IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-02510491.html
   My bibliography  Save this paper

Constitutionally consistent voting rules over single-peaked domains

Author

Listed:
  • Mihir Bhattacharya

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

Constitutional consistency requires that the voting rule produce the same outcome at any vote profile as the one it produces at its induced vote profile for any given set of voting rules (or constitution) consisting of the voting rule itself. We consider this type of consistency in two voting models with single-peaked preferences, one with a finite set of alternatives and the other, when the set of alternatives is the interval [0, 1]. We show that cumulative-threshold rules are the only unanimous, anonymous and constitutionally consistent voting rules. These rules assign monotone decreasing (increasing) thresholds to each alternative and pick the minimum (maximum) alternative from the range of the vote profile that receives more cumulative votes (votes received by all the alternatives smaller (or greater) than itself) than the threshold assigned to it. This class of rules consists of the min, max and median rules. The addition of continuity leads to the characterization of k-median rules in the interval voting model.

Suggested Citation

  • Mihir Bhattacharya, 2019. "Constitutionally consistent voting rules over single-peaked domains," Post-Print hal-02510491, HAL.
    • Handle: RePEc:hal:journl:hal-02510491
    DOI: 10.1007/s00355-018-1145-1
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mihir Bhattacharya, 2016. "Multilevel multidimensional consistent aggregators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 839-861, April.
    2. Binmore, K. G., 1975. "An example in group preference," Journal of Economic Theory, Elsevier, vol. 10(3), pages 377-385, June.
    3. Kim C. Border & J. S. Jordan, 1983. "Straightforward Elections, Unanimity and Phantom Voters," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 153-170.
    4. Salvador Barbera & Matthew O. Jackson, 2004. "Choosing How to Choose: Self-Stable Majority Rules and Constitutions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 1011-1048.
    5. Manfred NERMUTH, 1991. "Two-Stage Discrete Aggregation," Vienna Economics Papers vie9103, University of Vienna, Department of Economics.
    6. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65(2), pages 135-135.
    7. Jean Lainé & Ali Ozkes & Remzi Sanver, 2016. "Hyper-stable social welfare functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 157-182, January.
    8. Semih Koray & Arkadii Slinko, 2008. "Self-selective social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 129-149, June.
    9. Jean Lainé & Ali Ozkes & Remzi Sanver, 2016. "Hyper-stable social welfare functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 157-182, January.
    10. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    11. Semih Koray, 2000. "Self-Selective Social Choice Functions Verify Arrow and Gibbarad- Satterthwaite Theorems," Econometrica, Econometric Society, vol. 68(4), pages 981-996, July.
    12. Chandrasekher, Madhav, 2015. "Dynamically consistent voting rules," Journal of Economic Theory, Elsevier, vol. 160(C), pages 175-187.
    13. Chambers, Christopher P., 2008. "Consistent representative democracy," Games and Economic Behavior, Elsevier, vol. 62(2), pages 348-363, March.
    14. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    15. Chambers, Christopher P., 2009. "An axiomatic theory of political representation," Journal of Economic Theory, Elsevier, vol. 144(1), pages 375-389, January.
    16. Semih Koray & Bulent Unel, 2003. "Characterization of self-selective social choice functions on the tops-only domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 495-507, June.
    17. Rubinstein, Ariel, 1980. "Stability of decision systems under majority rule," Journal of Economic Theory, Elsevier, vol. 23(2), pages 150-159, October.
    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. Mihir Bhattacharya, 2016. "Multilevel multidimensional consistent aggregators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 839-861, April.
    2. Jean Lainé & Ali Ozkes & Remzi Sanver, 2016. "Hyper-stable social welfare functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 157-182, January.
    3. Tobias Rachidi, 2020. "Optimal Voting Mechanisms on Generalized Single-Peaked Domains," CRC TR 224 Discussion Paper Series crctr224_2020_214, University of Bonn and University of Mannheim, Germany.
    4. Reffgen, Alexander, 2015. "Strategy-proof social choice on multiple and multi-dimensional single-peaked domains," Journal of Economic Theory, Elsevier, vol. 157(C), pages 349-383.
    5. Berga, Dolors & Serizawa, Shigehiro, 2000. "Maximal Domain for Strategy-Proof Rules with One Public Good," Journal of Economic Theory, Elsevier, vol. 90(1), pages 39-61, January.
    6. Bonifacio, Agustín G. & Massó, Jordi & Neme, Pablo, 2023. "Preference restrictions for simple and strategy-proof rules: Local and weakly single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    7. Chambers, Christopher P., 2008. "Consistent representative democracy," Games and Economic Behavior, Elsevier, vol. 62(2), pages 348-363, March.
    8. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
    9. Azrieli, Yaron & Kim, Semin, 2016. "On the self-(in)stability of weighted majority rules," Games and Economic Behavior, Elsevier, vol. 100(C), pages 376-389.
    10. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
    11. Salvador Barbera & Matthew Jackson, 1991. "A Characterization of Strategy-Proof Social Choice Functions for Economies with Pure Public Goods," Discussion Papers 964, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. John A. Weymark, 2008. "Strategy‐Proofness and the Tops‐Only Property," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(1), pages 7-26, February.
    13. Le Breton, Michel & Weymark, John A., 1999. "Strategy-proof social choice with continuous separable preferences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 47-85, August.
    14. Chatterji, Shurojit & Zeng, Huaxia, 2018. "On random social choice functions with the tops-only property," Games and Economic Behavior, Elsevier, vol. 109(C), pages 413-435.
    15. Mostapha Diss, 2015. "Strategic manipulability of self-selective social choice rules," Annals of Operations Research, Springer, vol. 229(1), pages 347-376, June.
    16. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2017. "Immunity to credible deviations from the truth," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 129-140.
    17. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2018. "Strategy-proof location of public facilities," Games and Economic Behavior, Elsevier, vol. 112(C), pages 21-48.
    18. Barbera, S. & Masso, J. & Serizawa, S., 1998. "Strategy-Proof Voting on Compact Ranges," Games and Economic Behavior, Elsevier, vol. 25(2), pages 272-291, November.
    19. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2016. "A characterization of single-peaked preferences via random social choice functions," Theoretical Economics, Econometric Society, vol. 11(2), May.
    20. Bonifacio, Agustín G. & Massó, Jordi, 2020. "On strategy-proofness and semilattice single-peakedness," Games and Economic Behavior, Elsevier, vol. 124(C), pages 219-238.

    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:hal:journl:hal-02510491. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.