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An Outline of the Mathematical Theory of Democracy and Its Applications

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  • ANDRANICK TANGUIANE

    (FernUniversitat Hagen)

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.

Suggested Citation

  • Andranick Tanguiane, 1997. "An Outline of the Mathematical Theory of Democracy and Its Applications," Group Decision and Negotiation, Springer, vol. 6(3), pages 205-230, May.
    • Handle: RePEc:spr:grdene:v:6:y:1997:i:3:d:10.1023_a:1008651211402
    DOI: 10.1023/A:1008651211402
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    References listed on IDEAS

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    1. Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, vol. 2(1), pages 103-106, March.
    2. Armstrong, Thomas E., 1985. "Precisely dictatorial social welfare functions : Erratum and Addendum to `arrows theorem with restricted coalition algebras'," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 57-59, February.
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