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Mathematical theory of democracy and its applications 3. Applications

Mathematical theory of democracy and its applications 3. Applications. Andranik Tangian Hans-Böckler Foundation, Düsseldorf University of Karlsruhe andranik-tangian@boeckler.de. Plan of the course. Three blocks : Basics History, Arrow‘s paradox, indicators of representativeness, solution

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Mathematical theory of democracy and its applications 3. Applications

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  1. Mathematical theory of democracy and its applications3. Applications Andranik TangianHans-Böckler Foundation, Düsseldorf University of Karlsruheandranik-tangian@boeckler.de

  2. Plan of the course Three blocks : • Basics History, Arrow‘s paradox, indicators of representativeness, solution • Fundamentals: Model of Athens governance (president, assembly, magistrates, courts) and German Bundestag (parties and coalitions) • Applications MCDM, traffic control, financies

  3. Questions

  4. Individuals

  5. Candidates

  6. Representativeness Example: b11 = 1, b12= -1; r1qshown by color q1 q2 Protagonists ai1=1 Antagonists aiq=-1 ai2=-1 ai2=-1 ai2=1 ai2=1

  7. Indicator of popularity – „spatial“ representativeness

  8. Indicator of universality –„temporal“ representativeness

  9. Indicator of goodness – „specific“ representativeness

  10. MCDM: FU-Hagen outing 6 Candidate destinations 1. Casino of Hohensyburg 2. Hagen open air museum 3. Wiblingwerde 4. Schmallenberg 5. Soest 6. Münster 7. Cologne opera 5 1 3 2 4 7

  11. Team wishes (individual opinions)

  12. Indicators of candidate destinations

  13. 2-year plans to satisfy a majority once in each respect (cabinets)

  14. 3- and 5-year plans to satisfy a majority in each respect half the times (parliaments)

  15. Traffic control 10 Surveillance cameras 1-5 Hagen Ring 6-20 Important inter-sections 6 7 8 11 9 12 1 14 13 2 15 3 5 4 16 17 19 18 20

  16. Prevailing traffic flow at the Hagen ring during the lunch time + clockwise traffic flow prevails - counterclockwise traffic flow prevails

  17. Traffic flows all over Hagen +/- main traffic flow outside the Ring is towards/outside the city

  18. Intersection representativeness

  19. Best collective predictors of the Ring flow and statistical tests

  20. Predicting DAX from DJ NYSE Frankfurter Börse 15:30

  21. Week changes of DAX stock prices

  22. Week changes of DJ stock prices

  23. Anticipative representativeness of DJ stocks

  24. Best DAX collective predictors and statistical tests

  25. General summary Instruments: Indicators of representativeness: popularity, universality, goodness, … Theoretical implications: Arrow’s paradox,selection of representatives by lot, estimation of size of representative bodies, analogy with forces in physics, inefficiency of democracy in unstable society Societal applications: finding best candidates, parties, and coalitions Non-societal applications: MCDM, traffic control, finances (finding compromises, finding predictors, …) Calculus instead of logic check: finding optimal compromises, whereas ‘yes’–‘no’ logic retains only unobjectionable solutions

  26. Sources Tangian A. (2003) MCDM-Applications of the Mathematical Theory of Democracy: Choosing Travel Destginations, Preventing Traffic Jams, and Predicting Stock Exchange Trends. FernUniversität Hagen, Discussion Paper 333 Tangian A.S. (2007) Selecting predictors for traffic control by methods of the mathematical theory of democracy. European Journal of Operational Research, 181, 986–1003 Tangian A.S. (2008) Predicting DAX trends from Dow Jones data by methods of the mathematical theory of democracy. European Journal of Operational Research, 185, 1632--1662 Tangian A. (2008) A mathematical model of Athenian democracy. Social Choice and Welfare, 31, 537 – 572. First version: Tangian A. (2005) Decision making in politics and economics: 1. Mathematical model of classical democracy. University of Karlsruhe. Discussion Paper. http://www.wior.uni-karlsruhe.de/LS_Puppe/Personal/Papers-Tangian/modelclassdem.pdf

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