aaron Hamlin & Whitney Hua, 2023. "The case for approval voting," Constitutional Political Economy, Springer, vol. 34(3), pages 335-345, September.
    4. Erdamar, Bora & Sanver, M. Remzi & Sato, Shin, 2017. "Evaluationwise strategy-proofness," Games and Economic Behavior, Elsevier, vol. 106(C), pages 227-238.
    5. Eric Kamwa & Issofa Moyouwou, 2019. "Susceptibility to Manipulation by Sincere Truncation : the Case of Scoring Rules and Scoring Runoff Systems," Working Papers hal-02185965, HAL.
    6. Duddy, Conal, 2014. "Electing a representative committee by approval ballot: An impossibility result," Economics Letters, Elsevier, vol. 124(1), pages 14-16.
    7. Donald G. Saari & Jill Van Newenhizen, 1985. "A Case Against Bullet, Approval and Plurality Voting," Discussion Papers 637, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Andrea C. Hupman & Jay Simon, 2023. "The Legacy of Peter Fishburn: Foundational Work and Lasting Impact," Decision Analysis, INFORMS, vol. 20(1), pages 1-15, March.
    9. Stefano Vannucci, 2006. "The Proportional Lottery Protocol is Strongly Participatory and VNM-Strategy-Proof," Department of Economics University of Siena 490, Department of Economics, University of Siena.
    10. 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.
    11. Kamwa, Eric & Merlin, Vincent, 2015. "Scoring rules over subsets of alternatives: Consistency and paradoxes," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 130-138.
    12. Hannu Nurmi, 2004. "Monotonicity and its Cognates in the Theory of Choice," Public Choice, Springer, vol. 121(1), pages 25-49, October.
    13. Isabelle Lebon & Antoinette Baujard & Frédéric Gavrel & Herrade Igersheim & Jean-François Laslier, 2016. "Ce que le vote par approbation révèle des préférences des électeurs français," PSE Working Papers halshs-01409106, HAL.
    14. Donald G. Saari, 1986. "Symmetry, Voting, and Social Choice," Discussion Papers 712, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    15. Luis C. Corchón & Marco Serena, 2016. "Properties of Contests," Working Papers tax-mpg-rps-2018-10, Max Planck Institute for Tax Law and Public Finance.
    16. Jean-François Laslier, 2009. "The Leader Rule," Journal of Theoretical Politics, , vol. 21(1), pages 113-136, January.
    17. Eric Kamwa, 2023. "On two voting systems that combine approval and preferences: fallback voting and preference approval voting," Public Choice, Springer, vol. 196(1), pages 169-205, July.
    18. Lehtinen, Aki, 2008. "The welfare consequences of strategic behaviour under approval and plurality voting," European Journal of Political Economy, Elsevier, vol. 24(3), pages 688-704, September.
    19. John Cullinan & Samuel Hsiao & David Polett, 2014. "A Borda count for partially ordered ballots," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 913-926, April.
    20. Granić, Đura-Georg, 2017. "The problem of the divided majority: Preference aggregation under uncertainty," Journal of Economic Behavior & Organization, Elsevier, vol. 133(C), pages 21-38.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:pubcho:v:59:y:1988:i:2:p:101-120. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.