The development of information and communication technologies and computing power leads to the emergence of additional opportunities for modeling political processes. In the past decades, mathematical models have been developed mainly in a game-theoretic setting; today we witness an expanding stream of research applying agent-based (multi-agent) approach. This trend is quite natural. There have been changes in political participation and in the forms of collective interaction of individuals and groups, induced by digital technologies. Researchers have developed theoretical approaches to political participation, focusing on the network interaction and implementing the “bottom-up” logic that infers the macro-properties of the system from the characteristics and interactions of individual agents. Thus, the theoretical foundations for an agent-based modeling, most promising in its network version, have been developed. This approach, however, required a more complex description of the individual motivation and decision making in comparison to the dominant game-theoretic paradigm. One of the key points is that motivation is considered to be linked to the network position of agents, since the individual is guided by the actions of her neighbors. Thus, the course of the political process is determined not only by the properties and decisions of its participants, but also by the type of network architecture that connects them. Within this research framework, a computational experiment, assuming a controlled variation of parameters, plays a special role. Two main strategies of such an experiment are considered: the grid search and the Monte Carlo method. The prospects of agent-based modeling in its network form are related to the study of the dynamical political processes, taking into account the structures of trust and social capital, as well as the resources and mechanisms of collective action.

The advent of social media and increased digitization of social pro- cesses have had a dramatic impact on politics and, particularly, on political mobilization and communication. The political science methodology and toolkit have also adapted to these changes and absorbed a variety of new approaches and methods from the burgeoning field of data science. This paper provides an overview of some of the key methodological innovations to the political science toolkit drawn from data science and discusses the advantages and limitations of these new methods for studying protest activity and political mobilization in social media. We focus on supervised and unsupervised learning as two major groups of methods that can be applied to either facilitate data collection in almost real time or the analysis of big data on protest activity. We discuss overfitting, regularization, and hyperparameter selection via cross-validation in the context of supervised methods, and present topic modeling and social network analysis techniques within unsupervised methods. The strengths and weaknesses of these methods are illustrated with references to recent articles published in peer-reviewed journals. We conclude the paper with a discussion of the emerging methods that have not been used in political mobilization research yet and are open for further exploration by political scientists.

In this paper, I consider opportunities and limitations of modelling the political dynamics with the time-series instruments. Using the examples of the president Putin’s approval rating and readiness to join the collective actions with economic demands I demonstrate the analytical potential of autoregressive integrated moving ave- rage model (ARIMA), autoregressive distributed lag model (ADL), and error correction model (ECM). Modelling the political dynamics faces a string of analytical dilemmas. This paper aims at identifying the basic choices in application of the statistical instruments to dynamic processes and helping the other researchers to navigate through them. While it is hard to account in a single paper for all the developments in the discipline, which has been substantially advanced substantially and technically i the last three decades, this text also aims at stimulating the discussion on the opportunities and limitations when applied to Russian politics.

This paper serves as an exposition of the causal inference methods that are most popular in political science. Rather than focusing on technical details we present a brief summary of main ideas behind each method with the goal of making them accessible to a broad audience of researchers. We also provide a research design algorithm for each method. First, we focus on a general motivation behind causal inference methods. We discuss how the problem of causality arises in hypothesis testing and describe the relationship between democracy and economic development as a case in point. Second, we give an exposition of a general causality problem within the framework of Rubin Causal Model (RCM). We provide all basic definitions and then demonstrate how the problem of causal inference arise within RCM. Third, we describe the most frequently used methods of causal inference such as randomized experiments, regression discontinuity design, difference-in-difference design, and instrumental variables. For each method we give a reader a general description as well as steps of a research design. We also briefly discuss advantages and disadvantages of each method. Armed with this knowledge, a reader can use it to find the method that is the most appropriate for a research problem at hand. We conclude by arguing that the ideas of causal inference are useful for both quantitative and qualitative research.

The work is devoted to the urgent problem of the danger of the growth of extremist sentiments among young people caused by unpredictable changes in ideological attitudes (attitudes) in the group consciousness. Objectives: study of the dynamics of peripheral ideological concepts - one of the structural elements of ideo- logy; identifying the trend of changes in the ideological attitudes of student youth on the example of the South of Russia; assessment of the predictive capabilities of the system dynamic analysis methodology for calculating the dynamics of ideological processes. An attempt was made to approbate the author's method of studying ideological attitudes, which could be conditionally called quantitative narrative analysis. The empirical base was made up of data from a survey of 2500 students in the South of Russia and the results of a five-year monitoring of the development of the ideological situation. The theoretical basis is the morphological approach to the study of ideologies by Michael Frieden and the concept of the cognitive-ideological matrix. In the deve- lopment of this concept, the focus of the study was shifted from the morphology (structure) of ideologies to implicit processes occurring at the border of the cognitive-ideological matrix and the social environment. As a result, a descriptive mental model of peripheral ideological concepts and a conceptual model of their migration based on the Bass diffusion model were built, performed in the AnyLogic simulation system. The result of the study was the identification of a left-liberal trend using narrative analysis, which had replaced the significant predominance of conservative and national-patriotic ideological attitudes in the group youth consciousness. It is concluded that the model of migration of peripheral ideological concepts, created using the method of system dynamics and mathematical statistics, significantly expands the possibilities of forecasting ideological processes, but has some limitations.

The article deals with the methodological problems of quantitative studies of political regimes and regime transformations in the Arab Middle East. Special attention is given to the questions of conceptualization, operationalization and typology of political regimes and regime changes since the quantitative research results depend on the datasets used. The article considers two approaches to operationalization, categorization and quantification, which are aimed either at distinguishing of separate unordered categories, or at measuring and linear placement of the observations on the axis. The conceptual problems reviewed include conceptual stretching and operationalization of successful and unsuccessful regime transformations. The article states that structural approach dominates in the quantitative research of regime changes since the conditions and cause-and-effect relationships between contextual factors and the risk of regime change are studied. The article shows how the regime changes can be quantitatively studied at the global, regional and country levels. The article concludes that the structural approach in quantitative studies is methodologically correct since a large number of hypotheses can be tested, but the main disadvantage of such studies is the explanation of different political regime changes by the same set of nonpolitical factors. The quantitative analysis of the Arab spring on the basis of Arab Barometer at the level of individuals revealed the significance of the high education, employment, male gender, religiosity an young age. The article shows that survey provide rich data for quantitative research with large numbers of observations, but the quality of the conclusions will depend on the quality of survey data.

The article is dedicated to the development of the political communities in social networks analysis methods. Main stages of network approach in the political science is described in the research. Researchers review the most significant methods and techniques in the political online communities studies for the last decade. The article shows the contemporary Russian scientists contribution in the development of online communities learning techniques. Networks and social network analysis methods and techniques become universal scientific approaches for several scientific fields. Boundary-transcending trends were critical means of science integration. Researchers present the results of experiment in which evaluate the possibilities of study unobserved political groups using latent Dirichlet allocation (LDA) model. The brief LDA foundation history and possible modifications for social topic modeling based on social networks data are discribed in the review. Using sample from one feed aggregator telegram channel in period of 2020 autumn, the authors display the most valuable topics in the Russian segment of political communication. Also it provides communities ideological preferences. Modified qualitative sociological methods can be used in online political communities discursive features research without any specific computer science techniques. Since about 70% of the Internet data are generated in the social networks, velocity and volume data necessitate new data mining techniques, databases capacity and computation processes. In other words, it provides a big data approach in social network analysis.

The study of the features of the reproduction of political ideologies in social networks and the formation of user communities united by adherence to some political ideas is an urgent problem of contemporary political science. Social media has become an agent for the development of new forms of political activity, providing unprecedented opportunities for transferring and exchanging information, broadcasting political ideas, and involving people in virtual and real communities. Today, social media have become not just a means of transmitting information and a form of entertainment, but a special global form of social political interaction, increasingly penetrating into the most diverse aspects of society. In political interactions, the online services of new media can be described as a “third space”, a development of Ray Oldenburg's concept, in which he singles out a part of the social space not related to housing (“first place”) and work (“second place”). Online communities on social networks have become a mixed form of institutionalized political and informal non-political interactions, as exemplified by ideologically based social media groups. The transformations caused by the rapid development of the Internet and “new social media” are giving rise to a fundamentally new reality of social interaction, which combines two contradictory trends. On the one hand, the Internet and social media have expanded people's access to information and significantly increased the field of social interaction and communication, thereby creating the basis for uniting users on various grounds, including political and ideological views. On the other hand, such changes led to a crisis of trust between the participants. Users belonging to different political ideologies form stable “echo chambers” in their Internet environment, rigidly filtering the information they receive, locking themselves in and reproducing the attributes of only their political ideology and not allowing outsiders there. In our opinion, this requires a study that provides for a close study of ideological “echo chambers”, which seems necessary for understanding the processes of political communication and ways of reproducing political and ideological views in the online sphere.

Correlation coefficients between the results of political parties in the 2016 State Duma elections in the Russian Federation as a whole and in 26 regions, as well as in the elections of regional parliaments of 35 subjects of the Russian Federation in 2012-2015 were calculated. For the 2016 State Duma elections, data was used at all levels - regions, single-member electoral districts, TEC and PEC. It is noted that the “United Russia” correlations with all major parties are generally negative. A fairly high level of correlation is observed between the liberal parties. The main focus is on correlations between parliamentary opposition parties and parties with similar names. The correlation coefficients between the results of parties and candidates in the State Duma elections of 2011 and 2016 and the Presidential elections of 2012 and 2018 were also calculated, showing the stability of the geographical distribution of the electorate of the main parties. Regional differences in the nature of correlations between the main political parties are noted. It is assumed that correlations between parties reflect not so much their ideological closeness as the social closeness of their electorate. In this regard, it is noted that a positive correlation between the results of ideologically distant parties (“Yabloko” and the Communist party or “Yabloko” and “Rodina”) is associated with their reliance on the urban electorate and, perhaps, its most educated part. The reasons for voting for spoiler parties and the role of these parties in reducing the results of the main participants in the elections are discussed.

We can face the fact that the factor of military power has been gaining increasing influence in the world politics. In this regard one of key tasks of international relations` studies is the exploration of armed forces` building of the countries in the dynamics. The creating a three-dimensional picture of these processes is difficult without the use of mathematical indicators, which show the key features and “narrow places” of the development and the usage of war machines’ potential of the key countries in the world arena.
In this article the focal case of these studies with the usage of mathematical assessments is the Bundeswehr. The reason of the given choice is the changing German role and place in the Euro-Atlantic community and the world arena as the whole. Germany has been trying to become the status of full-fare world power. One of the inherent features of this process is the growing of the Bundeswehr`s potential that had begun in the second half of 2010-s and has had the perspective by the middle 2030-s.
The article presents mathematical indicators that allow to show a more voluminous assessment of the progress of building the Bundeswehr's potential and German military budget (both in general and in terms of articles of spending and other specific indicators) in comparison with other largest NATO member states. The research paper also examines the indicators that make it possible to “highlight” the peculiarities of the
Bundeswehr’s usage outside and inside the NATO zone of responsibility as well as issues the evolution of the foreign (allied) military presence on the territory of the FRG. The author tries to conclude the generalizations of German “war machine” development, basing on 11 mathematical indicators, 6 of which introduced into scientific circulation for the first time.

The article analyzes the perception of the USSR of Russian citizens. The case of the Moscow inhabitants’ narratives shows what the peculiarities of the image of the Soviet Union, and how the characteristics of socialization and other individual and collective experience influence the evaluation of the Soviet past and its legacy. The theoretical framework of the study is relied on the concept of nostalgia as a selective, changing, fragmented mnemonic phenomenon. The findings of the article are based on the results of an in-depth interview (N=11), which showed that people of different generations with different levels of education and disparate life experiences had a variety of perception of the Soviet past. Its formation largely depended on the context, including the characteristics of socialization. The representations of the older genera- tion about the Soviet Union are more holistic, the family played the main role in formation of their pictures of Soviet past. The image of the USSR among the younger generation is more contradictory and fragmentary, and social and political institutions played a significant role in its formation. Despite critical remarks about the USSR, the informants showed nostalgic sentiments. A comparison of the statements of the respondents about the present day and the Soviet times allows us to conclude that the main elements shaping these sentiments are a lack of feelings of unity and pride in the country, as well as a lack of a sense of the state's concern for people.

The article analyses the place of the Soviet past issues in the interparty discussion in contemporary Russia. The methodology of the study is based on the cleavage theory and the issue dimensions theory which consider confrontation as the engine of the political life. The lists of issues and most active participants are formed on the base of issue salience and issue ownership criteria. Factor analysis of party positions on these issues revealed two divisions: ‘Communists vs Anticommunists’ and ‘Liberals vs Statists’.
Factor loadings of these divisions are compared with parties' factor loadings in political dimensions on a wider range of issues: three main ones (systemic, authoritarian-democratic, socioeconomic) and seven additional – in three issues domains: domestic policy, social and economic policy, systemic domain (international relations + worldviews). It is detected that the ‘Communists vs Anticommunists’ division correlates well with the main socioeconomic dimension and its subtype ‘Communists vs Liberals’, but most strongly – with a sub-dimension ‘Soviet traditionalists vs Progressives’ from the systemic domain. The ‘Liberals vs Statists’ division appeared to correlate closely with the main authoritarian-democratic dimension, but much more – with the subtype ‘Liberals vs Loyalists’ from the domestic policy issue domain. It is concluded that the divisions on the issues of the Soviet past easily fit into the picture of political dimensions and even get lost in it.
Comparison of divisions over the Soviet past with electoral cleavages shows that these issues are not very important for the mass mind. High correlation coefficients are devalued by high p-levels, indicating that there is a typical “third factor” effect in the case. 

This article attempts to identify the main assumptions, prerequisites and techniques of the methods developed by some modern statisticians on the basis of T. Bayes' theorem for the purposes of social variables interactions assessment. The author underlined several advantages of the given approach as compared to more traditional quantitative methods and highlighted key research areas subject to evaluation by Bayesian estimates. First of all, this approach is compatible with game and decision theory, event analysis, hidden Markov chains, prediction using neural networks and other predictive algorithms of artificial intelligence.
The Bayesian approach differs significantly from traditional statistical methods (first of all, it is focused on finding the most probable, rather than the only true value of the feature coupling coefficient), hence a graphical interpretation was provided for such basic concepts and techniques as probabilistic inference, maximum likelihood estimation and Bayesian confidence network.
The described tools were used to test the hypothesis about the impact of life quality decrease on rise in Euroscepticism of EU citizens. ANOVA and correlation analysis of 27 thousand people’s responses to Eurobarometer questions addressed in November-December 2019 attributed strong likelihood to this assumption. Moreover, Bayesian approach allowed for a probabilistic conclusion that this hypothesis is more plausible than the link between Euroscepticism and respondents’ current financial situation (explanatory power of comparison to the past is relatively greater).