Electoral Systems in the Digital Age: Underlying Challenges and New Opportunities Part I. A Review of the Problems, Classic Protocols of Collective Choice

Keywords: public choice, positive voting, classical election technologies, coherence of voters' opinions, non-numerical statistics, ordinal scales, scale arithmetic, profile consistency, Kendall coefficient, linear convolution, criterion weights, nonlinear scaling, consistency indices, verbal-quantitative scales, qualimetry, pairwise comparisons, Kemeni median, Schulze heuristics, fuzzy sets, Monte Carlo method, voting profiles, transitivity, data consistency, p-value.


The article is devoted to the problem of democratic development of Ukraine.

The reasons for the need for a radical transformation of the electoral process in Ukraine have been considered from a theoretical standpoint. The main goal and sub-goals of the research have been formulated. The classical mathematical models of electoral technologies, selected for comparison with modern approaches have been described.

The basic principles of selection of methods for measuring the results of approval voting have been analyzed. The issues of constructing a verbal-numerical scale, assessing the consistency of voter decisions and applying statistical criteria to obtain a consolidated result have been considered.

The models selected for calculating the final election rating are analyzed. Mathematical algorithms of multicriteria selection based on the qualimetric approach and pairwise comparison on four variants of scales are given. Protocols for determining consensus alternatives using the Topsis method, the Kemeni – Young median, the Schulze heuristic procedure, and the fuzzy set approach are described.

The results of approbation of the selected protocols of approval of the voting system for the election model of 4 candidates on 7 questions of the ballot paper are given. The algorithm and the results of generating by the Monte Carlo method arrays of initial data with a size of 10,000 records, having a uniform and normal distribution with three variants of the bias parameter, are presented. To identify the sensitivity of the studied protocols to violations of the transitivity of individual preference profiles, the primary data arrays were transformed by replacing the nontransitive profiles with an equivalent number of transitive ones without presenting a preference to any alternative. Based on the assessment of the correlation of the final ratings, their sensitivity to the type of distribution and to violations of the transitivity of individual judgments, it was concluded that it is advisable to use the Kemeny median to determine the voting results. The use of the proposed method for transforming primary data also makes it possible to use the Condorcet, Dodgson, Saati and Schulze protocols. The results of this study indicate that there is a fundamental possibility of transition to a new digital paradigm of the electoral process based on the approving principle of voting.


Download data is not yet available.


1. Aleskerov F. T., Khabina E. L., Shvarts D. A. (2012). Binarnyye otnosheniya, grafy i kollektivnyye resheniya [Binary relations, graphs, and collective solutions]. 2nd ed., rev. and suppl. Moscow: FIZMATLIT [in Russian].
2. Lazarsfeld P., and Genri N. (1973). Matematicheskiye metody v sotsialnykh naukakh [Mathematical methods in social sciences]. Moscow: “Progress” [in Russian].
3. Mirkin B. G. (1974). Problema gruppovogo vybora [The problem of group selection]. Moscow: «Nauka», Chief editorial office of literature in physics and mathematics [in Russian].
4. Moulin H. (1991). Kooperativnoye prinyatye resheniy: Aksiomy i modeli [Axioms of Cooperative Decision Making]. Trans. from English. Moscow: “Mir” [in Russian].
5. Aleskerov F. T., and Orteshuk P. (1995). Vybory. Golosovaniye. Partii [Elections. Voting. Parties]. Moscow: “Akademiya” [in Russian].
6. Volskiy V. I., and Lezina Z. M. (1991). Golosovaniye v malykh gruppakh: protsedury i metody sravnitelnogo analiza [Voting in small groups: procedures and methods of comparative analysis]. Moscow: “Nauka”. Chief editorial office of literature in physics and mathematics [in Russian].
7. Arrow K. J. (2004). Kollektivnyy vybor i individualnyye tsennosti [Social Choice and Individual Values]. Trans. from English. Moscow: Publishing house of State University – Higher School of Economics [in Russian].
8. Litvak B. G. (1982). Ekspertnaya informatsiya: Metody polucheniya i analiza [Experimental information: methods for obtaining and analysis]. Moscow: “Radio i svyaz” [in Russian].
9. Mueller D. (2007). Obshchestvennyy vybor III [Public Choice III]. Trans. form English. A. P. Zaostrovtsev, A. S. Skorobogatov (Eds.). Moscow: State University – Higher School of Economics, Institute “Economic Scholl” [in Russian].
10. (1972) Statisticheskoye izmereniye kachestvennykh kharakteristik [Statistical Measurement of Qualitative Characteristics]. Trans. from English. Ye. M. Chetyrkin (Ed.). Moscow: “Statistika” [in Russian].
11. Voloshin A. F., and Mashchenko S. F. (2010). Modeli ta metody pryiniattia rishen [Models and methods for decision making]. 2nd ed., rev. and suppl. Kyiv: “Kyivskyi universitet” [in Ukrainian].
12. Nureyev R. M. (2005). Teoriya obshchestvennogo vybora [The theory of public choice]. Moscow: State University – Higher School of Economics [in Russian].
13. Klima R. E., and Khodzh Dzh. K. (2007). Matematika vyborov [The mathematics of elections]. Moscow: Moscow Center for Continuous Mathematical Education [in Russian].
14. Kichmarenko A. D., and Ogulenko A. P. (2013). Teoriya prinyatiya resheniy. Razdel: Teoriya golosovaniya [The theory of decision making. Section: The theory of voting]. Odessa: Mechnikov State University of Odessa [in Russian].
15. Petrovskiy A. B. (2009). Teoriya prinyatiya resheniy [The theory of decision making]. Moscow: “Akademiya” [in Russian].
16. Torra V. (2014). Matematika i vybory. Prinyatiye resheniy [Matemáticas y toma de dicisiones]. Trans. from Spanish. Moscow: De Agostini [in Russian].
17. Tangian A. (2014). Mathematical Theory of Democracy. Springer-Verlag Berlin Heidelberg.
18. Khudoley D. M. (2017). Paradoksy Kondorse i ikh resheniye [Condorcet paradoxes and their solution]. Vestnik Permskogo universiteta. Yuridicheskiye nauki – Bulletin of Perm University. Law, 37, 288–302 [in Russian].
19. Saati T. (2015). Ob izmerenii neosyazayemogo. Podkhod k otnositelnym izmereniyam na osnove glavnogo sobstvennogo vektora matritsy parnykh sravneniy [Measuring the intangible. An approach to relative measurements on the basis of the main eigenvector of the matrix of paired comparisons]. Elektronnyy zhurnal “Cloud of Science” – Electronic journal “Cloud of Science”, vol. 2, issue 1. Retrieved from http HYPERLINK "http://cloudofcience.ru/.
20. Boltenkov V. A., Kuvayeva V. I., and Pozniak A. V. (2017). Analiz metodіv konsensusnoho agreguvannia rangovykh perevah [Analysis of median methods for consensus rank preferences aggregation]. Informatika i matematicheskiye metody v modelirovanii – Informatics and Mathematical Methods in Simulation, vol. 7, issue 4, 307–317 [in Ukrainian].
21. (1977) Statisticheskiye metody analiza ekspertnykh otsenok [Statisical methods for analysis of expert opinions]. Uchenyye zapiski po statistike – Academic Writings on Statistics, vol. 29. Moscow: “Nauka” [in Russian].
22. Totsenko V. G. (2002). Metody i sistemy pidtrymky pryiniattia rishen. Algorytmichnyi aspekt [Methods and systems for decision making support. The algorithmic aspect]. Kyiv: “Naukova dumka” [in Ukrainian].
23. Totsenko V. G. (2005). Metody opredeleniya gruppovykh mnogokriterialnykh ordilnykh otsenok s uchetom kompetentosti ekspertov [Methods for determining group multi-criteria orderly assessments with consideration to the expert competence]. Problemy upravleniya i informatiki – Problems of Management and Informatics, 8, 84–89 [in Russian].
24. Endriss U. (Ed.) (2017). Trends in Computational Social Choice. ILLC, University of Amsterdam.
25. Boltenkov V.A., Kuvayeva V.I., and Chervonenko P.P. (2018). Primeneniye metodov sotsialnogo vybora v zadachakh agregirovaniya otsenok v rangovykh shkalakh [Applications of social choice methods in the problems of aggregation of estimates in random scales]. Sistemnyye tekhnologii – System Technologies, 2(115), 93–102 [in Russian].
26. Mokhonchuk B. S. Vyborcha systema Ukrainy yak konstytatsiino-pravovyi instytut [The election system in Ukraine: a constitutional and legal institute]. PhD thesis. Retrieved from http://nauka.nlu.edu.ua/download/diss/Moxonchuk/d_Moxonchuk.pdf [in Ukrainian].
27. Fowler J. H. (2005). Turnout in a Small World. In: The Social Logic of Politics: Personal Networks as Contexts for Political Behaviour. A. Zuckerman (Ed.). Philadelphia: Temple University Press, pp. 269–287.
28. Nickerson D. W. (2008). Is Voting Contagious? Evidence from Two Field Experiments. American Political Science Review, 102, 49–57.
29. O’Connor B., Balasubramanyan R., Routledge B., Smith N. (2010). From tweets to polls: Linking text sentiment to public opinion time series. Proceedings of the 4th International AAAI Conference on Weblogs and Social Media (ICWSM'10). Washington, DC, pp. 122–129.
30. Darwish, K., Magdy W., and Zanouda T. (2017). Trump vs. Hillary: What Went Viral During the 2016 US Presidential Election. Proceedings of 9th International Conference “Social Informatics”. Oxford, UK, September 13–15, 2017. Part I, pp. 143–161.
31. Marakulin V. M. Obshchestvennyy vybor i politicheskaya konkurentsiya [The social choice and political competition]. URL: http://math.isu.ru/ru/chairs/me/files/materials2010/byk_mar3.pdf [in Russian].
32. Khakhanov V. I., Soslakova T. I., Chumachenko S. V., and Litvinova Ye. I. (2017). Kiber-sotsialnyi kompiyuting. Naukoyemkiye tekhnologii v infokommunikatsiyakh: obrabotka informatsii, kiberbezopasnost, informatsionnaya borba [The cyber-social computing. RD intensive technologies in info-communications: processing of information, cyber-security, and information war]. V. M. Bezruk, V. V. Barannik (Eds.). Kharkov: “Lider” [in Russian].
33. Luce D., and Raiffa H. (1961). Igry i resheniya. Vvedeniye i kriticheskiy obzor [Games and Decisions. Introduction and Critical Survey]. Trans. from English. Moscow: Publishing house of foreign literature [in Russian].
34. Khomenyuk V. V. (1983). Elementy teorii mnogotselevoy optimizatsii [Elements of multiobjective optimization theory]. Moscow: “Nauka” [in Russian].
35. Cox Gary W. (2004). Tsina holosu. Stratehichna koordynatsiia u vyborchykh systemakh svitu [Making Votes Count. Strategic Coordination in the World’s Electoral Systems]. Trans. from English. Kyiv: National University of Kyiv Mohyla Academy [in Ukrainian].
36. Borodin A. D. (2005). Soglasovannost kollektivnykh deystviy v povedenii rossiyskikh izbirateley [The concerted action in the behavior of Russian voters]. Ekonomicheskiy zhurnal VSHE – Economic Journal of Higher School of Economics, 1, 74–81 [in Russian].
37. Orlov A. I. (2010). Organizatsionno-ekonomicheskoye modelirovaniye: teoriya prinyatiya resheniy [The organizational and economic modeling: the theory of decision making]. Moscow: KNORUS [in Russian].
38. Chernorutskiy I. G. (2005). Metody prinyatiya resheniy [Methods of decision making]. Saint-Petersburg: BKhV-Peterburg [in Russian].
39. Bukharin S. N., Tsyganov V. V. (2007). Metody i tekhnologii informatsionnykh voyn [Methods and technologies of information wars]. Moscow: “Akademicheskiy proyekt” [in Russian].
40. Kachynska K. A., Varycheva D. I., and Svyrydenko S. V. (2017). Internet-tekhnolohii: otsinka priorytetnosti manipuliuvannia svidomostiu za dopomohoiu metodiv ranzhuvannia [Internet technologies: an assessment of priority of consciousness manipulation by ranking methods]. Informatsiya i pravo – Information and Law, 4(23), 49–61 [in Ukrainian].
41. Approval voting. Retrieved from https://ru.qwe.wiki/wiki/Approval_voting
42. Zadeh L. A. (1965). Fuzzy Sets. Inform. a. Control, 8, 338–353.
43. Zadeh L. A. (1976). Ponyatiye lingvisticheskoy peremennoy i yego primeneniye k prinyatiyu priblizhennykh resheniy [The concept of linguistic variable and its applications in making approximate decisions]. Moscow: “Mir” [in Russian].
44. Pospelov D. A. (Ed.) (1986). Nechetkiye mnozhestva v modelyakh upravleniya i iskusstvennogo intellekta [Fuzzy sets in the models of management and artificial intellect]. Moscow: “Nauka”, Chief editorial office of literature in physics and mathematics [in Russian].
45. Poleshchuk O., and Komarov E. (2011). Studies in Fuzziness and Soft Computing. Berlin Heidelberg: Springer-Verlag.
46. Poleshchuk A. N. (2003). Postroyeniye integralnykh modeley v ramkakh nechetkoy ekspertnoy informatsii [Constructing integral models on the basis of fuzzy expert information]. Lesnoy vestnik – Forest Bulletin, 5, 160–167 [in Russian].
47. Poleshchuk A. N. (2002). Metody predstavleniya ekspertnoy informatsii v vide sovokupnosti term-mnozhestv polnykh ortogonalnykh semanticheskikh prostranstv [Methods for presentation of expert information in form of totality of term-sets of full orthogonal semantic spaces]. Lesnoy vestnik – Forest Bulletin, 5, 198–216 [in Russian].
48. Poleshchuk A. N. (2003). Metody predvaritelnoy obrabotki nechetkoy ekspertnoy informatsii na etape yeye formalizatsii [Methods for preliminary processing of information at the phase of its formalization]. Lesnoy vestnik – Forest Bulletin, 5, 160–167 [in Russian].
49. Poleshchuk A. N., and Poleshchuk I. A. (2003). Nechetkaya klasterizatsiya elementov mnozhestva polnykh ortogonalnykh semanticheskikh prostranstv [Fuzzy clustering of elements of the set of full orthogonal semantic spaces]. Lesnoy vestnik – Forest Bulletin, 1, 117–127 [in Russian].

Abstract views: 3
PDF Downloads: 3
How to Cite
SINYTSKYI, M. (2021). Electoral Systems in the Digital Age: Underlying Challenges and New Opportunities Part I. A Review of the Problems, Classic Protocols of Collective Choice. Scientific Bulletin of the National Academy of Statistics, Accounting and Audit, (4), 113-124. Retrieved from https://nasoa-journal.com.ua/index.php/journal/article/view/233