This paper summarizes the author's studies in mathematical theory of d
emocracy (Tanguiane 1991, 1993, 1994, 1997). The main consideration is
the formalization of the notion of representativeness measured by the
weight of the coalition represented in each event of decision making.
The representativeness is used to estimate the quality of individual
representatives (president) and two forms of representative bodies lik
e cabinet (named by analogy with the cabinet of ministers) and council
(parliament). In particular, we suggest a solution to Arrow's paradox
by proving that there always exists an Arrovian dictator who is more
representative of the society than a dictator in a proper sense. We al
so outline possible applications of the model to Gallup polls, multicr
iteria decision making, and analysis of political situations.