A mathematical model of Athenian democracy

نویسنده

  • Andranik Tangian
چکیده

A mathematical model of Athenian democracy (594–322 BC) is considered. Indicators of popularity, universality, and goodness are introduced to evaluate single political leaders, the Assembly, the Council of 500, and magistrates. The popularity is a spatial characteristic of representativeness, the average percentage of the population whose opinion is represented on a number of questions. The universality is a temporal aspect of representativeness, the frequency of cases (percentage of questions) when the opinion of a majority is represented. The goodness is the specific representativeness, the average group-represented-to-majority ratio. Among other things, these indicators are used to evaluate representatives and representative bodies selected by lot (=lottery), as it has been practiced in Athens since the Draconic Laws (621 BC). It is shown that selection by lot guarantees a good representation of the society. These results are manifestations of the same general principles which back up Gallup polls of public opinion and methods of quality control, which use limited random samples to make statistical conclusions on the totality. In illustration, the model is applied to the German Parliament (Bundestag) elections 2002. The popularity and the universality of five leading parties are estimated, and optimal parliaments and optimal cabinets with few members are found.

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عنوان ژورنال:
  • Social Choice and Welfare

دوره 31  شماره 

صفحات  -

تاریخ انتشار 2008