© 2020

Analytical Theory of Democracy

History, Mathematics and Applications


Part of the Studies in Choice and Welfare book series (WELFARE)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. History

    1. Front Matter
      Pages 1-2
    2. Andranik Tangian
      Pages 3-43
    3. Andranik Tangian
      Pages 45-66
    4. Andranik Tangian
      Pages 175-260
  3. Mathematics

    1. Front Matter
      Pages 261-262
    2. Andranik Tangian
      Pages 263-315
    3. Andranik Tangian
      Pages 317-351
    4. Andranik Tangian
      Pages 353-403
    5. Andranik Tangian
      Pages 447-497
    6. Andranik Tangian
      Pages 499-508
  4. Applications

    1. Front Matter
      Pages 509-510
    2. Andranik Tangian
      Pages 511-526
    3. Andranik Tangian
      Pages 527-579
    4. Andranik Tangian
      Pages 581-608
    5. Andranik Tangian
      Pages 609-653

About this book


This book operationalizes the idea of political representation, which is fundamental to modern democracies. Both individual representatives and representative bodies are evaluated using the indices of popularity (the average percentage of the population whose opinion is represented on topical policy issues) and universality (the percentage of issues for which the prevailing public opinion is represented). Viewed as objective functions, these indices can aid in the search for optimal representatives and representative bodies. By replacing the consistency analysis of the social choice axioms with the calculation of the best compromises, the paradoxes of social choice, such as those of Condorcet and Arrow, can be overcome. These indices also form the core of an alternative election method that is aimed at enhancing policy representation — a recent concept of political representation, which is not supported by the conventional voting systems shaped during the American and French Revolutions. This method is tested in a series of election experiments that focus on implementation details. In addition, non-societal applications such as MCDM, finance or traffic control are considered, where the objects that reflect the properties or behavior of other objects are regarded as their “representatives.” Given its scope, the book will appeal to political scientists, economists and operations researchers, as well as to politicians interested in improving democratic performance and electoral system design.


Arrow's Paradox Condorcet's Paradox Representative Democracy Representativeness Social Choice Analytical Theory of Democracy Mathematics and Democracy Policy Representation Election methods

Authors and affiliations

  1. 1.Karlsruhe Institute of TechnologyDüsseldorfGermany

About the authors

Andranik Tangian is Professor at the Karlsruhe Institute of Technology, 
Institute of Economics, Germany.

Bibliographic information

Industry Sectors
Finance, Business & Banking


“It is a product of profound, multi-disciplinary scholarship that will no doubt benefit many a cohort of future students and instructors of welfare economics, economic policy, political science, constitutional law and political philosophy.” (Hannu Nurmi, Journal of Economics, Vol. 130, 2020)