An Outline of the Mathematical Theory of Democracy and Its Applications

This paper summarizes the authors studies in mathematical theory ofdemoocracy (Tanguiane 1991, 1993, 1994, 1997). The main consideration is theformalization of the notion of representativeness measured by the weight ofthe coalition represented in each event of decision making. Therepresentativeness is used to estimate the quality of individualrepresentatives (president) and two forms of representative bodies likecabinet (named by analogy with the cabinet of ministers) and council(parliament). In particular, we suggest a solution to Arrows paradox byproving that there always exists an Arrovian dictator who is morerepresentative of the society than a dictator in a proper sense. We alsooutline possible applications of the model to Gallup polls, multicriteriadecision making, and analysis of political situations.