Books
Later publications
Tangian, Andranik (2023-04) Apportionment in times of digitalization. ECON Working Papers #161. Karlsruhe: Karlsruhe Institute of Technology. PDF: https://www.econstor.eu/bitstream/10419/271097/1/1845180046.pdf
Tangian, Andranik (2022-01 a). 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: https://doi.org/10.5445/IR/1000143156.
Tangian, Andranik (2022-01 b). Analysis of the 2021 Bundestag Elections 2/4. Political Spectrum. ECON Working Papers #152. Karlsruhe: Karlsruhe Institute of Technology. DOI: https://doi.org/10.5445/IR/1000143157.
Tangian, Andranik (2022-01 c). Analysis of the 2021 Bundestag Elections 3/4. Tackling the Bundestag Growth. ECON Working Papers #153. Karlsruhe: Karlsruhe Institute of Technology. DOI: https://doi.org/10.5445/IR/1000143158.
Tangian, Andranik (2022-01 d). Analysis of the 2021 Bundestag Elections 4/4. The Third Vote Application. ECON Working Papers #154. Karlsruhe: Karlsruhe Institute of Technology. DOI: https://doi.org/10.5445/IR/1000143159.
History
The mathematical approach to politics goes back to (Aristotle 340 BC) who explained the difference between democracy, oligarchy and mixed constitution in terms of vote weighting (Tangian 2020-03-31, Sect. 1.6). The historical mathematization of social choice principles is reviewed by (McLean and Urken 1995). Modern mathematical studies in democracy are due to the game, public choice and social choice theories, which emerged after the World War II.
In 1960s, the notion of policy representation has been introduced. 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 (Budge and McDonald 2007) and monitored through the MANIFESTO data base that quantitatively characterizes parties’ election programs in about 50 democratic states since 1945 (Volkens et al. 2013). 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 (Garzia and Marschall 2014).
The theoretical aspects of how to best satisfy a society with a composite program first considered by (Tanguiane 1994-01) and (Brams et al. 1998) is now studied within the relatively new discipline of judgment aggregation (List and Puppe 2009, Grossi and Pigozzi 2014). The mathematical theory of democracy focuses, in particular, on the practical aspects of the same topic (Tangian 2014/2013-08-12, 2020-03-31). The name “mathematical theory of democracy” is due to Professor Nikolai Vorobyov who commented on the first findings of this kind (Tangian 1989-07, 1989-10, 1991-04) at the Leningrad game theory seminar in March 1987.
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 (Tangian 1994-01). 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 (Tangian 2020-03-31, 2022-01 a-c).
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 (Tangian 2017-01 b, 2020-03-31, 2022-01 d). The name “Third Vote” has been used in electoral experiments where the new method had to complement the two-vote German system (Amrhein et al. 2016, 2019; Tangian 2017-11, 2019-06). 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 (Tangian 2021-08).
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
Inefficiency of democracy in an unstable society (Tanguiane 1993-07)
Quantitative analysis and alternative interpretation of Arrow’s impossibility theorem (Tangian 1994-01, 2010-06)
Analysis of Athenian democracy based on selection of public officers by lot (Tangian 2008-12)
Analysis of election outcomes with estimations of the representativeness of election winners and parliament factions (Tangian 2013-03, 2014/2013-08-12, 2017-01 a, 2022-01 a)
Analysis of national political spectra (Tangian 2019-03, 2022-01-2)
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 (Tangian 2008-03-16)
Traffic light control and coordination, since situations at certain crossroads represent in advance the situation at some other crossroads (Tangian 2007-09)
References
Amrhein, Marius; Diemer, Antonia; Tangian, Andranik (2016) “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.
Amrhein, Marius; Diemer, Antonia; Eßwein, Bastian; Waldeck, Maximilian; Schäfer, Sebastian (2019). Web Page “The Third Vote – Die Stimme für Ihre politische Meinung”. Karlsruhe: Karlsruhe Institute of Technology, Institute ECON. https://studierendenwahl.econ.kit.edu/
Aristotle (340 BC). Politics, Book 3. Cambridge MA: Harvard University Press; 1944. #1280a.7–1280a.25.
Brams, Steven J; Kilgour, D Marc; Zwicker, William S (1998). “The paradox of multiple elections”. Social Choice and Welfare, 15 (2): 211–236.DOI: https://doi.org/10.1007/s003550050101.
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: https://doi.org/10.1016/j.electstud.2006.02.001.
Garzia, Diego; Marschall, Stefan, eds. (2014). Matching voters with parties and candidates: voting advice applications in a comparative perspective. Colchester UK: ECPR Press.
Grossi, Davide; Pigozzi, Gabriella (2014). Judgment aggregation: a primer. San Rafael CA: Morgan and Claypool Publishers
List, Christian; Puppe, Clemens (2009). “Judgment aggregation: a survey”. In Anand, Paul; Puppe, Clemens; Pattranaik, Prasanta (eds.). Oxford handbook of rational and social choice. Oxford: Oxford University Press. 457–482.
McLean, Iain; Urken, Arnold Bernard, eds. (1995). Classics of social choice. Ann Arbor MI: University of Michigan Press.
Tangian, Andranik (1989-07). “Interpretation of dictator in Arrow’s model as a collective representative”. Matematicheskoe Modelirovanie (in Russian), 1 (7): 51–92.
Tangian, Andranik (1989-10). “A model of collective representation under democracy”. Matematicheskoe Modelirovanie (in Russian), 1 (10): 80–125.
Tanguiane, Andranick (Andranik Tangian) (1991-04). Aggregation and representation of preferences: Introduction to mathematical theory of democracy. Berlin-Heidelberg: Springer. DOI: https://doi.org/10.1007/978-3-642-76516-2.
Tanguiane Andranick (Andranik Tangian) (1993-07). “Inefficiency of democratic decision making in an unstable society”. Social Choice and Welfare, 10 (3): 249–300.DOI: https://doi.org/10.1007/BF00182508.
Tanguiane (Tangian), Andranick (1994-01). “Arrow’s paradox and mathematical theory of democracy”. Social Choice and Welfare, 11 (1): 1–82. DOI: https://doi.org/10.1007/BF00182898.
Tangian, Andranik (2007-09-01). “Selecting predictors for traffic control by methods of the mathematical theory of democracy”. European Journal of Operational Research, 181 (2): 986–1003. DOI: https://doi.org/10.1016/j.ejor.2006.06.036
Tangian, Andranik (2008-12). “A mathematical model of Athenian democracy”. Social Choice and Welfare. 31 (4): 537–572. DOI: https://doi.org/10.1007/s00355-008-0295-y
Tangian, Andranik (2008-03-16). “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: https://doi.org/10.1016/j.ejor.2006.08.011.
Tangian, Andranik (2010-06). “Computational 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: https://doi.org/10.1007/s00355-009-0433-1.
Tangian, Andranik (2013-03). “German parliamentary elections 2009 from the viewpoint of direct democracy”. Social Choice and Welfare, 40 (3): 833–869.DOI: https://doi.org/10.1007/s00355-011-0646-y.
Tangian, Andranik (2014 / 2013-08-12). Mathematical theory of democracy. Studies in Choice and Welfare. Berlin-Heidelberg: Springer. DOI: https://doi.org/10.1007/978-3-642-38724-1.
Tangian, Andranik (2017-01a). “Policy representation of a parliament: the case of the German Bundestag 2013 election”. Group Decision and Negotiation, 26 (1): 151–179. DOI: https://doi.org/10.1007/s10726-016-9507-5.
Tangian, Andranik (2017-01b). “An election method to improve policy representation of a parliament”. Group Decision and Negotiation, 26 (1): 181–196. DOI: https://doi.org/10.1007/s10726-016-9508-4.
Tangian, Andranik (2017-11). “The Third Vote experiment: Enhancing policy representation of a student parliament”. Group Decision and Negotiation, 26 (4): 1091–1124. DOI : https://doi.org/10.1007/s10726-017-9540-z
Tangian, Andranik (2019-03-06). “Visualizing the political spectrum of Germany by contiguously ordering the party policy profiles”. In Skiadis, Christos H.; Bozeman, James R. (eds.). Data Analysis and Applications 2. London: ISTE-Wiley, 193–208. DOI: https://doi.org/10.1002/9781119579465.ch14
Tangian, Andranik (2019-11-06) “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.
Tangian, Andranik (2020-03-31). Analytical theory of democracy. Vols. 1 and 2. Studies in Choice and Welfare. Cham, Switzerland: Springer. DOI: https://doi.org/10.1007/978-3-030-39691-6.
Tangian, Andranik (2021-08). “MCDM application of the Third Vote”. Group Decision and Negotiation, 30 (4): 775–787. DOI: https://doi.org/10.1007/s10726-021-09733-2.
Tangian, Andranik (2022-01 a). Analysis of the 2021 Bundestag Elections 1/4. Representativeness of the Parties and the Bundestag. ECON Working Papers. Vol. 151. Karlsruhe: Karlsruhe Institute of Technology. DOI: https://doi.org/10.5445/IR/1000143156.
Tangian, Andranik (2022-01 b). Analysis of the 2021 Bundestag Elections 2/4. Political Spectrum. ECON Working Papers. Vol. 152. Karlsruhe: Karlsruhe Institute of Technology. DOI: https://doi.org/10.5445/IR/1000143157.
Tangian, Andranik (2022-01 c). Analysis of the 2021 Bundestag Elections 3/4. Tackling the Bundestag Growth. ECON Working Papers, Vol. 153. Karlsruhe: Karlsruhe Institute of Technology. DOI: https://doi.org/10.5445/IR/1000143158.
Tangian, Andranik (2022-01 d). Analysis of the 2021 Bundestag Elections 4/4. The Third Vote Application (https://publikatione n.bibliothek.kit.edu/1000143159). ECON Working Papers, 154. Karlsruhe: Karlsruhe Institute of Technology. DOI: https://doi.org/10.5445/IR/1000143159.
Volkens, Andrea; Bara, Judith; Budge, Ian; McDonald, Michael D; Klingemann, Hans-Dieter, eds. (2013). Mapping policy preferences from texts: Statistical solutions for manifesto analysts. Oxford: Oxford University Press.