Analytical theory of democracy. History, mathematics and applications. Vol. 1 and Vol. 2 (Q2308887)

Mathematics plays many crucial roles in various areas of science and humanities. Thus, it is not unusual to think that mathematics may have important roles in democracy of a country. But, there is hardly any book available describing history of democracy, theory, and applications of mathematics in democracy except the book ``Analytical theory of democracy. History, Mathematics and Applications'' (volumes 1 and 2) by Andranik Tangian. The author considered both the historical and theoretical foundations of democracy with equal importance in this book. The book consists of two volumes. In volume 1, the author focused on theoretical foundations of democracy. Part I of volume 1 consists of five chapters. These chapters discuss history of democracy from the perspective of Ancient Athens, the Roman Republic, medieval republics in Italy, the Age of Enlightenment, and modernity. All these chapters contain non-mathematical foundations of democracy. In part II of volume 1, there are six chapters. These six chapters deal with modelling direct democracy of the Athenian type, relationships between democracy and dictatorship as in the Ancient Rome, etc. These chapters laid foundations for democracy from the perspective of mathematics. Volume II consists of applications in public opinion poll, the 2013 German Bundestag election, the 2016 Third Vote experiment, the 2017 Third Vote experiment, the 2018 Third Vote experiment. Moreover, applications include multi criteria decision makings for choosing a library name and a place for an outing, stock exchange predictions, etc. Thus, the book ``Analytical theory of democracy. History, Mathematics and Applications'' is one of the outstanding books in the common area of mathematics of democracy, voting theory, and social choice theory. As a reviewer of this book (volumes 1 and 2), I found this book of Professor Tangian very important from the view point of researchers, who want to do research on historical and mathematical ideas related to democracy, social choice theory, and voting theory. Like any other book, this book (volumes 1 and 2) has a few typographical errors. It is to be expected that these typographical errors will be corrected in next edition of this book. Overall, 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.