In this book, different quantitative approaches to the study of electoral systems have been developed: game-theoretic, decision-theoretic, statistical, probabilistic, combinatorial, geometric, and optimization ones. All the authors are prominent scholars from these disciplines. Quantitative approaches offer a powerful tool to detect inconsistencies or poor performance in actual systems. Applications to concrete settings such as EU, American Congress, regional, and committee voting are discussed.

In this book, different quantitative approaches to the study of electoral systems have been developed: game-theoretic, decision-theoretic, statistical, probabilistic, combinatorial, geometric, and optimization ones. All the authors are prominent scholars from these disciplines. Quantitative approaches offer a powerful tool to detect inconsistencies or poor performance in actual systems. Applications to concrete settings such as EU, American Congress, regional, and committee voting are discussed.

Wie funktioniert die Wahl des Deutschen Bundestags? Wie errechnen sich Sitze in Schweizer Kantonsparlamenten? Kann man Stimmzahlen uberhaupt fair auf Mandate umrechnen? Sitzzuteilungsmethoden und ihre wichtigsten formalen Eigenschaften sind das Thema dieses Kompaktkurses. Verhaltniswahlsysteme und ihre Methoden, Stimmenzahlen am Ende einer demokratischen Wahl in Mandate zu verrechnen, werden hier ausfuhrlich und anschaulich behandelt. Zahlreiche Beispiele mit aktuellen Wahlergebnissen sichern dabei Realitatsnahe. Verfassungsrechtliche und politikwissenschaftliche Anspruche, denen Sitzzuteilungsmethoden gerecht werden mussen, werden ebenfalls erlautert und heben den interdisziplinaren Charakter der Fragestellung hervor.

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.

Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimization problem. Using tools from convex analysis, the problem is solved generally for a wide class of optimality criteria such as D-, A-, or E-optimality. The book then offers a complementary approach that calls for the study of the symmetry properties of the design problem, exploiting such notions as matrix majorization and the Kiefer matrix ordering. The results are illustrated with optimal designs for polynomial fit models, Bayes designs, balanced incomplete block designs, exchangeable designs on the cube, rotatable designs on the sphere, and many other examples. Since the book's initial publication in 1993, readers have used its methods to derive optimal designs on the circle, optimal mixture designs, and optimal designs in other statistical models. Using local linearization techniques, the methods described in the book prove useful even for nonlinear cases, in identifying practical designs of experiments.