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The Fate of the Square Root Law for Correlated Voting

In: Voting Power and Procedures

Author

Listed:
  • Werner Kirsch

    (FernUniversität in Hagen)

  • Jessica Langner

    (FernUniversität in Hagen)

Abstract
We consider two-tier voting systems and try to determine optimal weights for a fair representation in such systems. A prominent example of such a voting system is the Council of Ministers of the European Union. Under the assumption of independence of the voters, the square root law gives a fair distribution of power (based on the Penrose–Banzhaf power index) and a fair distribution of weights (based on the concept of the majority deficit), both given in the book by Felsenthal and Machover. In this paper, special emphasis is given to the case of correlated voters. The cooperative behaviour of the voters is modeled by suitable adoptions of spin systems known from statistical physics. Under certain assumptions we are able to compute the optimal weights as well as the average deviation of the council’s vote from the public vote which we call the democracy deficit.

Suggested Citation

  • Werner Kirsch & Jessica Langner, 2014. "The Fate of the Square Root Law for Correlated Voting," Studies in Choice and Welfare, in: Rudolf Fara & Dennis Leech & Maurice Salles (ed.), Voting Power and Procedures, edition 127, pages 147-158, Springer.
    • Handle: RePEc:spr:stcchp:978-3-319-05158-1_9
    DOI: 10.1007/978-3-319-05158-1_9
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    Cited by:

    1. Le Breton, Michel & Lepelley, Dominique & Macé, Antonin & Merlin, Vincent, 2017. "Le mécanisme optimal de vote au sein du conseil des représentants d’un système fédéral," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 203-248, Mars-Juin.
    2. Kirsch, Werner & Toth, Gabor, 2022. "Collective bias models in two-tier voting systems and the democracy deficit," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 118-137.
    3. Grimmett, Geoffrey R., 2019. "On influence and compromise in two-tier voting systems," Mathematical Social Sciences, Elsevier, vol. 100(C), pages 35-45.

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