Analytical Theory of Democracy

1. Front Matter

   Pages i-xxv

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2. History

   1. Front Matter

      Pages 1-2

      PDF

   2. Athenian Democracy

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      Pages 3-43

   3. Echoes of Democracy in Ancient Rome

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      Pages 45-66

   4. Revival of Democracy in Italian Medieval City-Republics

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      Pages 67-106

   5. Enlightenment and the End of Traditional Democracy

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      Pages 107-173

   6. Modernity and Schism in Understanding Democracy

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      Pages 175-260

3. Mathematics

   1. Front Matter

      Pages 261-262

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   2. Direct Democracy

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      Pages 263-315

   3. Dictatorship and Democracy

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      Pages 317-351

   4. Representative Democracy

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      Pages 353-403

   5. Policy Representation Across the Political Spectrum

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      Pages 405-446

   6. Election Method to Enhance Policy Representation

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      Pages 447-497

   7. Concluding Discussion

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      Pages 499-508

4. Applications

   1. Front Matter

      Pages 509-510

      PDF

   2. Simple Applications

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      Pages 511-526

   3. Analysis of the 2013 German Bundestag Election

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      Pages 527-579

   4. Constructing the 2013 German Political Spectrum

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      Pages 581-608

   5. The 2016 Third Vote Experiment: Heuristic Test

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      Pages 609-653

   6. The 2017 Third Vote Experiment: Choice of Questions

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      Pages 655-691

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
• democracy

“I strongly recommend this book to mathematicians along with social scientists, who want to do research in common domain of democracy, social choice theory, voting theory, and mathematics.” (Santanu Acharjee, zbMATH 1511.91001, 2023)

“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)

• Karlsruhe Institute of Technology, Düsseldorf, Germany

  Andranik Tangian

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

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