IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2506.15323.html

Minimal Stable Voting Rules

Author

Listed:
  • H'ector Hermida-Rivera

Abstract

In this paper, I characterize minimal stable voting rules and minimal self-stable constitutions (i.e., pairs of voting rules) for societies in which only power matters. To do so, I first let players' preference profiles over voting rules satisfy four natural axioms commonly used in the analysis of power: non-dominance, anonymity, null player and swing player. I then provide simple notions of minimal stability and minimal self-stability, and show that the families of minimal stable voting rules and minimal self-stable constitutions are fairly small. Finally, I conclude that political parties have evolved to ensure the minimal self-stability of otherwise not minimal self-stable constitutions.

Suggested Citation

  • H'ector Hermida-Rivera, 2025. "Minimal Stable Voting Rules," Papers 2506.15323, arXiv.org.
    • Handle: RePEc:arx:papers:2506.15323
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2506.15323
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Klaus Kultti & Paavo Miettinen, 2009. "Stability of Constitutions," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(6), pages 891-896, December.
    2. Roth, Alvin E, 1977. "The Shapley Value as a von Neumann-Morgenstern Utility," Econometrica, Econometric Society, vol. 45(3), pages 657-664, April.
    3. Kultti, Klaus & Miettinen, Paavo, 2007. "Stable set and voting rules," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 164-171, March.
    4. Tijs, S., 1981. "Bounds for the core of a game and the t-value," Other publications TiSEM ebc650eb-f25e-4802-ba0b-2, Tilburg University, School of Economics and Management.
    5. Roth, Alvin E., 1977. "Utility functions for simple games," Journal of Economic Theory, Elsevier, vol. 16(2), pages 481-489, December.
    6. 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.
    7. Voigt, Stefan, 1997. "Positive Constitutional Economics: A Survey," Public Choice, Springer, vol. 90(1-4), pages 11-53, March.
    8. repec:cup:apsrev:v:63:y:1969:i:01:p:40-56_26 is not listed on IDEAS
    9. Lagunoff, Roger, 2009. "Dynamic stability and reform of political institutions," Games and Economic Behavior, Elsevier, vol. 67(2), pages 569-583, November.
    10. 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.
    11. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Daeyoung Jeong & Semin Kim, 2024. "On the (robust) ex post stability of constitutions," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 26(4), August.
    13. Cesarino Bertini & Josep Freixas & Gianfranco Gambarelli & Izabella Stach, 2013. "Comparing Power Indices," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-19.
    14. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    15. Stefan Voigt, 2011. "Positive constitutional economics II—a survey of recent developments," Public Choice, Springer, vol. 146(1), pages 205-256, January.
    16. Robert J. Weber, 1979. "Subjectivity in the Valuation of Games," Cowles Foundation Discussion Papers 515, Cowles Foundation for Research in Economics, Yale University.
    17. Danilo Coelho, 2005. "Maximin choice of voting rules for committees," Economics of Governance, Springer, vol. 6(2), pages 159-175, July.
    18. Cesarino Bertini & Gianfranco Gambarelli & Izabella Stach, 2008. "A Public Help Index," Springer Books, in: Matthew Braham & Frank Steffen (ed.), Power, Freedom, and Voting, chapter 5, pages 83-98, Springer.
    19. Jeong, Daeyoung & Kim, Semin, 2023. "Stable constitutions," Games and Economic Behavior, Elsevier, vol. 142(C), pages 794-811.
    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. Héctor Hermida‐Rivera & Toygar T. Kerman, 2025. "Binary Self‐Selective Voting Rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 27(3), June.
    2. Jeong, Daeyoung & Kim, Semin, 2023. "Stable constitutions," Games and Economic Behavior, Elsevier, vol. 142(C), pages 794-811.
    3. 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.
    4. van den Brink, René & Rusinowska, Agnieszka, 2022. "The degree measure as utility function over positions in graphs and digraphs," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1033-1044.
    5. Federico Valenciano & Annick Laruelle, 2003. "Potential, Value And Probability," Working Papers. Serie AD 2003-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    6. Maria Montero & Martin Sefton & Ping Zhang, 2008. "Enlargement and the balance of power: an experimental study," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(1), pages 69-87, January.
    7. van den Brink, René & Rusinowska, Agnieszka, 2024. "Degree centrality, von Neumann–Morgenstern expected utility and externalities in networks," European Journal of Operational Research, Elsevier, vol. 319(2), pages 669-677.
    8. Frimpong Boamah, Emmanuel, 2018. "Constitutional economics of Ghana’s decentralization," World Development, Elsevier, vol. 110(C), pages 256-267.
    9. Sebastian Garmann, 2018. "God save the queen, god save us all? Monarchies and institutional quality," Scottish Journal of Political Economy, Scottish Economic Society, vol. 65(2), pages 186-204, May.
    10. Omer Edhan, 2012. "Representations Of Positive Projections On Lipschitz Vector," Discussion Paper Series dp624, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    11. Randall G. Holcombe, 2020. "James M. Buchanan’s constitutional project: past and future," Public Choice, Springer, vol. 183(3), pages 371-387, June.
    12. Gerichhausen, M. & Berkhout, E.D. & Hamers, H.J.M. & Manyong, V.M., 2008. "A Game Theoretic Approach to Analyse Cooperation between Rural Households in Northern Nigeria," Discussion Paper 2008-62, Tilburg University, Center for Economic Research.
    13. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    14. Lars P. Feld & Ekkehard A. Köhler, 2023. "Standing on the shoulders of giants or science? Lessons from ordoliberalism," Public Choice, Springer, vol. 195(3), pages 197-211, June.
    15. J. Keith Murnighan & Alvin E. Roth, 1978. "Large Group Bargaining in a Characteristic Function Game," Journal of Conflict Resolution, Peace Science Society (International), vol. 22(2), pages 299-317, June.
    16. Llerena, Francesc & Mauri, Llúcia, 2017. "On the existence of the Dutta–Ray’s egalitarian solution," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 92-99.
    17. Gerichhausen, M. & Berkhout, E.D. & Hamers, H.J.M. & Manyong, V.M., 2009. "A quantitative framework to analyse cooperation between rural households," Agricultural Systems, Elsevier, vol. 101(3), pages 173-185, July.
    18. Lenger Alexander & Goldschmidt Nils, 2011. "Ordnungsökonomik als angewandte Wissenschaft. Zur notwendigen Zusammenführung von Theorie und Praxis / Constitutional Economics as an Applied Social Science. About the Essential Combination of Theory and Practice On the," ORDO. Jahrbuch für die Ordnung von Wirtschaft und Gesellschaft, De Gruyter, vol. 62(1), pages 343-364, January.
    19. Pongou, Roland & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Power theories for multi-choice organizations and political rules: Rank-order equivalence," Operations Research Perspectives, Elsevier, vol. 1(1), pages 42-49.
    20. Takahiro Suzuki & Stefano Moretti & Michele Aleandri, 2025. "Ranking alternatives from opinions on criteria," Papers 2504.06676, arXiv.org.

    More about this item

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

    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:arx:papers:2506.15323. 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: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    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.