Statistical test for the mathematical theory of democracy

In economics and other social sciences, complex processes are often represented by numerical models of reality which more or less well reflect behavioral relationships and interactions. Such attempts are the subject of a lecture course "Mathematical Theory of Democracy" by the author at the Faculty of Economics of the Karlsruhe Institute of Technology. One new result in this field is presented here in the form of a statistical test to decide whether a political party or coalition of parties represents a majority of the population. For this purpose, party or coalition positions on a sample of policy issues, like introduction of a legal nationwide minimum wage, privatization of railways, and others, are compared with the results of public opinion polls on the same issues. The test is based on estimating the "statistical significance" of the coincidence observed (i.e. how likely is the coincidence by chance) to the end of accepting or rejecting the representativeness hypothesis. The test is developed for single parties and coalitions of two or three parties. It is illustrated with an estimation of representativeness of five major German parties and their potential coalitions basing on the official party manifestos published before the German parliamentary elections 2009 and on relevant polls of public opinion. -- Mathematical theory of democracy ; statistical test ; parties ; coalitions ; representativeness ; Bernoulli matrices ; sums of random vectors