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An investigation of new methods of mathematical modelling and mechanism design in the social, economic and political sciences

2013
The project has been carried out as part of the HSE Program of Fundamental Studies.

Research objects: models and methods of decision making theory and intelligent data analysis.

Object of research: models and methods of decision-making theory and intelligent data analysis

Research goals: study of new methods and approaches in the field of mathematical modelling and design of mechanisms in the social, economic and political sciences

 

Methodology:  social choice theory, game theory, multi-criteria decision-making, intellectual data analysis. The mathematical methods used in the study are optimization methods and methods of combinatorics, cluster analysis, probability theory, statistics, etc. Applied studies used internet data, economic journal databases and a database of university entrants.

Application of results:The results obtained find applicationin regulating the energy and banking sectors, analysis of ethnic and political tensions, analysis of influential groups in elected bodies, multi-criteria decision making, computational text interpretation and analyses of internet data, uncertainty analysis of expert information, ranking alternatives and constructing aggregate ratings, organizing admissions in universities, and research into universities’ effectiveness.

The following results were obtained:

‒ the analytical decision rule with the values of criteria importance measured on an ordinal scale, and the optimization decision rule for problems with criteria measured on the first ordinal metric scale were elaborated

‒ a modification of the Nitzan‒Kelly index for evaluating coalitional manipulability of social choice rules was proposed; the maximal difference of probabilistic measures in IAC and IANC models was studied; the representation of threshold procedure as a scoring rule was found

‒ the problem of determining regions of the Russian Federation that have a similar development structure was solved by the pattern analysis method of socio-economic development indicators

‒ a new model of data envelopment analysis that takes into account the heterogeneity of the set of objects was proposed and elaborated

‒ a simulation model of the stock exchange, which uses information about different types of players and their possible interaction, was constructed

‒ a modelling of the optimal hedge ratio given inter-day and intraday risk trading positions was conducted within an analysis of financial sector effectiveness

‒ a choice of strategy in terms of bank regulatory actions involving systemically important banks was analyzed on the basis of the previously developed game-theory models of strategic interaction between banks

‒ five new (aggregated) ratings of economics, management and political science journals were constructed using ordinal aggregation methods of known bibliometric indicators by applying the theory of social choice for constructing rankings in various applied problems

‒ direct and superposition (two-stage) social choice procedures were studied for their compliance with conditions of rationality, monotonicity and threshold uncompensability

‒ several problems for finding optimal output power generator and determining the competitiveness of renewable energy sources and electricity storage systems were investigated within the development of organizational models and mechanisms

‒ the generalized problem of bankruptcy was investigated, which is closer to the actual economic practice than its classic formulation

‒ a new method was proposed and investigated for analyzing the formation of cartels as a non-cooperative game in which players (firms) are the strategies of the coalition

‒ in the study of double-sided matchings the existence of a stable matching was proven in cases when preferences are interval orders; the relationship between stable matchings and generalized systems of passing scores of universities was shown

‒ generalized power indices depending on participants’ preferences were studied axiomatically; the relationship between these indices and classical indices was shown; the mean value theorem for generalized power indices was proven

‒ ethnic heterogeneity using major indexes was analyzed in the study of models of ethnic and political tension, ethnic heterogeneity index application in various problems of socio-economic and political analysis was considered

‒ change in the influence of groups and factions in Ukraine’s Verkhovna Rada for the period 1990‒2012 were analyzed in the framework of applying power indices

‒ a general methodology of data aggregation (summarization) was developed in the framework of research on cluster analysis and computational text interpretation; the effectiveness of a previously developed measure of proximity based on the annotated suffix tree compared with the two most popular methods was shown

‒ a concept of volatility in the cluster analysis of the data was introduced and studied; a new clustering algorithm was developed based on the computing of volatility

‒ an index of ignorance decreasing when combining evidence and conflict measure between the evidence was determined and studied within the Dempster‒Shafer theory; the relationship between conflict measure and index decreasing of ignorance for different types of evidence was studied numerically and analytically

‒ global asymmetry measures and functionals for non-noisy and noisy images were introduced and studied in the framework of stability studies for finding parameters of image symmetry

Foreign partners:

 

1)  Prof. Claude d'Aspremont,PhD, Center for Operations Research and Econometrics, Université Catholique de Louvain, Louvain-la-Neuve, Belgium, http://www.core.ucl.ac.be/OFFICES/CVs/CV_D'ASPREMONT_Claude.pdf;

2) Prof. Hannu Salonen, PhD, Department of Economics and PCRC, University of Turku, Finland, http://www.utu.fi/en/units/tse/units/department-economics/contact_information/personnel/Pages/Hannu-Salonen.aspx;

3) Prof. Walter Trockel, PhD, Institute of Mathematical Economics at Bielefeld University, http://www.imw.uni-bielefeld.de/n/index.php?option=com_content&view=article&id=83&Itemid=76;

4) Prof. Gerhard-Wilhelm Weber, PhD, Institute of Applied Mathematics, Middle East Technical University, http://www.mendeley.com/profiles/gerhard-wilhelm-weber/;

5) Prof. Anna Khmelnitskaya, PhD, University of Twente, The Netherlands http://wwwhome.math.utwente.nl/~khmelnitskayaab/

Publications:


Лепский А. Е. Об оценивании конфликта и уменьшения незнания в теории Демпстера-Шейфера // В кн.: Сборник научных трудов VII международной конференции «Интегрированные модели и мягкие вычисления в искусственном интеллекте», Коломна, 20-22 мая 2013 года Т. 1. Физматлит, 2013. С. 436-448.
Podinovski, Podinovskaya (Olga V. Podinovskaya). New multicriterial decision rules in criteria importance theory / Пер. с рус. // Доклады Академии наук. 2013. Vol. 88. No. 1. P. 486-488.
Podinovski. Potential optimality of Pareto optima // Pocedia computer science. 2013. Vol. 17. P. 1107-1112.
Рубчинский А. А. Квазисправедливый делёж с несколькими участниками // В кн.: XIII Международная научная конференция по проблемам развития экономики и общества. В 4 кн. Кн. 2. / Отв. ред.: Е. Г. Ясин. Кн. 2. М. : Издательский дом НИУ ВШЭ, 2012. С. 387-395.
Подиновский В. В. Количественная важность критериев и аддитивные функции ценности // Журнал вычислительной математики и математической физики. 2013. Т. 53. № 1. С. 133-142.
Подиновский В. В., Подиновская О. В. Новые многокритериальные решающие правила в теории важности критериев // Доклады Академии наук. 2013. Т. 451. № 1. С. 21-23.
Merikas A., Merika A., Penikas H. I. Dry Bulk Time Charter Rates Joint Return Distribution Modeling: Copula-Approach // Procedia Computer Science. 2013. Vol. 17. P. 1125-1133. doi
Lepskiy A. Estimation of Conflict and Decreasing of Ignorance in Dempster-Shafer Theory // Procedia Computer Science. 2013. Vol. 17. P. 1113-1120. doi
Сборник научных трудов VII международной конференции «Интегрированные модели и мягкие вычисления в искусственном интеллекте», Коломна, 20-22 мая 2013 года Т. 1. Физматлит, 2013.
Веселова Ю. А. Сложность порядковых правил коллективного выбора
Алескеров Ф. Т., Гохберг Л. М., Егорова Л. Г., Сагиева Г. С., Мячин А. Л. Анализ данных науки, образования и инновационной деятельности с использованием методов анализа паттернов / Высшая школа экономики. Серия WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2012. № 07.
Lepskiy A. Determination of Symmetry Parameters of Objects in Noisy Images // Pattern Recognition and Image Analysis. 2013. Vol. 23. P. 408-414.
Mirkin B. Choosing the number of clusters // WIREs Data Mining and Knowledge Discovery. 2011. No. 3. P. 252-260.
Субочев А. Н., Алескеров Ф. Т., Писляков В. В. Построение рейтингов журналов по экономике с помощью методов теории коллективного выбора / Издательский дом ВШЭ. Серия WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2013. № 3.
Камалова Р. У. Уровень экономического развития как фактор динамики уровня демократии в посткоммунистических государствах // В кн.: Труды семинара «Математическое моделирование политических систем и процессов» / Под общ. ред.: А. С. Ахременко. Вып. 2. М. : Издательство Московского университета, 2013. С. 69-90.
Aleskerov F. T., Petrushchenko S. DEA by sequential exclusion of alternatives / Издательский дом ВШЭ. Series WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2013. No. WP7/2013/02.
Миркин Б. Г. О ПОНЯТИИ НАУЧНОГО ВКЛАДА И ЕГО ИЗМЕРИТЕЛЯХ // Управление большими системами: сборник трудов. 2013. С. 1-16.
Aleskerov F. T., Holler M., Kamalova R. Power distribution in the Weimar Reichstag in 1919-1933 // Annals of Operations Research. 2014. Vol. 215. No. 1. P. 25-37. doi
Péter Biró, Kiselgof S. G. College admissions with stable score - limits / Institute of Economics, Research Centre for Economic and Regional Studies, Hungarian Academy of Sciences. Series MT-DP "Discussion Papers of Hungarian Academy of Sciences". 2013. No. 6.
Bronevich A. G., Lepskiy A., Umansky V., Yakushev D. Recognition of Cross Profiles of Roadbed Based on Polygonal Representations, in: Proc. 5th International Conference Pattern Recognition and Machine Intelligence (PReMI'2013) Vol. LNCS 8251. Berlin, Heidelberg : Springer, 2013. P. 270-276.
Lepskiy A. About Relation between the Measure of Conflict and Decreasing of Ignorance in Theory of Evidence, in: Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13). P., Beijing, Amsterdam : Atlantis Press, 2013. P. 355-362.
Veselova Y. A. The manipulability index in the IANC model, in: Clusters, orders, trees: methods and applications. In Honor of Boris Mirkin's 70th Birthday / Ed. by F. T. Aleskerov, B. I. Goldengorin, P. M. Pardalos. Vol. 92. Berlin : Springer, 2014. P. 391-404.
Vladislav V. Podinovski. Non-dominance and potential optimality for partial preference relations // European Journal of Operational Research. 2013. Vol. 229. P. 482-486. doi
Mirkin B. Summary and semi-average similarity criteria for individual clusters, in: Models, Algorithms, and Technologies for Network Analysis / Ed. by Boris I. Goldengorin, Valery A. Kalyagin, Panos M. Pardalos. Vol. 59. NY : Springer, 2013. P. 101-126.
Mirkin B., Svetlova L., Lei H. MFWK-Means: Minkowski Metric Fuzzy Weighted K-Means for high dimensional data clustering, in: Information Reuse and Integration (Proceedings of the 2013 IEEE 14th International Conference on Information Reuse and Integration). Piscataway : IEEE, 2013. P. 692-699.
Mirkin B., Nascimento S., Felizardo R. Laplacian normalization for deriving thematic fuzzy clusters with an additive spectral approach // Expert Systems: The Journal of Knowledge Engineering. 2013. Vol. 30. No. 4. P. 294-305.
Péter Biró, Sofya Kiselgof. College admissions with stable score-limits // Central European Journal of Operations Research. 2015. Vol. 23. No. 4. P. 727-741. doi
Fuad Aleskerov, Evgeny Mitichkin, Sergey Shvydun, Vyacheslav Yakuba. Super-threshold Procedures and Their Application to the Search Problem // Procedia Computer Science. 2013. No. 17. P. 1121-1124. doi