IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v56y2021i1d10.1007_s00355-020-01274-y.html
   My bibliography  Save this article

A diagram for analyzing ordinal voting systems

Author

Listed:
  • Andrew C. Eggers

    (Nuffield College, University of Oxford)

Abstract

I introduce a diagram for describing and analyzing single-winner elections in which voters rank the candidates—a class of voting systems including positional methods (e.g. plurality, Borda count, anti-plurality), Condorcet methods, and instant-runoff voting (i.e. ranked-choice voting or the alternative vote). The diagram shows how the outcome of an election depends on each candidate’s share of top rankings as a function of the voting system and the pattern of lower rankings. Using as examples two Brexit polls, a mayoral election in San Francisco, and the US’s first instant-runoff congressional election (all since 2018), I show how the diagram can concisely present preferences and results under different voting systems, identify Condorcet cycles, highlight system properties such as join-inconsistency and the no-show paradox, and illuminate strategic voting incentives.

Suggested Citation

  • Andrew C. Eggers, 2021. "A diagram for analyzing ordinal voting systems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(1), pages 143-171, January.
    • Handle: RePEc:spr:sochwe:v:56:y:2021:i:1:d:10.1007_s00355-020-01274-y
    DOI: 10.1007/s00355-020-01274-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-020-01274-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00355-020-01274-y?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. Mostapha Diss & Abdelmonaim Tlidi, 2018. "Another perspective on Borda’s paradox," Theory and Decision, Springer, vol. 84(1), pages 99-121, January.
    2. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2011. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 2, number 2.
    3. Peter Emerson, 2013. "The original Borda count and partial voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 353-358, February.
    4. Conal Duddy, 2017. "Geometry of run-off elections," Public Choice, Springer, vol. 173(3), pages 267-288, December.
    5. Saari, Donald G. & Valognes, Fabrice, 1999. "The geometry of Black's single peakedness and related conditions," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 429-456, December.
    6. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521731607, September.
    7. Katz, Jonathan N. & King, Gary, 1999. "A Statistical Model for Multiparty Electoral Data," American Political Science Review, Cambridge University Press, vol. 93(1), pages 15-32, March.
    8. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521516051, September.
    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. Maurice Salles, 2014. "‘Social choice and welfare’ at 30: its role in the development of social choice theory and welfare economics," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 1-16, January.
    2. Neal D. Hulkower & John Neatrour, 2019. "The Power of None," SAGE Open, , vol. 9(1), pages 21582440198, March.
    3. Piggins, Ashley & Salerno, Gillian, 2016. "Sen cycles and externalities," Economics Letters, Elsevier, vol. 149(C), pages 25-27.
    4. Eric Kamwa, 2022. "Scoring Rules, Ballot Truncation, and the Truncation Paradox," Working Papers hal-03632662, HAL.
    5. Eric Kamwa, 2022. "Scoring rules, ballot truncation, and the truncation paradox," Public Choice, Springer, vol. 192(1), pages 79-97, July.
    6. Terzopoulou, Zoi & Endriss, Ulle, 2021. "The Borda class," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 31-40.
    7. Wu-Hsiung Huang, 2014. "Singularity and Arrow’s paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 671-706, March.
    8. Wesley H. Holliday & Eric Pacuit, 2020. "Arrow’s decisive coalitions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 463-505, March.
    9. Eric Kamwa, 2019. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Group Decision and Negotiation, Springer, vol. 28(3), pages 519-541, June.
    10. Thomas Ratliff & Donald Saari, 2014. "Complexities of electing diverse committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 55-71, June.
    11. Conal Duddy & Ashley Piggins & William Zwicker, 2016. "Aggregation of binary evaluations: a Borda-like approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 301-333, February.
    12. Shmuel Nitzan, 2010. "Demystifying the ‘metric approach to social compromise with the unanimity criterion’," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(1), pages 25-28, June.
    13. Eric Kamwa, 2018. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Working Papers hal-01786590, HAL.
    14. Pierre Dehez & Victor Ginsburgh, 2020. "Approval voting and Shapley ranking," Public Choice, Springer, vol. 184(3), pages 415-428, September.
    15. Peter Emerson, 2013. "The original Borda count and partial voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 353-358, February.
    16. Donald G. Saari, 2014. "A New Way to Analyze Paired Comparison Rules," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 647-655, August.
    17. Hulkower, Neal D., 2021. "Contre-degustation Olympiades du Vin According to Borda," Working Papers 321848, American Association of Wine Economists.
    18. Donald Saari, 2010. "Peter Emerson (ed): Designing an all-inclusive democracy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 331-335, July.
    19. Muhammad Mahajne & Shmuel Nitzan & Oscar Volij, 2013. "LEVEL r CONSENSUS AND STABLE SOCIAL CHOICE," Working Papers 1305, Ben-Gurion University of the Negev, Department of Economics.
    20. Wesley H. Holliday & Chase Norman & Eric Pacuit & Saam Zahedian, 2022. "Impossibility theorems involving weakenings of expansion consistency and resoluteness in voting," Papers 2208.06907, arXiv.org, revised Mar 2023.

    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:spr:sochwe:v:56:y:2021:i:1:d:10.1007_s00355-020-01274-y. 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.