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On the self-(in)stability of weighted majority rules

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  • Azrieli, Yaron
  • Kim, Semin

Abstract

A voting rule f is self-stable (Barberà and Jackson, 2004) if any alternative rule g does not have sufficient support in the society to replace f, where the decision between f and g is based on the rule f itself. While Barberà and Jackson focused on anonymous rules in which all agents have the same voting power, we consider here the larger class of weighted majority rules. Our main result is a characterization of self-stability in this setup, which shows that only few rules of a very particular form satisfy this criterion. This result provides a possible explanation for the tendency of societies to use more conservative rules when it comes to changing the voting rule. We discuss self-stability in this latter case, where a different rule F may be used to decide between f and g.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:gamebe:v:100:y:2016:i:c:p:376-389
    DOI: 10.1016/j.geb.2016.10.010
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    References listed on IDEAS

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    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. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-1819, November.
    3. Barbera, Salvador & Bevia, Carmen, 2002. "Self-Selection Consistent Functions," Journal of Economic Theory, Elsevier, vol. 105(2), pages 263-277, August.
    4. Yaron Azrieli & Semin Kim, 2014. "Pareto Efficiency And Weighted Majority Rules," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 1067-1088, November.
    5. Salvador Barbera & Matthew O. Jackson, 2006. "On the Weights of Nations: Assigning Voting Weights in a Heterogeneous Union," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 317-339, April.
    6. Kultti, Klaus & Miettinen, Paavo, 2007. "Stable set and voting rules," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 164-171, March.
    7. repec:cup:apsrev:v:63:y:1969:i:01:p:40-56_26 is not listed on IDEAS
    8. 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.
    9. 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.
    10. Semih Koray, 2000. "Self-Selective Social Choice Functions Verify Arrow and Gibbarad- Satterthwaite Theorems," Econometrica, Econometric Society, vol. 68(4), pages 981-996, July.
    11. Danilo Coelho, 2005. "Maximin choice of voting rules for committees," Economics of Governance, Springer, vol. 6(2), pages 159-175, July.
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    Cited by:

    1. Hermida-Rivera, Héctor, 2025. "Minimal stable voting rules," Games and Economic Behavior, Elsevier, vol. 153(C), pages 541-553.
    2. Jeong, Daeyoung & Kim, Semin, 2023. "Stable constitutions," Games and Economic Behavior, Elsevier, vol. 142(C), pages 794-811.
    3. Satoshi Nakada & Shmuel Nitzan & Takashi Ui, 2025. "Robust Voting under Uncertainty," Papers 2507.22655, arXiv.org.
    4. Daeyoung Jeong & Semin Kim, 2018. "Stable Constitutions," Working papers 2018rwp-139, Yonsei University, Yonsei Economics Research Institute.
    5. Semin Kim, 2023. "On the (Robust) Ex-post Stability of Constitutions," Working papers 2023rwp-212, Yonsei University, Yonsei Economics Research Institute.
    6. 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.
    7. Daeyoung Jeong & Semin Kim, 2017. "Interim Self-Stable Decision Rules," Working papers 2017rwp-108, Yonsei University, Yonsei Economics Research Institute.

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    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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