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Measuring Majority Tyranny: Axiomatic Approach

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  • 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
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    References listed on IDEAS

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    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, December.
    4. Steven J. Brams & D. Marc Kilgour, 2001. "Fallback Bargaining," Group Decision and Negotiation, Springer, vol. 10(4), pages 287-316, July.
    5. 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.
    6. 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.
    7. Baharad, Eyal & Nitzan, Shmuel, 2002. "Ameliorating Majority Decisiveness through Expression of Preference Intensity," American Political Science Review, Cambridge University Press, vol. 96(4), pages 745-754, December.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
    13. Fishburn, Peter C., 1974. "Paradoxes of Voting," American Political Science Review, Cambridge University Press, vol. 68(2), pages 537-546, June.
    14. 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.
    15. Nicolaus Tideman, 1995. "The Single Transferable Vote," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 27-38, Winter.
    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.
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    Cited by:

    1. Mostapha Diss & Clinton Gubong Gassi & Issofa Moyouwou, 2022. "Social acceptability and the majoritarian compromise rule," Working Papers 2022-05, CRESE.

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    More about this item

    Keywords

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

    JEL classification:

    • Z - Other Special Topics

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