The mathematical theory of democracy is applied to analyze the German Bundestag elections 2009 and to evaluate five German leading parties and their coalitions from the viewpoint of direct democracy. For this purpose, the positions of the parties on over 30 topical issues are compared with results of public opinion polls. The outcomes are summarized in the party indices of popularity (the average percentage of the population represented) and universality (frequency of representing a majority). It is shown that the election winner 2009, the conservative party CDU/CSU, has a quite low representativeness (ranked fourth), whereas the most representative is the left party die Linke which received only 11.9% votes. It is concluded that voters are not very consistent with their own political profiles, disregard party manifestos, and are likely driven by political traditions, even if outdated, or by personal images of politicians. To bridge approaches of representative and direct democracy, some modifications to the election procedure are proposed, which, among other things, complicate vote manipulations.
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