Social:Mathematical theory of democracy

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Short description: Social choice theories

The mathematical theory of democracy is an interdisciplinary branch of the public choice and social choice theories conceptualized by Andranik Tangian. It operationalizes the fundamental idea to modern democracies – that of political representation, in particular focusing on policy representation, i.e. how well the electorate's policy preferences are represented by the party system and the government. The representative capability is measured by means of dedicated indices that are used both for analytical purposes and practical applications.

History

The mathematical approach to politics goes back to Aristotle,[1] who explained the difference between democracy, oligarchy and mixed constitution in terms of vote weighting.[2] The historical mathematization of social choice principles is reviewed by Iain McLean and Arnold Urken.[3] Modern mathematical studies in democracy are due to the game, public choice and social choice theories, which emerged after the World War II; for reviews see.[4][5]

In 1960s, the notion of policy representation has been introduced.[6] It deals with how well the party system and the government represent the electorate's policy preferences on numerous policy issues. Policy representation is currently intensively studied[7] and monitored through the MANIFESTO data base that quantitatively characterizes parties' election programs in about 50 democratic states since 1945.[8] In 1989, it was operationalized in the Dutch voting advice application (VAA) StemWijzer (= ‘VoteMatch’), which helps to find the party that best represents the user's policy preferences. Since then it has been launched on the internet and adapted by about 20 countries as well as by the European Union.[9]

The theoretical aspects of how to best satisfy a society with a composite program first considered by Andranik Tangian[10] and Steven Brams with coauthors[11] is now studied within the relatively new discipline of judgment aggregation.[12][13][14][15] The mathematical theory of democracy focuses, in particular, on the practical aspects of the same topic.[16][17] The name "mathematical theory of democracy" is due to the game theorist Nikolai Vorobyov who commented on the first findings of this kind in the late 1980s.[18][19][20]

Content of the theory

Like the social choice theory, the mathematical theory of democracy analyzes the collective choice from a given list of candidates. However, these theories differ in both the methodology and the data used. The social choice theory operates on the voters’ preference orders of the candidates and applies an axiomatic approach to find impeccable solutions. The mathematical theory of democracy is based on the candidates’ and the electorate's positions on topical political questions and finds the representatives (deputes, president) and representative bodies (parliament, committee, cabinet) that best represent the public opinion. For this purpose, several quantitative indices to assess and compare the representative capability are introduced.

It has been proven that compromise candidates and representative bodies can always be found, even if there is no perfect solution in terms of social choice theory. Among other things, it is proven that even among the axiomatically prohibited Arrow's dictators there always exist good representatives of the society (e.g. to be elected as presidents), which implies a principal possibility of democracy in every society – contrary to the common interpretation of Arrow's impossibility theorem.[10] The further results deal with the characteristics and special features of individual representatives (such as members of parliament, chairmen, presidents) and the committees (such as parliaments, commissions, cabinets, coalitions and juries).[17][21][22][23]

Third Vote

Main page: Social:Third Vote

The Third Vote is an election method developed within the framework of the mathematical theory of democracy to expand the concept of political representation.[17][24][25] The name "Third Vote" has been used in electoral experiments where the new method had to complement the two-vote German system.[26][27][28][29] Its aim is to draw voters' attention from individual politicians with their charisma and communication skills to specific policy issues. The question "Who should be elected?'" is replaced by the question "What do we choose?" (Party platform). Instead of candidate names, the Third Vote ballot asks for Yes/No answers to the questions raised in the candidates’ manifestos. The same is demanded by voting advice applications (VAA), but the answers are processed in a different way. In contrast to VAAs, the voter receives no advice which party best represents the voter's position. Instead, the Third Vote procedure determines the policy profile of the entire electorate with the balances of public opinion on each issue (pro and cons percentages on individual topics). The election winner is the candidate whose policy profile best matches with the policy profile of the entire electorate.

If the candidates are political parties competing for parliamentary seats, the latter are allocated to the parties in proportion to the closeness of their policy profiles to that of the electorate. When considering decision options instead of candidates, the questions focus on their specific characteristics.[30]

The multi-voter paradoxes of Condorcet and Kenneth Arrow are circumvented because the entire electorate with its opinion profile is viewed as a single agent, or a single voter.

Applications

Societal applications

Non-societal applications

Since some interrelated objects or processes "represent" one another with certain time delays, revealing the best "representatives" or "anticipators" can be used for predictions. This technique is implemented in the following applications:

  • Predicting share price fluctuations, since some of them (e.g. in the USA) "represent in advance" some other share price fluctuations (e.g. in Germany)[37]
  • Traffic light control and coordination, since situations at certain crossroads represent in advance the situation at some other crossroads[38]

References

  1. ↑ Miroiu, Adrian; Partenie, Catalin (2019). "Collective choice in Aristotle". Constitutional Political Economy 30 (3): 261–281. doi:10.1007/s10602-019-09279-1. 
  2. ↑ Aristotle (340 BC). Politics, Book 3. Cambridge MA: Harward University Press; 1944. pp. 1280a.7–25. 
  3. ↑ McLean, Iain, ed (1995). Classics of social choice. Ann Arbor MI: University of Michigan Press. 
  4. ↑ Simeone, Bruno, ed (2006). Mathematics and Democracy. Berlin-Heidelberg: Springer. 
  5. ↑ Brams, Steven (2008). Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures. Princeton, NJ: Princeton University Press. 
  6. ↑ Miller, Warren Edward; Stokes, Donald Elkinton (1963). "Constituency influence in Congress". American Political Science Review 57 (1): 45–56. doi:10.2307/1952717. 
  7. ↑ Budge, Ian; McDonald, Michael D (2007). "Election and party system effects on policy representation: Bringing time into a comparative perspective". Electoral Studies 26 (1): 168–179. doi:10.1016/j.electstud.2006.02.001. 
  8. ↑ Volkens, Andrea, ed (2013). Mapping policy preferences from texts: Statistical solutions for manifesto analysts. Oxford: Oxford University Press. 
  9. ↑ Garzia, Diego; Marschall, Stefan (eds.) (2014). Matching voters with parties and candidates: voting advice applications in a comparative perspective. Colchester UK: ECPR Press. 
  10. ↑ 10.0 10.1 Tanguiane (Tangian), Andranick (1994). "Arrow's paradox and mathematical theory of democracy". Social Choice and Welfare 11 (1): 1–82. doi:10.1007/BF00182898. 
  11. ↑ Brams, Steven J; Kilgour, D Marc; Zwicker, William S (1998). "The paradox of multiple elections". Social Choice and Welfare 15 (2): 211–236. doi:10.1007/s003550050101. 
  12. ↑ List, Christian; Puppe, Clemens (2009). "Judgment aggregation: a survey". in Anand, Paul; Puppe, Clemens; Pattranaik, Prasanta. Oxford: Oxford University Press. pp. 457–482. 
  13. ↑ List, Christian (2012). "The theory of judgment aggregation: an introductory review". Synthese 187 (1): 179–207. doi:10.1007/s11229-011-0025-3. http://eprints.lse.ac.uk/27596/1/The_theory_of_judgment_aggregation_%28LSERO%29.pdf. 
  14. ↑ Grossi, Davide; Pigozzi, Gabriella (2014). Judgment aggregation: a primer. San Rafael CA: Morgan and Claypool Publishers. 
  15. ↑ Lang, Jérôme; Pigozzi, Gabriella; Slavkovik, Marija; van der Torre, Leendert (Leon); Vesic, Srdjan S (2017). "A partial taxonomy of judgment aggregation rules and their properties". Social Choice and Welfare 48 (2): 327–356. doi:10.1007/s00355-016-1006-8. 
  16. ↑ 16.0 16.1 Tangian, Andranik (2014). Mathematical theory of democracy. Studies in Choice and Welfare. Berlin-Heidelberg: Springer. doi:10.1007/978-3-642-38724-1. ISBN 978-3-642-38723-4. 
  17. ↑ 17.0 17.1 17.2 17.3 Tangian, Andranik (2020). Analytical theory of democracy. Vols. 1 and 2. Studies in Choice and Welfare. Cham, Switzerland: Springer. doi:10.1007/978-3-030-39691-6. ISBN 978-3-030-39690-9. 
  18. ↑ Andranik Tangian (1989). "Interpretation of dictator in Arrow's model as a collective representative" (in Russian). Matematicheskoe Modelirovanie 1 (7): 51–92. 
  19. ↑ Andranik Tangian (1989). "A model of collective representation under democracy" (in Russian). Matematicheskoe Modelirovanie 1 (10): 80–125. 
  20. ↑ Tanguiane (Andranik Tangian), Andranick (1991). Aggregation and representation of preferences: introduction to mathematical theory of democracy. Berlin-Heidelberg: Springer. doi:10.1007/978-3-642-76516-2. ISBN 978-3-642-76516-2. 
  21. ↑ 21.0 21.1 Tangian, Andranik (2022). Analysis of the 2021 Bundestag Elections 1/4. Representativeness of the Parties and the Bundestag. ECON Working Papers. 151. Karlsruhe: Karlsruhe Institute of Technology. doi:10.5445/IR/1000143156. https://publikationen.bibliothek.kit.edu/1000143156. Retrieved August 8, 2022. 
  22. ↑ 22.0 22.1 Tangian, Andranik (2022). Analysis of the 2021 Bundestag Elections 2/4. Political Spectrum. ECON Working Papers. 152. Karlsruhe: Karlsruhe Institute of Technology. doi:10.5445/IR/1000143157. https://publikationen.bibliothek.kit.edu/1000143157. Retrieved August 8, 2022. 
  23. ↑ Tangian, Andranik (2022). Analysis of the 2021 Bundestag Elections 3/4. Tackling the Bundestag Growth. ECON Working Papers. 153. Karlsruhe: Karlsruhe Institute of Technology. doi:10.5445/IR/1000143158. https://publikationen.bibliothek.kit.edu/1000143158. Retrieved August 8, 2022. 
  24. ↑ Tangian, Andranik (2017). "An election method to improve policy representation of a parliament". Group Decision and Negotiation 26 (1): 181–196. doi:10.1007/S10726-016-9508-4. 
  25. ↑ Tangian, Andranik (2022). Analysis of the 2021 Bundestag Elections 4/4. The Third Vote Application. ECON Working Papers. 154. Karlsruhe: Karlsruhe Institute of Technology. doi:10.5445/IR/1000143159. https://publikationen.bibliothek.kit.edu/1000143159. Retrieved August 8, 2022. 
  26. ↑ Tangian, Andranik (2017). "The Third Vote experiment: Enhancing policy representation of a student parliament". Group Decision and Negotiation 26 (4): 1091–1124. doi:10.1007/S10726-017-9540-Z. 
  27. ↑ Amrhein, Marius; Diemer, Antonia; Eßwein, Bastian; Waldeck, Maximilian; Schäfer, Sebastian. "The Third Vote (web page)". Karlsruhe Institute of Technology, Institute ECON. https://studierendenwahl.econ.kit.edu/. 
  28. ↑ "Turning a political education instrument (voting advice application) in a new election method", World Forum for Democracy 2016, Lab 7: Reloading Elections (Strasbourg: Council of Europe), 7-9 November 2016, https://www.coe.int/en/web/world-forum-democracy/2016-lab-7-reloading-elections, retrieved 15 December 2020 
  29. ↑ "Well Informed Vote", World Forum for Democracy 2019, Lab 5: Voting under the Influence (Strasbourg: Council of Europe), 6-8 November 2019, https://www.coe.int/en/web/world-forum-democracy/lab-5-voting-under-the-influence, retrieved 15 December 2020 
  30. ↑ Tangian, Andranik (2021). "MCDM application of the Third Vote". Group Decision and Negotiation 30 (4): 775–787. doi:10.1007/s10726-021-09733-2. ISSN 0926-2644. https://link.springer.com/content/pdf/10.1007/s10726-021-09733-2.pdf. 
  31. ↑ Tanguiane (Tangian), Andranick (1993). "Inefficiency of democratic decision making in an unstable society". Social Choice and Welfare 10 (3): 249–300. doi:10.1007/BF00182508. 
  32. ↑ Tangian, Andranik (2010). "Application of the mathematical theory of democracy to Arrow's Impossibility Theorem (How dictatorial are Arrow's dictators?)". Social Choice and Welfare 35 (1): 135–167. doi:10.1007/s00355-009-0433-1. 
  33. ↑ Tangian, Andranik (2008). "A mathematical model of Athenian democracy". Social Choice and Welfare 31 (4): 537–572. doi:10.1007/s00355-008-0295-y. 
  34. ↑ Tangian, Andranik (2010). "German parliamentary elections 2009 from the viewpoint of direct democracy". Social Choice and Welfare 40 (3): 833–869. doi:10.1007/s00355-011-0646-y. 
  35. ↑ Tangian, Andranik (2017). "Policy representation of a parliament: the case of the German Bundestag 2013 election". Group Decision and Negotiation 26 (1): 151–179. doi:10.1007/S10726-016-9507-5. 
  36. ↑ Tangian, Andranik (2019). "Visualizing the political spectrum of Germany by contiguously ordering the party policy profiles". in Skiadis, Christos H.. Data Analysis and Applications 2. London: ISTE-Wiley. pp. 193–208. doi:10.1002/9781119579465.ch14. ISBN 9781119579465. https://onlinelibrary.wiley.com/doi/abs/10.1002/9781119579465.ch14. 
  37. ↑ Tangian, Andranik (2008). "Predicting DAX trends from Dow Jones data by methods of the mathematical theory of democracy". European Journal of Operational Research 185 (3): 1632–1662. doi:10.1016/j.ejor.2006.08.011. 
  38. ↑ Tangian, Andranik (2007). "Selecting predictors for traffic control by methods of the mathematical theory of democracy". European Journal of Operational Research 181 (2): 986–1003. doi:10.1016/j.ejor.2006.06.036. 



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