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Mathematics - Applications | Proportional Representation

Proportional Representation

Apportionment Methods and Their Applications

Pukelsheim, Friedrich

2014, XXI, 234 p. 3 illus.

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  • With a foreword by Andrew Duff, MEP
  • A rigorous study of electoral systems in Europe
  • A detailed compendium of provable quantitative properties in representation systems
  • Examples of method intrinsic properties: seat biases, majorization relations, double proportionality, and many more
The book offers a rigorous description of the procedures that proportional representation systems use to translate vote counts into seat numbers. Since the methodological analysis is guided by practical needs, plenty of empirical instances are provided and reviewed to motivate the development, and to illustrate the results. Concrete examples, like the 2009 elections to the European Parliament in each of the 27 Member States and the 2013 election to the German Bundestag, are analyzed in full detail. The level of mathematical exposition, as well as the relation to political sciences and constitutional jurisprudence makes this book suitable for special graduate courses and seminars.

Content Level » Graduate

Keywords » apportionment methodology - electoral system design - proportional representation systems

Related subjects » Applications - Political Science - Social Sciences & Law

Table of contents 

Exposing Methods: The 2009 European Parliament Elections.- Imposing Constitutionality: The 2009 Bundestag Election.- From Reals to Integers: Rounding Functions, Rounding Rules.- Divisor Methods of Apportionment: Divide and Round.- Quota Methods of Apportionment: Divide and Rank.- Targeting the House Size: Discrepancy Distribution.- Favoring Some at the Expense of Others: Seat Biases.- Preferring Stronger Parties to Weaker Parties: Majorization.- Securing System Consistency: Coherence and Paradoxes.- Appraising Electoral Equality: Goodness-of-Fit Criteria.- Tracing Peculiarities: Vote Thresholds and Majority Clauses.- Truncating Seat Ranges: Minimum-Maximum Restrictions.- Proportionality and Personalization: BWG 2013.- Representing Districts and Parties: Double Proportionality.

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