Proportional representation : apportionment methods and their applications / Friedrich Pukelsheim with a forword by Andrew Duff MEP.

Includes bibliographical references and index.

1. Exposing methods: the 2000 European Parliament elections -- 2. Imposing constitutionality: the 2009 Bundestag election -- 3. From reals to integers: rounding functions, rounding rules -- 4. Divisor methods of apportionment: divide and round -- 5. Quota methods of apportionment: divide and rank -- 6. Targeting the house size: discrepancy distribution -- 7. Favoring some at the expense of others: seat blases -- 8. Preferring stronger parties to weaker parties: majorization -- 9. Securing system consistency: coherence and paradoxes -- 10. Appraising electoral equality: goodness-of-fit criteria -- 11. Tracing peculiarities: vote thresholds and majority clauses -- 12. Truncating seat ranges: minimum-maximum restrictions -- 13. Proportionality and personalization: BWG 2013 -- 14. Representing districts and parties: double proportionality.

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.