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Securing System Consistency: Coherence and Paradoxes

In: Proportional Representation

Author

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  • Friedrich Pukelsheim

    (Universität Augsburg, Institut für Mathematik)

Abstract

This chapter assesses apportionment methods from an overall viewpoint as to whether vote weights and seat numbers always correspond in a fair manner. A new organizing principle turns out to be decisive: coherence. It demands that every solution for a general apportionment problem agrees with the solutions for all embedded subproblems. The Coherence Theorem states that an apportionment method is coherent if and only if it is compatible with a divisor method. The ground for the proof is prepared by showing that coherent methods are house size monotone and vote ratio monotone. In contrast, quota methods may produce non-monotonic results of a seemingly paradoxical nature.

Suggested Citation

  • Friedrich Pukelsheim, 2017. "Securing System Consistency: Coherence and Paradoxes," Springer Books, in: Proportional Representation, edition 2, chapter 0, pages 159-183, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-64707-4_9
    DOI: 10.1007/978-3-319-64707-4_9
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