Tangian A. Mathematical Theory of Democracy

Springer, 2014. — 629 p.This book consists of three main parts: ‘History’, ‘Theory’ and ‘Applications’. The fourth part, ‘Appendix’, contains computational formulas and statistical tables.
Part I, ‘History’, contains five chapters that focus on important steps in the development of democracy and its philosophical comprehension by political thinkers. These chapters are devoted to Ancient Athens, the Roman Republic, medieval republics in Italy, the Age of Enlightenment, and the modernity up to the present. Each chapter outlines the contemporary mathematical findings relevant to democracy.
Part II, ‘Theory’, also contains five chapters that in a sense mirror the historical ones. They deal with modeling direct democracy of Athenian type, analyzing the relationships between democracy and dictatorship like that in Rome, revealing the bottlenecks of republican representative democracy, developing a probabilistic approach to representatives that dates back to the Age of Enlightenment, and discussing a method to improve the performance of representative democracy, responding to the current political agenda. For illustration, the method discussed is applied to hypothetically redistribute the seats in the German Bundestag, achieving a considerable gain in its representativeness.
Four chapters of Part III, ‘Applications’, among other things, elaborate on the idea that from the mathematical standpoint, neither the ‘society’ nor ‘representatives’ are necessarily human, so some objects can represent the behavior of other objects. In particular, American stock prices ‘represent in advance’ the fluctuations of German stock prices, so that American ‘representatives’ of German stocks can be used for financial predictions. Similarly, the traffic situations at one street’s intersections ‘represent in advance’ the situations at other intersections, which can be used to anticipate traffic jams and prevent them by switching on the ‘green wave’ of traffic lights in the appropriate direction.
The non-societal applications demonstrate that the mathematical theory of democracy is based on quite general principles beyond the societal specificity. Consequently, democracy itself can be regarded as a rather universal approach to social organization over and above national, cultural, ethnical or religious particularities.History.
Athenian Democracy.
Echoes of Democracy in Ancient Rome.
Revival of Democracy in Italian Medieval 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.