An Outline of the Mathematical Theory of Democracy and Its Applications

Andranick Tanguiane
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Andranick Tanguiane: FernUniversitat Hagen

Group Decision and Negotiation, 1997, vol. 6, issue 3, No 1, 205-230

Abstract: Abstract This paper summarizes the author‘s 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 Arrow‘s 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.

Keywords: social choice; Arrow‘s paradox; representatives; cabinets; councils; mathematical theory of democracy; Gallup polls; multicriteria decision making (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1008651211402

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