Technical characteristics of the report: volume – 458 pages, 1 part, 65 figures, 69 tables, 330 references.
Keywords: design of economic mechanisms, decision making theory, social choice theory, game theory, imprecise probability, data mining.
Research objects:models and methods of decision making theory and intelligent data analysis.
Research goals: obtaining of new theoretical and applied results in mathematical modeling and design of mechanisms in the social, economic and political spheres, using methods of decision theory, game theory, and data mining.
Methodology: rational choice theory, game theory, criteria importance theory,intellectual data analysis. Mathematical methods used in the study are different numerical methods and the methods of combinatorics, cluster analysis, probability theory, statistics, etc.
For applied studies, internet data was used, economic journals databases and database of university entrants.
The following results have been obtained:
- algebraic properties of probabilistic models IANC (Impartial Anonymous and Neutral Culture model) in the problem of estimating the degree of manipulability of social choice rules;
- it has been shown that the problems of the organization of public-private partnerships can be considered as game problems on polyhedral sets of admissible strategies of the players; these problems may be solved via tender procedures;
- it has been shown that the benefits from the choice of procedure for voting at elections to the Board of Directors of the company depends on the ownership structure;
- the pro-cyclical effect of the introduction of the system of banking regulation Basel II has been analyzed; the recommendations to reduce this effect are given;
- the dependence of European banks using derivatives of the value of these organizations has been investigated;
- two analytical ordinal decision rules and one algorithmic ordinal decision rule have been developed for multi-criteria decision-making problems in the framework of the theory of importance of the criteria;
- the modified method of analyzing text using annotated suffix trees has been used to establish the relationships between a set of texts and key phrases, to establish the relationships between a set of texts and the taxonomy of the subject field;
- averaged stochastic measures of informativeness, defined on the set of random features of non-deterministic have been introduced and studied, some optimization problems of finding minimal and stable to noisy representations of contour images using geometric measures of informativeness in length have been stated and investigated;
- the optimization problem of finding of threshold of separation crisis and regular events have been formulated and solved in the framework of study of behavioral model of stock exchange;
- the problem of coincidence of positions of candidates in probabilistic models of voting in case of a marginal neutrality of voters with converging positions has been investigated;
- axioms for major indices of influence in the problem of voting with the quota have been constructed;
- the problem of expansion of the classical model of matchings for the case of preferences being simple semi-orders has been investigated;
- an aggregated ranking of countries according to their level of democratic development and the classification of countries according to their competitiveness have been constructed with the application of theory of choice and ranking of alternatives in the majority graph;
- the most general statement of fair division problem has been studied for different definitions of fairness, the general structure of the attainable set is defined, the algorithm for finding a finite set in the space of income has been developed;
- algorithms for choosing the alternatives from large sets (in particular, for Internet data) have been developed or modified;
- the potential of Russian universities has been analyzed using Data Envelopment Analysis Model.
The area of application of obtained results includes voting procedures construction and analysis, multi-criteria choice, pattern recognition, internet search, ranking alternatives and building aggregated rankings, organizing college admission process.
1) Prof. Kenneth Joseph Arrow, PhD, Stanford University, California, USA,http://en.wikipedia.org/wiki/Kenneth_Arrow;
2) Prof. Eyal Winter, PhD, Director of the Center for the Study of Rationality the Hebrew University of Jerusalem, Israel, http://www.ma.huji.ac.il/~mseyal/documents/VitaeDec11.pdf;
3) Prof. HannuVartiainen, PhD, Director of Helsinki Center of Economic Research (HECER) and Finnish Doctoral Programme in Economics (FDPE) University of Helsinki, Finland, http://personal.inet.fi/tiede/yjs-hv/;
4) Prof. R. Tyrrell Rockafellar,PhD, University of Washington, Seattle, USA, http://en.wikipedia.org/wiki/R._Tyrrell_Rockafellar;
5) Prof. Shmuel Zamir, PhD, Center for the Study of Rationality of Hebrew University of Jerusalem, Israel,http://www.ma.huji.ac.il/~zamir/;
6) 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;
7) Prof. Stan Uryasev,PhD, Director of the Risk Management and Financial Engineering Lab and Director of PhD Program with Concentration in Quantitative Finance at the University of Florida, USA,http://www.ise.ufl.edu/uryasev/;
8) Prof. Trevor Fenner, PhD, University of London, UK, http://www.dcs.bbk.ac.uk/~trevor/;
9) Prof. Fred McMorris, PhD, Illinois Institute of Technology, Chicago, USA, http://www.iit.edu/csl/about/dean/pdfs/mcmorris_vita_web_08S.pdf;
10) Dr. Susana Nascimento, PhD, New University of Lisbon, Portugal, http://centria.di.fct.unl.pt/~snt/;
11) Prof. Fred Roberts, PhD, Rutgers University, New Jersey, USA, http://cait.rutgers.edu/cait/fred-roberts.