Securing System Consistency: Coherence and Paradoxes

Friedrich Pukelsheim
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Friedrich Pukelsheim: Universität Augsburg, Institut für Mathematik

Chapter Chapter 9 in Proportional Representation, 2017, pp 159-183 from Springer

Abstract: 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.

Date: 2017
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DOI: 10.1007/978-3-319-64707-4_9

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