IDEAS home Printed from https://ideas.repec.org/p/hig/wpaper/194-ec-2018.html
   My bibliography  Save this paper

Measuring Majority Tyranny: Axiomatic Approach

Author

Listed:
  • Aleksei Yu. Kondratev

    () (National Research University Higher School of Economics)

  • Alexander S. Nesterov

    () (National Research University Higher School of Economics)

Abstract

We study voting rules with respect to how they allow or limit a majority to dominate minorities. For this purpose we propose a novel quantitative criterion for voting rules: the quali ed mutual majority criterion (q; k)-MM. For a xed total number of m candidates, a voting rule satis es (q; k)-MM if whenever some k candidates receive top k ranks in an arbitrary order from a majority that consists of more than q 2 (0; 1) of voters, the voting rule selects one of these k candidates. The standard majority criterion is equivalent to (1=2; 1)-MM. The standard mutual majority criterion (MM) is equivalent to (1=2; k)-MM, where k is arbitrary. We nd the bounds on the size of the majority q for several important voting rules, including the plurality rule, the plurality with runo rule, Black's rule, Condorcet least reversal rule, Dodgson's rule, Simpson's rule, Young's rule and monotonic scoring rules; for most of these rules we show that the bound is tight.

Suggested Citation

  • Aleksei Yu. Kondratev & Alexander S. Nesterov, 2018. "Measuring Majority Tyranny: Axiomatic Approach," HSE Working papers WP BRP 194/EC/2018, National Research University Higher School of Economics.
  • Handle: RePEc:hig:wpaper:194/ec/2018
    as

    Download full text from publisher

    File URL: https://wp.hse.ru/data/2018/07/05/1153007617/194EC2018.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    2. Young, H. P., 1977. "Extending Condorcet's rule," Journal of Economic Theory, Elsevier, vol. 16(2), pages 335-353, December.
    3. Nitzan,Shmuel, 2009. "Collective Preference and Choice," Cambridge Books, Cambridge University Press, number 9780521722131, August.
    4. repec:spr:grdene:v:10:y:2001:i:4:d:10.1023_a:1011252808608 is not listed on IDEAS
    5. Ferejohn, John A. & Grether, David M., 1974. "On a class of rational social decision procedures," Journal of Economic Theory, Elsevier, vol. 8(4), pages 471-482, August.
    6. Eyal Baharad & Shmuel Nitzan, 2007. "The Costs of Implementing the Majority Principle: The Golden Voting Rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 69-84, April.
    7. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
    8. repec:cup:apsrev:v:68:y:1974:i:02:p:537-546_11 is not listed on IDEAS
    9. Bilge Yilmaz & Murat R. Sertel, 1999. "The majoritarian compromise is majoritarian-optimal and subgame-perfect implementable," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 615-627.
    10. Paul B. Simpson, 1969. "On Defining Areas of Voter Choice: Professor Tullock on Stable Voting," The Quarterly Journal of Economics, Oxford University Press, vol. 83(3), pages 478-490.
    11. Markus Schulze, 2011. "A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(2), pages 267-303, February.
    12. repec:cup:apsrev:v:96:y:2002:i:04:p:745-754_00 is not listed on IDEAS
    13. Nicolaus Tideman, 1995. "The Single Transferable Vote," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 27-38, Winter.
    14. Steven J. Brams & D. Marc Kilgour, 2001. "Fallback Bargaining," Group Decision and Negotiation, Springer, vol. 10(4), pages 287-316, July.
    15. Stein, William E. & Mizzi, Philip J. & Pfaffenberger, Roger C., 1994. "A stochastic dominance analysis of ranked voting systems with scoring," European Journal of Operational Research, Elsevier, vol. 74(1), pages 78-85, April.
    16. I. Good, 1971. "A note on condorcet sets," Public Choice, Springer, vol. 10(1), pages 97-101, March.
    17. J. Craven, 1971. "Majority Voting and Social Choice," Review of Economic Studies, Oxford University Press, vol. 38(2), pages 265-267.
    18. Donald G. Saari, 2000. "Mathematical structure of voting paradoxes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(1), pages 55-102.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Majority tyranny; single winner elections; plurality voting rule; plurality with runo ; instant runo voting; mutual majority criterion; voting rules;

    JEL classification:

    • Z - Other Special Topics

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hig:wpaper:194/ec/2018. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamil Abdulaev) or (Victoria Elkina). General contact details of provider: http://edirc.repec.org/data/hsecoru.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.