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Liberal political equality does not imply proportional representation

Author

Listed:
  • Stefan Wintein

    (Erasmus University Rotterdam)

  • Conrad Heilmann

    (Erasmus University Rotterdam)

Abstract

In their article ‘Liberal political equality implies proportional representation’, which was published in Social Choice and Welfare 33(4):617–627 in 2009, Eliora van der Hout and Anthony J. McGann claim that any seat-allocation rule that satisfies certain ‘Liberal axioms’ produces results essentially equivalent to proportional representation. We show that their claim and its proof are wanting. Firstly, the Liberal axioms are only defined for seat-allocation rules that satisfy a further axiom, which we call Independence of Vote Realization (IVR). Secondly, the proportional rule is the only anonymous seat-allocation rule that satisfies IVR. Thirdly, the claim’s proof raises the suspicion that reformulating the Liberal axioms in order to save the claim won’t work. Fourthly, we vindicate this suspicion by providing a seat-allocation rule which satisfies reformulated Liberal axioms but which fails to produce results essentially equivalent to proportional representation. Thus, the attention that their claim received in the literature on normative democratic theory notwithstanding, van der Hout and McGann have not established that liberal political equality implies proportional representation.

Suggested Citation

  • Stefan Wintein & Conrad Heilmann, 2022. "Liberal political equality does not imply proportional representation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(1), pages 63-91, July.
    • Handle: RePEc:spr:sochwe:v:59:y:2022:i:1:d:10.1007_s00355-021-01385-0
    DOI: 10.1007/s00355-021-01385-0
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    References listed on IDEAS

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    1. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
    2. Eliora Hout & Anthony McGann, 2009. "Liberal political equality implies proportional representation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(4), pages 617-627, November.
    3. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
    4. Van der Hout, Eliora & McGann, Anthony J., 2009. "Proportional Representation Within the Limits of Liberalism Alone," British Journal of Political Science, Cambridge University Press, vol. 39(4), pages 735-754, October.
    5. Eerik Lagerspetz, 2016. "Social Choice and Democratic Values," Studies in Choice and Welfare, Springer, edition 1, number 978-3-319-23261-4, June.
    6. Moulin, Herve, 1985. "Egalitarianism and Utilitarianism in Quasi-linear Bargaining," Econometrica, Econometric Society, vol. 53(1), pages 49-67, January.
    7. Robert E. Goodin & Christian List, 2006. "A Conditional Defense of Plurality Rule: Generalizing May's Theorem in a Restricted Informational Environment," American Journal of Political Science, John Wiley & Sons, vol. 50(4), pages 940-949, October.
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