Tangian, Andranik: Mathematical Theory of Democracy. Studies in Social Choice and Welfare

A doctorate in one—albeit particularly prestigious—of the institutes of the USSR Academy of Sciences is an unlikely background for a democratic theorist. Yet, it is with this background that Andranik Tangian, now a resident of Germany, has taken up the task of writing a comprehensive treatise on the development of democratic thinking from its early beginnings ca. 500 BC to the modern days. Tangian’s is not the first attempt to cover the entire time span of democracy, but his is arguably one of the first works to delve into the mathematical principles underlying democratic theory in a systematic and comprehensive manner. While many previous works have dealt with themathematics of democratic choice making institutions, a particularly valuable contribution of Tangian is the focus on principles of representation in general and of random sampling of decision makers, in particular. The book consists of three parts: history, theory and applications. The first deals in some detail with the main episodes in the development of democracy: the Greek city states, the republican period of Rome, the latemedieval city states of northern Italy, the French thinkers of the Enlightenment and the emerging US and French constitutional principles. The thinkers Tangian mostly relies on in discussing the democratic developments in the antiquity are Polybius, Aristotle, Plato and Cicero. The theory of mixed forms of government is one of the upshots of the discussion. Another is the importance of choices by lotteries in the ancient Greek city states. Of Roman writers Pliny the Younger gets a rather extensive treatment because of hiswell-known role as the pioneer of strategic thinking in voting institutions. The discussion on medieval developments also singles out familiar names: Ramon Lull, Nicolaus Cusanus, Marsilius of Padova, William of Ockham, Francesco