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  • © 2017

Proportional Representation

Apportionment Methods and Their Applications

  • 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

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xxvii
  2. Divisor Methods of Apportionment: Divide and Round

    • Friedrich Pukelsheim
    Pages 71-93
  3. Quota Methods of Apportionment: Divide and Rank

    • Friedrich Pukelsheim
    Pages 95-105
  4. Targeting the House Size: Discrepancy Distribution

    • Friedrich Pukelsheim
    Pages 107-125
  5. Favoring Some at the Expense of Others: Seat Biases

    • Friedrich Pukelsheim
    Pages 127-147
  6. Securing System Consistency: Coherence and Paradoxes

    • Friedrich Pukelsheim
    Pages 159-183
  7. Appraising Electoral Equality: Goodness-of-Fit Criteria

    • Friedrich Pukelsheim
    Pages 185-205
  8. Truncating Seat Ranges: Minimum-Maximum Restrictions

    • Friedrich Pukelsheim
    Pages 225-245
  9. Proportionality and Personalization: BWG 2013

    • Friedrich Pukelsheim
    Pages 247-257
  10. Double-Proportional Divisor Methods: Technicalities

    • Friedrich Pukelsheim
    Pages 275-295
  11. Biographical Digest

    • Friedrich Pukelsheim
    Pages 297-318
  12. Back Matter

    Pages 319-342

About this book

The book offers an in-depth study of the translation of vote counts into seat numbers in proportional representation systems  – an approach guided by practical needs. It also provides plenty of empirical instances illustrating the results. It analyzes in detail the 2014 elections to the European Parliament in the 28 member states, as well as the 2009 and 2013 elections to the German Bundestag. This second edition is a complete revision and expanded version of the first edition published in 2014, and many empirical election results that serve as examples have been updated. Further, a final chapter has been added assembling biographical sketches and authoritative quotes from individuals who pioneered the development of apportionment methodology. The mathematical exposition and the interrelations with political science and constitutional jurisprudence make this an apt resource for interdisciplinary courses and seminars on electoral systems and apportionment methods.

Authors and Affiliations

  • Institut für Mathematik, Universität Augsburg, Augsburg, Germany

    Friedrich Pukelsheim

About the author

Friedrich Pukelsheim is professor emeritus of University of Augsburg, where he held the Chair for Stochastics and its Applications from 1983 to 2014. The book grew out of interdisciplinary courses and seminars on electoral systems and apportionment methods conducted during many years in Augsburg and at other academic institutions.  
Pukelsheim has published extensively on apportionment issues in journals of mathematics, statistics, political sciences, state law, and history. He has testified as an expert witness before legal and political bodies, including the European Parliament, the German Bundestag, and several German State Diets and Swiss Canton Parliaments.  


Bibliographic Information

Buy it now

Buying options

eBook USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access