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.

The C.I.M.E. Summer School at Como in 1986 was the first in that series on the subject of combinatorial optimization. Situated between combinatorics, computer science and operations research, the subject draws on a variety of mathematical methods to deal with problems motivated by real-life applications. Recent research has focussed on the connections to theoretical computer science, in particular to computational complexity and algorithmic issues. The Summer School's activity centered on the 4 main lecture courses, the notes of which are included in this volume:

This monograph offers a systematic quantitative approach to the analysis, evaluation, and design of electoral systems. Today, electoral reform is of concern to newborn democracies as well as many old ones. The authors use mathematical models and automatic procedures, when possible, to solve some of the problems that arise in the comparison of existing systems as well as in the construction of new ones. One distinctive feature of the book is the emphasis on single- and multiple-criteria optimization methods. This powerful tool kit will help political researchers evaluate and choose an appropriate electoral system. A general formal model is included as well as a coding system to describe, identify, and classify electoral systems. Evaluation criteria and the corresponding performance indicators are discussed. A treatment of electoral formulas as algorithms to minimize actual cost functions or disproportionality indexes is also included. Neutral automatic procedures for political districting are presented, and the process of electoral reform is analyzed from historical and political points of view.