Mathematical Theory of Democracy

Dr. Dr. Andranik Tangian is head of referat `Policy modeling’ of the Institute for Economic and Social Research (WSI) in the Hans-Böckler-Foundation, Düsseldorf, and Professor of the Karlsruhe Institute of Technology

From the reviews:“This book is much more technical and goes into more theoretical depth, and … it is worth seeking out if you are looking for this type of treatment. … Tangian has managed to write about an incredibly wide range of topics in great mathematical, historical, and philosophical depth, and yet the book is very readable. … reader who wishes to dedicate the required time and energy will learn quite a bit about Democracy, its history, its limitations, and its strengths.” (Darren Glass, MAA Reviews, February, 2014)“The book consists of three parts: history, theory and applications. … Andranik Tangian has written an impressive volume, not only in size, but particularly in terms of the fields covered. The author’s erudition is remarkable. … The historical part of the book is suitable for independent study … . Parts two and three … are suitable for advanced doctoral courses in welfare economics, political science and applied mathematics.” (Hannu Nurmi, Journal of Economics, Vol. 111, 2014)“The author provides a novel viewpoint, engaging analyses in a stimulating historical context, and interesting new methods and suggestions which certainly have the strong merit of being oriented towards practical concerns. … overall, this is a well-written engaging book offering new ideas which are certainly worth considering when attempting practical reforms to modern-day democratic institutions and is well worth reading.” (Swapan Das Gupta, zbMATH, Vol. 1283, 2014)

• History: Athenian Democracy.- Echoes of Democracy in Ancient Rome.- Revival of Democracy in Italian Mediaval City-Republics.- Enlightenment and the End of Traditional Democracy.- Modernity and Schism in Understanding Democracy.- Theory: Direct Democracy.- Dictatorship and Democracy.- Representative Democracy.- Statistically Testing the Representative Capacity.- Concluding Discussion: Bridging Representative and Direct Democracies.- Applications: Simple Applications.- Application to Collective Multicriteria Decisions.- Application to Stock Exchange Predictions.- Application to Traffic Control.- Appendix: Computational Formulas.- Probabilities of Unequal Choices by Vote and by Candidate Scores.- Statistical Significance of Representative Capacity.