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The whole and its parts: On the coherence theorem of Balinski and Young

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  • Palomares, Antonio
  • Pukelsheim, Friedrich
  • Ramírez, Victoriano

Abstract

A new proof of the Coherence Theorem of Balinski and Young is presented. The theorem elucidates the methods used to apportion parliamentary seats among political parties proportionately to their vote counts, or among geographical districts proportionately to their population figures. A proportional apportionment method is coherent when each seat apportionment among all claimants is such that every part of it is a valid solution for the subset of claimants concerned. The Coherence Theorem states that every coherent apportionment method is compatible with a divisor method.

Suggested Citation

  • Palomares, Antonio & Pukelsheim, Friedrich & Ramírez, Victoriano, 2016. "The whole and its parts: On the coherence theorem of Balinski and Young," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 11-19.
    • Handle: RePEc:eee:matsoc:v:83:y:2016:i:c:p:11-19
    DOI: 10.1016/j.mathsocsci.2016.06.001
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    References listed on IDEAS

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    1. Balinski, Michel & Ramirez, Victoriano, 1999. "Parametric methods of apportionment, rounding and production," Mathematical Social Sciences, Elsevier, vol. 37(2), pages 107-122, March.
    2. Michel Balinski & Victoriano Ramirez, 2014. "Parametric vs. divisor methods of apportionment," Annals of Operations Research, Springer, vol. 215(1), pages 39-48, April.
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    Cited by:

    1. Balázs R Sziklai & Károly Héberger, 2020. "Apportionment and districting by Sum of Ranking Differences," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-20, March.

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