Polarized Ukraine 2014: Opinion and Territorial Split Demonstrated with the Bounded Confidence XY Model, Parameterized by Twitter Data

TL;DR

This paper combines social media analysis and agent-based modeling to understand Ukraine's 2014 polarization, revealing emotional intensity as a key factor driving sudden shifts in opinion and collective behavior.

Contribution

It introduces a novel approach by parameterizing an extended Bounded-Confidence XY Model with Twitter data to analyze polarization dynamics in Ukraine.

Findings

Emotional intensity significantly influences polarization transitions.

A critical emotional intensity level triggers a sudden increase in opinion bimodality.

The model captures spatiotemporal polarization patterns during Ukraine's crisis.

Abstract

Multiple countries have recently experienced extreme political polarization, which in some cases led to escalation of hate crime, violence and political instability. Beside the much discussed presidential elections in the United States and France, Britain's Brexit vote and Turkish constitutional referendum, showed signs of extreme polarization. Among the countries affected, Ukraine faced some of the gravest consequences. In an attempt to understand the mechanisms of these phenomena, we here combine social media analysis with agent-based modeling of opinion dynamics, targeting Ukraine's crisis of 2014. We use Twitter data to quantify changes in the opinion divide and parameterize an extended Bounded-Confidence XY Model, which provides a spatiotemporal description of the polarization dynamics. We demonstrate that the level of emotional intensity is a major driving force for polarization that can lead to a spontaneous onset of collective behavior at a certain degree of homophily and conformity. We find that the critical level of emotional intensity corresponds to a polarization transition, marked by a sudden increase in the degree of involvement and in the opinion bimodality.

Equations

$${\theta }_i(t+\Delta t)={\tan }^{-1}\left[\frac{1}{N}\frac{{\sum }_{j,|j-i|\le r}{p}_j\sin ({\theta }_j(t))}{{\sum }_{j,|j-i|\le r}{p}_j\cos ({\theta }_j(t))}\right]+\xi (\eta ,t),$$

$$\phi =\frac{1}{N}\left|\sum _{j=1}^N\exp (ı{\theta }_j)\right|,$$

$$Q=\left|\frac{1}{N}\sum _{j=1}^N\exp (ı2{\theta }_j)\right|.$$

$$\gamma =\frac{{\mu }_3}{{\mu }_2^{3/2}},$$

$$k=\frac{{\mu }_4}{{\mu }_2^2},$$

Full text

I Introduction

Ukraine represents a bright example of a nearly evenly split society with two opposing camps, where the East/South gravitates towards Russia while the West/North towards European neighbors Belletal14 . The overall political vector in the country sways between political parties and leaders that on the one side seek closer ties to the West and in particular Europe and on the other hand to the East and in particular Russia. The Orange Revolution in 2004 brought pro-western politicians to power, however, in the 2010 elections a pro-eastern politician, Viktor Yanukovych, was elected for president, not least because of major support in the eastern regions of Ukraine (see Fig. 1). In November 2013, after Yanukovych failed to sign a political association and free trade agreement with the European Union, protests in Ukraine erupted. The initially peaceful rallies became violent in January 2014 after the government passed laws to suppress the protests. In February 2014, the violence escalated, which led to the removal of Yanukovych from office by the parliament. Meanwhile a separatist and anti-interim-government movement rose with the support of Russia in eastern and southern parts of Ukraine, and ignited a military conflict. Crimea was annexed by the Russian Federation after a referendum that was denounced internationally as illegitimate and illegal. Later in 2014, the crisis resulted in further territorial separation with over 2.6 million internally displaced persons and refugees and a formation of self-proclaimed states in Donetsk and Luhansk EuropeanCommission16 . These events escalated the polarization in the country that has grown over the years. As the two political sides became more extreme in their views in the course of the events a dialogue and therefore a peaceful solution has become increasingly difficult. The extreme opinion divide affected not only society as a whole but also destabilized multiple families and local communities.

In this paper, we present a novel approach, in which we combine rich social media data with the power of methods of statistical physics, to study political opinion polarization mechanisms, seeking to understand what mechanisms turned Ukraine into a irreconcilably polarized state. Though the integration of the two approaches has been increasingly discussed HelbingBalietti11 ; BirkinMalleson12 , there are only few studies so far that have actually attempted to combine these Serranoetal15 ; Randetal15 ; goncalvez.b:2011 ; weng.l:2012 ; takayasu.m:2015 . None of them, however, studies polarization and integrates the unstructured data analysis comprehensively with the computational model. In the past studies there has been a methodological gap between the social media analysis and agent-based modeling, which has limited the relation between the two to rather qualitative statements. We are presenting an approach here that elaborately links the two approaches. Combining them has the advantage to parameterize the computational model and validate it by empirical evidence and on the other hand to make use of the rich social media data in a theory-guided way beyond mere descriptives. This holds the potential to gain new insights into the underlying social mechanisms of polarization. In the following, we will describe a new computational model of polarization, a 2D lattice agent-based model, that is informed by the theoretical work on polarization discussed below and that brings in the spatial dimension and emphasizes the role of regional differences. We then look at the empirical polarization dynamics in the Ukrainian Twittersphere, before parameterizing the model with the analyzed Twitter data, hereby validating the model. The combination of the two approaches reveals the important role that emotional intensity levels play in polarization thus far not sufficiently accounted for by classical theoretical or empirical studies of polarization. The few studies that investigate the role of emotions in polarization have usually focussed on very specific emotions, e.g. “self-conscious” emotions like pride and embarrassment/shame and showed that these emotions can reinforce conformity and polarization Suhay15 . In this paper, we do not focus on specific emotions, but, rather examine the role of emotional intensity levels and show how these emotional intensity levels can be a decisive driver in polarization.

II Opinion Polarization

Opinion polarization has been intensely studied over the last few decades, initiated by the observation that groups tend to adopt positions that are more extreme than the initial individual positions of its members Isenberg86 ; MoscoviciZavalloni69 . One explanation of this phenomenon is based on the Social Comparison Theory, which suggests that people want to be perceived in a more favorable way than what we perceive to be the average tendency. Through observations they determine what the average tendency is and then they express a slightly more extreme opinion than the perceived average opinion Isenberg86 ; DeGroot74 ; Sunstein02 . There is clear evidence for this assumption from numerous experimental studies Isenberg86 ; BaronRoper76 ; Myersetak77 . Moreover, due to the homophily phenomenon McPhersonetal01 , which states that people are more likely to interact with those who are similar to them with respect to socio-economic background Currarinietal09 as well as attitudes Dandekaretal13 , people are more likely to socially compare themselves to similar peers. Group polarization phenomena are also explained drawing on the Persuasive Argument Theory, which states that people are more likely to change their opinion when presented with persuasive arguments. Group polarization can occur when the group discourse is manipulated through biased information or misinformation, exposing a group to false persuasive arguments Isenberg86 ; Sunstein02 ; Burnstein82 . The theory is strongly supported by empirical evidence from numerous experimental studies Isenberg86 ; EbbsenBowers74 ; VinokurBurnstein78 . The two mechanisms, social comparison and persuasive argument usually co-occur. For instance, persuasive arguments in an environment of biased information can further push an individual to adopt a more extreme attitude than expressed in the group they compare themselves to. Another mechanism with respect to polarization dynamics is the Biased Assimilation LordLepper79 in opinion formation processes, which maintains that people are likely to keep their original position and draw support for it if confronted with mixed or inconclusive arguments. This mechanism, which again is empirically well established Milleretal93 ; Munro02 ; TaberLodge06 , shows that people are only to a limited extent open to change their opinions and this can contribute to polarization dynamics. In fact, Dandekar et al. Dandekaretal13 show that the two earlier described mechanisms and in particular the social comparison mechanism, is not sufficient to produce polarization, the biased assimilation mechanism has to be added.

Polarization processes have been empirically investigated through experimental studies as mentioned previously and to a lesser extent through survey based studies Baker05 ; Dimocketal14 . Furthermore, applied statistical physics and agent-based modeling approaches Dandekaretal13 ; BaldassarriBearman07 ; Castellanoetal09 ; Masetal13 have been used extensively to study polarization mechanisms through computer simulations. Prominent are for instance bounded confidence models of opinion dynamics, stochastic models for the evolution of continuous-valued opinions within a finite group of individuals that explore conditions for consensus and opinion fragmentation, introduced by Deffuant et al. Deffuantetal00 and further elaborated by numerous studies HegselmannKrause ; Fortunatoetal05 ; Lorenz07 . We will draw inspiration from these models as well. The challenges of using statistical physics models for modeling social phenomena are known. The tractable models are usually oversimplified and too general and thus lack flexibility required to reflect the features of a particular social phenomena. Moreover, while computational studies are rigorous in investigating the specific mechanisms and dynamics of polarization they often lack empirical foundation and thus it remains often unclear to what extent these often abstract models accurately represent phenomena we see in real world. More recently, social media (e.g. Twitter and Facebook) data have been increasingly used to study opinion polarization Bakshyetal15 ; Conoveretal11 ; YardiBoyd10 ; AsherBandeiraSpaiser . Gruzd and Tsyganova GruzdTsyganova14 , for instance, use Ukrainian Vkontakte data to demonstrate the split between the two political camps in Ukraine (pro-East vs. pro-West) during the Maidan protests. Twitter has also played a quite important role as a contested public debate arena throughout the crisis in Ukraine Stern (2014); Ronzhyn (2014). Studies with social media data have revealed the strong effect of homophily in online social networks, which may lead to phenomena like the echo chamber Colleonietal14 ; Barbera15 ; AsherBandeiraSpaiser , where opinions are amplified through communication and repetition inside an “enclosed” social system. Echo chambers can prevent people from noticing contrary persuasive arguments and they skew the perceived average that people take into consideration in social comparison processes. Though social media data is potentially rich, i.e. fine-grained, time-resolved, relational, geo-coded, etc., without an explicit theoretical underpinning, the studies of polarization on social media remain usually rather descriptive. By combining rich social media data with the power of methods of statistical physics a better understanding of specific political opinion polarization mechanisms is sought in this paper.

III Methods

III.1 Political opinion mining of Twitter data

We used the archived Twitter API Streaming data from October 2013 to September 2014 provided by the Archive Team archive . The archived data is the freely available Twitter Streaming API Spritzer Sample, which collects 1% of all public tweets in real-time. The Twitter Streaming API Spritzer Sample allows for unfiltered data analysis and hence for capturing the full discourse picture comparing to a more narrow, focussed (e.g. based on certain hashtags, user networks etc.) approach facilitated by data using the Twitter REST API Leeetal17 that would disregard discourse contributions beyond the specified search queries. The data for January 2014 was missing and we did not find any other archive providing this data. The tweet data is stored in JSON format. The data was processed and analyzed in Python. Specifically, the data was filtered for Russian/Ukrainian language (excluding Twitter users who specified being from Russia), cleared of SPAM, and then filtered for political content with an extensive set of keywords (see the electronic supplementary material for details). We used the tweets to determine the political affiliation of each Twitter user using a set of keywords indicating neutral, pro- or anti-West attitudes and a set of keywords indicating neutral, pro- or anti-Russian attitudes (see the electronic supplementary material for details). Moreover, we conducted a sentiment analysis of the tweets, in order to determine the political affiliation for previously seemingly neutral Twitter users. For this purpose we utilized the SentiStrength system for automatic sentiment analysis, built an Ukrainian sentiment words dictionary (see the electronic supplementary material) and extended the SentiStrength Russian sentiment words dictionary to make it equivalent to the Ukrainian sentiment words dictionary (see the electronic supplementary material for details). Our classification algorithm scanned all tweets for each user and checked whether the tweet contained any of the keywords and any of the sentiment words specified and calculated overall scores for political “West” and “East” affiliation as well as sentiment scores (see the electronic supplementary material for details). For the geo-plots in Fig. 3C,D, we focused on the data of the last week in September 2014. We scanned the Twitter data of each user for two possible geographical information, the value of their “location” tag and/or geo/place “coordinates” tag which is a latitude and a longitude coordinate value. The vast majority of users have the default option “geo_enabled:false”, thus do not provide precise geographical information attached to the tweet, a few more provide profile “location” information, but overall, geographical data is often not specified and thus missing. We therefore ended up with only 493 Twitter users for whom we had a geographical information. The “West” and “East” political affiliation scores of these 493 Twitter users were plotted in Fig. 3C,D (see the electronic supplementary material for details).

III.2 Bounded Confidence XY Model of Opinion Polarization

We model opinion dynamics in an assembly of interactive agents placed on a two-dimensional lattice of finite size, which emulates a regional opinion distribution and localization. Each opinion is represented by a vector that can freely rotate in plane, similar to that in the $XY$ model of a magnet, and is characterized by the length $p$ (emotional intensity, i.e. fervent strength of an opinion) and polar angle $\theta$ (orientation). This allows us to model a continuous opinion spectrum with respect to the specified direction by a cosine of the angle between the vectors, which can vary in the range between -1 (agent opposes the opinion) and 1 (agent fully supports the opinion). Each agent can interact with a fixed number of nearest neighbors. The social interactions are introduced via local mean field, similar to the Vicsek model vicsek.t:1995 : the new orientation of each vector is calculated as a mean of the average direction of the neighbors and agent’s own orientation:

[TABLE]

where $N$ is the number of interacting agents, $\xi$ is the angular noise variable uniformly distributed in the interval $[-\eta/2,\eta/2]$ and $\eta$ is the noise strength. The noise is added to model the level of conformity of the individual: zero noise, $\eta=0$ corresponds to full conformity, $\eta=2\pi$ allows an individual to deviate from the group opinion by an unlimited value. A contribution of each interacting agent is weighted by the emotional intensity of its opinion $p$. The interaction has a limited range $r$, which sets the number of nearest neighbors considered. In 2D, interaction range $r=2$ corresponds to 24 interaction peers, $r=3$ gives 48 peers, etc (see the electronic supplementary material for details). In addition to this, the interaction is selective so that the vectors align only with those neighbors, whose orientation (opinion) deviates by an angle less than some fixed value $\alpha$ from their own opinion vector. This rule is inspired by the bounded confidence model, or Deffuant model Deffuantetal00 , and allows one to imitate systems with different levels of opinion tolerance romensky.m:2014 . Scaled value $\alpha/\pi$ denotes a fraction of the opinion spectrum that is taken into account by each individual, e.g. $\alpha/\pi=0.1$ corresponds to 10% closest opinions taken into account. Note that our model does not explicitly include any intrinsic preference to agent’s own opinion (i.e. orientation of the opinion vector $i$ in the previous time step) because using a relatively small values of $\eta$ and $\alpha$ already allows to achieve a socially realistic behavior.

We model a finite system with the boundary conditions set by two fixed rows of agents on each side. The boundary vectors are fixed according to the following scheme: the left and upper rows are oriented to the left ($\theta=\pi$), imitating a bias towards “West” and the right and bottom rows are fixed to point in the opposite direction ($\theta=0$), thus mimicking a bias towards “East”. When other agents interact with the boundary vectors this introduces a spatially dependent local bias that can account for geographical inhomogeneity in opinions, thus imitating cultural or ethnic differences, information bias, etc. (see the electronic supplementary material for details; see also the interactive model applet ).

These model settings reflect the theoretical assumptions about polarization described above. The orientation represents political attitudes and the local mean field calculation of new orientations for each agent represents the social comparison theory assumptions. The homophily effect is included through the bounded confidence feature, where agents align only with those neighbors, whose political orientation is similar to their own. Furthermore, the biased assimilation mechanism is reflected in the noise variable that determines the agents’ willingness to change opinion (conformity level). Finally, the persuasive argument theory assumption, in particular with respect to the contribution of biased information to polarization, is simulated via the boundary conditions. We have added a further parameter to our model, the emotional intensity, i.e. vector length, that represents the level of emotional strength and vehemence of a political opinion. This parameter reflects results we have obtained from Twitter data sentiment analysis discussed in the next sections. It also builds on recent computational models and big data analysis of opinion dynamics Sobkowicz12 ; Sobkowicz13 , which showcase the importance of emotions, and in particular of negative emotions, for people’s engagement in political debates and for opinion formations and changes.

We modeled evolution of the opinion spectrum in the described system starting from randomized initial distributions of agents’ emotional intensity and orientations based on general uniform distributions. The emotional intensity levels for each agent were kept fixed in each simulation while the orientations evolved due to noise and interactions. For each opinion spectrum extracted from Twitter data, we performed a simulation until a steady state was reached. After that, the following statistics were collected: steady state distribution of the opinion along the “East-West” scale, as defined by the boundary conditions, mean order parameter, and bimodality index.

We should note here that in this setup the week-by-week series of calculated properties do not reflect the real time, nor the actual system’s dynamics as the history of the individuals as well as previous steady states are ignored. To follow the variation of collective properties, ideally one should look at the evolution of each user’s opinion and derive the group behavior from the corresponding statistics. For this purpose, one would need to either parameterize the individual opinions from the empirical data directly or solve the inverse problem and introduce the variation of opinions based on the instantaneous statistical averages. As we could reach only a random sample of the tweets, it was not possible to follow the former route and track individual users. The empirical data we have are discontinuous. Moreover, we have no appropriate model for individual psychology. Therefore, we decided not to introduce an artificial evolution of the opinions. As the individual history is lost, we can only follow the variation of the averages corresponding to the snapshot of Twitter data.

III.3 Model parameterization with Twitter data

To parameterize the Bounded confidence XY model we used weekly distributions of the overall users’ emotional intensity scores. For each week, the overall emotional intensity of each user was defined from the mean of the average sentiment scores on a continuous scale from 0 to 5, with 0 corresponding to a neutral average user’s opinion and 5 reflecting an extremely emotional average opinion. This measure did not contain any information about political affiliation, so that each non-zero value could correspond to either pro-West or pro-East user’s political attitude. The data was sampled with a bin size of 1 for all non-zero opinions and a resulting discrete distribution was normalized by the total number of users per week giving probabilities for each discrete value of overall emotional intensity (0 to 5). This distribution was then applied to the simulated system to define the length $p$ of each opinion vector. In each simulation, values of $p$ were assigned to agents at random, according to obtained discrete weekly distributions of overall emotional intensity, and kept constant throughout the simulation. The simulated system consisted of 14641 agents placed in nodes of $120\times 120$ lattice. We performed at least $10^{6}$ update cycles to determine the structure of the steady state. Each statistics was averaged over at least 5 independent runs. We computed the bimodality coefficient as $\beta={(\gamma^{2}+1)}/{k}$, where $\gamma$ is the skewness and $k$ is the kurtosis of weekly distributions of average opinion scores in Twitter data or weekly distributions of cosines of orientations $\theta$ of opinion vectors in simulations.

IV Results

IV.1 Opinion Polarization in the Ukrainian Twittersphere

To validate the model assumptions, we used Twitter Streaming data from October 2013 to September 2014 provided by the Archive Team. We use Twitter data because it provides fine-grained, time-series and rich data on recent political opinion dynamics in Ukraine, otherwise not available. To determine the political affiliation of the Twitter users in our data, we used a political affiliation classification procedure based on keyword and sentiment analysis suggested and tested by Spaiser et al. Spaiseretal (see the electronic supplementary material for details). As a result, every Twitter user was assigned two scores, a “West” score and an “East” score, representing their political position in a pro-against-European (West)/pro-against-Russian (East) opinion space (see Fig. 3A,B) and an emotional intensity score, combining their sentiment analysis scores.

Our Twitter analyzes show that political polarization did indeed take place in the Ukrainian Twittersphere between October 2013 and September 2014. Fig. 2A shows a discontinuous increase in emotional users in February 2014, while the total number of users and the number of neutral ones increased steadily. Fig. 2B depicts a ratio of emotional/neutral opinions, where a jump from values of about 1.0 to about 1.4 is visible around February as well. We added to this figure the key political incidents in Ukraine during this year, so the discontinuous changes in the data can be related to actual political events. This shows that the biggest discontinuous change in February took place around the time when the Maidan protests escalated and 100 people died on a single day. These results inspired the inclusion of emotional intensity levels as a parameter in the computational model. In addition to an abrupt increase in the total number of users (Figs. 2A,C), users’ involvement in the topic also changed discontinuously (Fig. 2D). The dynamics of the average number of tweets per user completely resembles that of the emotional level of tweets (Fig. 2B), with a characteristic jump around week 19 (February 2014).

Fig. 3A,B moreover shows the polarization in a continuous two-dimensional space defined by pro-against-European (West)/pro-against-Russian (East) scores. This figure shows that the polarization resulted in appearance of two main opinion clusters, those who are pro-East and against-the-West on the one side and those who are against East but who are also quite critical of the West on the other side (see the electronic supplementary material for details). This in fact reflects most current surveys that show the disappointment of many Western oriented Ukrainians with the pro-West Poroshenko government Gallup15 .

Our Twitter data analysis confirms that political affiliation follows the expected geographical pattern. People who are pro-East and against-West are more likely to be located in the Eastern and Southern parts of Ukraine, while Ukrainians with rather an against-East and (critical) pro-West attitude are to be found in the Western and Northern territories (see Fig. 3C,D). This analysis is a validation of our classification procedure, since the geographical distribution of the Twitter users with their respective political affiliation scores matches the actual geographical political camp distributions in Ukraine (see Fig. 1).

IV.2 Validating the Bounded Confidence XY Model of Opinion Polarization with Twitter data

To quantify the opinion divide, we present here the bimodality index for the opinion spectrum (see Materials and Methods for the definition), as we found it to be most sensitive to the changes of the spectrum, therefore, the best integral characteristic of the observed behavior. The changes in the bimodality coefficient over 12 months from October 2013 are shown in Fig. 4A,B. In the Twitter data the bimodality keeps as low as 0.2 to 0.26 from the start of observation until week 18 (February 2014) but then demonstrates sudden increase to 0.35 to 0.40 within the next two or three weeks, after which it stays high, and the original value is never restored. This sudden increase of the bimodality reflects a formation of two distinct political camps and clearly shows that the opinion divide has suffered a significant deepening in this short period. Moreover, we see that the deepening was non-recoverable in the short term. The computational model, parameterized with the Twitter emotional intensity spectrum for each respective week, captures this behavior well and shows a similar qualitative trend. In a simulation with $\alpha=0.15\pi$, the bimodality coefficient jumps from ca. 0.60 – 0.65 to 0.8 – 0.85 during the same period. The quantitative difference in the values is mostly due to the use of cosine function. We should note that, although the model is parameterized by the Twitter data, it is not bound to reproduce the distribution, as the vectors are allowed to change the orientation, and this behavior follows only from the specific anisotropic interactions between the agents. We repeated the simulations with a different interaction parameter $\alpha=1.0$, corresponding to agents without any resistance to opinion change and found no jump in the bimodality. Therefore, the opinion divide is conditioned by both the restriction of confidence and by conformity (noise) levels, thus confirming the homophily and biased assimilation assumptions. Moreover, the drastic change in bimodality corresponds to the sudden increase of the emotional intensity, which we noted in the data in Fig. 2B.

IV.3 Onset of Opinion Clustering and Formation of Territorial Domains

The increase in emotional intensity leads to important consequences in the spatial dimension. In the weeks before and early at the outbreak of the crisis, the simulations display large diversity of the opinions (Fig. 5C) characterized by the large number (Fig. 5A) of small (Fig. 5B) opinion domains (clusters). This picture, however, changes further into the crisis, around week 19, when a smaller number of larger opinion domains is formed. While clusters rarely exceed 100 agents before the critical weeks 17-18, starting from week 19 we observe clusters of up to 5000 agents and the numbers rarely drop below 1000. That the behavior becomes expressly collective is consistent with the rise of emotional intensity and of the fraction of involved agents (those with non-zero valence), which increases the number of interactions within each individual’s circle and thus the local aligning field. This is further confirmed by Fig. 5F,G showing the polar opinion histogram for the two critical time points, week 18 and 19 obtained from simulation analyses. The distributions are visibly gravitating towards 0 or 180 degrees (“East” and “West”) in both sets. The fraction of neutral opinions drops from week 18 to week 19 and the distribution of opinions in each subgroup becomes very narrow.

Simulation analysis moreover shows that the opinion divide induces also territorial splitting. Subfigures Fig. 5C,D show the in-plane opinion distribution. We plotted the opinions as predicted by the model just before the jump in the bimodality (week 18 – C) and immediately after that (week 19 – D). The change in the distribution between these points is dramatic: while the predicted data for week 18 show a merely uniform distribution of both “East” and “West” orientations, the picture for week 19 features two distinct clusters with predominant “West” orientation in the lower left corner and domination of the “East” orientation in the top right corner. These orientations correspond to vector directions in the preset boundary conditions. Each domain contains practically no opposing opinion, as they are squeezed out to the periphery and then to the opposing domain as the steady state develops. We can see small islands of mixed/neutral opinion in the middle of the simulation domain. The prediction of the territorial divide matches also well the geo-location data shown in Fig. 3C,D. We should stress however that the biased boundary conditions alone are not sufficient to produce any large domains even in the system with limited confidence (Fig. 5C, see the electronic supplementary material for details), although they definitely facilitate this collective behaviour.

The simulation allows us to analyze the steady states of the system and provides insights into the mechanisms of sudden onset of polarization, clustering, and territorial splitting (see the electronic supplementary material for details). We in particular examined varying levels of noise, restriction angles and vector lengths. High noise (low conformity) corresponds to a globally disordered behaviour (without any prominent consensus or polarization) and the range of higher $\alpha$ allows only states with polar order (global consensus). Smaller restriction angles, $\alpha<0.4\pi$, on the other hand produce regions of prevalence of the bipolar states, thus structure the system in a polar or bipolar way. A combination of small restriction angle (strongly bounded confidence) and high noise (low conformity) does not produce any global order and is rather unrealistic since at these conditions the system represents a set of selective but randomly vacillating agents. Polarized states are generally only possible at low noise (high conformity) and small restriction angles (strongly bounded confidence). The changing level of emotional intensity pushes the boundary between the polarized and non-polarized societies moreover outwards, thus extending the range of the polarized states, and brings the originally weakly polarized society to a highly polarized one. This splitting resembles in appearance a phase separation in dissimilar liquids (e.g. oil in water). The important difference of our system from the liquid state systems is that the agents are not dissimilar from the beginning but the dissimilarity and effective repulsion between the opposite arises from strong social interactions that dictate cohesion between the like opinions. Another important observation here is that the transition is driven primarily by the increase of emotional level while the other parameters (conformity, confidence) stay constant. We should stress that the source of and the original direction of the emotional agents were not crucial. The key properties of the model that determine the nature of the steady states (non-polar, polar or bipolar) are the high conformity and strongly bounded confidence.

V Conclusion

We have analyzed the opinion dynamics over a recent period of political unrest in Ukraine. Based on the Twitter data, we registered an onset of emotional intensity of tweets that corresponded to rising levels of involvement of the population in the political feud, fueled by the action of the government, collisions of the opposing groups, and foreign military activities. The escalating opinion divide around the time became apparent among others in the jump of the opinion bimodality index. We proposed an agent-based lattice model to study political polarization as a collective behavior including the spatial dimension of polarization. By parameterizing the model with Twitter data at distinct time points, we predicted the onset of collective behavior and territorial splitting of the opinion. We demonstrated that the tendency of territorial splitting is conditioned by the high conformity and homophily in the society and is driven by the growth in emotional intensity. Our analyzes demonstrate clearly the importance of emotional intensity for polarization, a factor that has been largely ignored thus far in classic theoretical and empirical literature on polarization with a few noteworthy exceptions as discussed earlier. Specifically, while our analyzes confirm the importance of social comparison, homophily, persuasive argument and biased assimilation mechanisms and their specific interactions for polarization, they also show that these mechanisms are not sufficient to ignite the extreme societal polarization we can observe for instance in Ukraine. The emotional intensity is a key reinforcement mechanism that has to be added.

Our analysis seem also to suggest a link between polarization and separatist trends. The polarization dynamics that we establish for February 2014 in the data and simulation increases in fact further around April and May 2014, when the self-declared Donetsk and Luhansk People’s Republics were formed in the South-East of Ukraine. This seems to suggest that the opinion split may facilitate the separatist trends on its own. The observed phenomenon is not unique to Ukraine, and similar processes of deepening polarization leading to separatism are well known elsewhere (e.g. Northern Ireland). In most cases, however, the separatism is related to more obvious ethnic, racial, or religious differences between the communities, while in Ukraine the division is more subtle and roots in small cultural differences, which were artificially enhanced by external factors. And our results show how dangerous targeted agitation can be when it is backed by modern information warfare techniques Cottiero15 ; Aro2016 as it boils emotions making polarized world views increasingly irreconcilable.

Ethics

Tweets were collected and analysed in accordance with the Twitter Privacy Policy and the Twitter Terms of Service.

Data accessibility

The datasets supporting the conclusions of this article are provided by the Archive Team archive .

Authors’ contributions

MR: Development and Testing of the Bounded Confidence XY Model, Parametrization and Testing of the Model with Twitter Data, Development of Ukrainian dictionary for sentiment analysis, Preparing graphics, Writing the paper, VS: Processing and Analyzing Twitter data, Preparing graphics, Writing the paper, TI: Development of the Bounded Confidence XY Model, Writing the paper, VL: Development of the Bounded Confidence XY Model, Writing the paper.

Acknowledgements

The authors thank Ian Harper for help with programming and testing of the web applet.

Supplementary Methods

Further Model Specifications

Supplementary Figure S1 illustrates interactions in the Bounded Confidence XY model. The red opinion vector interacts with its 24 neighbors located within two nearest lattice nodes in any direction $r=2$. In this illustration, each of the 24 neighbors has orientation relative to the focal (red) vector less than $\alpha$ and therefore all 24 agents contribute to future orientation of the focal vector. For simplicity, all vectors in Supplementary Fig. S1 are shown to have same length. In all simulations, the initial orientations of all agents except the ones at the system’s boundary were drawn randomly from the uniform distribution in the interval $[-\pi,\pi]$.

To quantify formation of territorially isolated domains in our model, we performed a simple cluster analysis. We define a cluster based on two criteria: distance and relative orientation between the agents. Therefore, a cluster is a set of connected agents, each of which is within the cutoff distance (defined by $r$) from one or more other opinion vectors from the same cluster and a relative orientation between any two neighbors in the cluster is less or equal to restriction angle $\alpha$. Conversely, two agents will not belong to the same cluster, if there is no continuous path on the neighbor network leading from the first agent to the second or if this path is broken because the angle between two neighbors is larger than $\alpha$ and hence the opinion vectors do not interact. For each update step we calculated size of each cluster, maximal cluster size and total number of clusters.

We characterised orientational ordering in our model using two order parameters. Polar order parameter was used to quantify the average degree of opinion agreement between the agents

[TABLE]

where $\imath$ is the imaginary unit and $\theta_{j}$ is the direction of each vector $j$. This order parameter turns zero in the isotropic phase, when opinions of all agents are very different from each other, and assumes finite positive values in the ordered phase, reaching unity when global consensus settles in.

To characterise opinion polarization in our model we use the following bipolar order parameter

[TABLE]

When the two vectors are oriented perfectly collinearly, $Q=1$. Note that a perfectly polarly ordered phase is characterized by $\varphi=Q=1$, as the polar ordering implies the bipolar ordering. A bipolarly ordered phase requires only $Q=1$ while the polar order parameter can take any value $\varphi<1$. Therefore, requirements for the polar order are more restrictive.

For each weekly distribution of opinions, both for the Twitter data and in simulations, we computed the bimodality coefficient (see main text, Methods) by first calculating the skewness and kurtosis of the distribution. Skewness is defined as the third standardised moment around the mean

[TABLE]

where $\mu_{2}$ and $\mu_{3}$ are the second and the third cumulants, respectively. Kurtosis is computed as the fourth central moment

[TABLE]

where $\mu_{2}$ and $\mu_{4}$ are the second and the fourth cumulants, respectively.

The model phase diagrams, shown in Supplementary Figs. S2 A-D, demonstrate three different steady states of the system. The high noise (low conformity) generally corresponds to a globally disordered behavior (without any prominent consensus or polarization). The region of disordered behavior shrinks as the restriction angle $\alpha$ is increased (Supplementary Fig. S2 A). The lesser restriction leads to more interactions between the nearest neighbours and to the onset of order (consensus). At lower noise, below the transition line we observe either polar or bipolar structuring of the system (Supplementary Fig. S2 B). The range of higher $\alpha$ allows only states with global consensus, while at $\alpha<0.4\pi$ we see the region of prevalence of the bipolar polarized states. In other words, the polarized states are only possible at low noise (high conformity) and small restriction angles (strongly bounded confidence). The change in level of emotional intensity pushes the boundary between the polarized and non-polarized societies outwards (Supplementary Fig. S2 B), thus extending the range of the polarized states, and brings the originally weakly polarized society to a highly polarized one. The most important observation here is that the transition happens just due to the increase of emotional intensity while the other parameters (conformity, confidence) stay constant. Supplementary Figures S2 C,D show phase diagrams for unparameterized systems at different simulation parameters. For a larger system, $s=240$ constituting of 58081 agents, the area of bipolar ordering is slightly reduced as compared to the standard system size ($s=120$) used in this study. The shrinking happens because the influence of biased boundary vectors is decreased due to larger system size. If the agents have larger interaction range, $r=3$ (i.e. each vectors interacts with up to 48 nearest neighbors), the region of bipolar ordering expands to larger restriction angles and noise values because longer correlation range becomes possible and effect of the boundary bias is more pronounced at these conditions. Finally, if all boundary vectors are fixed in one direction (in this case to the East, $\theta=0$), the area of bipolar polarization shrinks significantly but does not disappear. At these conditions bipolar ordering also displays more sensitivity with respect to noise than to restriction angle.

Twitter Data

The archived Twitter Streaming API Spritzer Sample tweet data was stored in JSON (JavaScript Oobject Notation) file format, which is the most common open standard data format to transmit data objects in asynchronous browser/server communication. The data was then processed and analyzed in Python using the Python Natural Language Text Processing Toolkit (NLTK) (Bird et al., 2009; Perkins, 2010). NTLK is a collection of various classes, interfaces and functions for natural language processing, including important text mining methods. It was developed at the University of Pennsylvania and is widely used in computational linguistics, machine learning, and cognitive science (see in particular https://nltk.googlecode.com/svn/trunk/doc/api/index.html).

The collected tweets were filtered, first for Russian and Ukrainian language, identifying respective alphabet characters in the tweet text. Tweets, where Twitter users specified being from Russia or any region/town in Russia were removed from the data. We also filtered for SPAM tweets (around 17% of all the tweets in our data), using the following keywords, based on word count analyses: porn, phone, games, androidgames, minecraft, ipadgames, loosing weight, gold, mtvstars, crossword, barbie, sony, holidays, shop, TV series, volkswagen, sales, starlet, apartments, estate, bmw, mercedes, sex, happysex, viagra, stock, prostitutes, teen, price, diet, buy, credit in English, Ukrainian and Russian language. Tweets containing these words were removed from the data. Furthermore, we filtered the data for political context with an extensive set of keywords to remove irrelevant tweets and therefore unnecessary noise from the data: protest, mobilization, Ukraine, kiborgi, glory to the heroes (one word hashtag in Ukrainian and Russian - geroiamslava), junta, government, duma, kremlin, parliament, rada, premier ministry, president, minister, ministry, political action, demonstration, opposition, power, authorities, democracy, nationalists, communists, liberals, Putin, Poroshenko, political party, politics, politicians, political, policy, revolution, citizen, criticism, critics, agitation, sanctions, censoring, illegal, legal, solidarity, assembly, rally, law, regulation, resistance, civil disobedience, resist, reforms, communism, capitalism, administration, news, society, violation, RNBO, Iaijtheniukh, ukr, ukry, khokhly, okraina, ruina, raguli, poproshenko, papashenko, papasha, bacon to the heroes (a wordplay in Russian with glory to the heroes - geroiamsala), civil war, nazis, Bandera, banderlogi, bandery, banderovtsy, benderovets, visitka Iarosha, titushki, EuroMaidan, U_revolution, peaceful march, radio freedom, inforesist, Aronets, avtomaijdan, Ukraine truth news (one word hashtag), SOS Maidan (one word hashtag), digital Maidan (one word hashtag), Maidan history (one word hashtag), sidemaidan, Maidan, freedom, Ukrainian, NATO for Ukraine (one word hashtag), will, choice, against, anti-Maidan, ukrop, Europe, USA, Kiev, Timoshenko, Cameron, dead, killed, negotiations, military service, Zakharchenko, police, Obama, war, activists, right sector, Azarov, upper, leader, Jatseniuk, Turchinov, Klitchko, MID, Nayyem, briginets, constitution, Avakov, MVD, Yushenko, Kuchma, Kravchuk, Kharkov, Grushevskogo, warriors, soldiers, prisoners, Euro, EU, military, Sloviansk, army, West, East, Mariupol, reconciliations, NATO, ATO, crimealook, conflict, Medvedchuk, Medvedchukov, geo-politics, confrontation, Strasbourg, crisis, Lutsenko, Tusk, peace, world, Vladimirova, Vladimir, relations, unity, national, help, oligarchs, glory to Ukraine (one word hashtag), hundred, over, own will, self-determination, power, annexion, annexing, separatism, separatist, rebels, freedom fighters, freedom fight, moskali (meaning Moscow sympathizers), [Russian] official, Putin khujlo (offensive word, one word hashtag), luganda, lungandon, daunbas, zrada, occupants, MGB, Zakhar, Russian peace (one word hashtag), Russian world (one word hashtag), Putin is murder (one word hashtag), Putler, Putin help (one word hashtag), putinism, insurgents, insurgency, small/so what Russia, Crimea is ours (one word hashtag), At least Crimea is our (one word hashtag), punitive, ptnpnkh, ptn, pnkh, vata, vatnik, glory to Russia (one word hashtag), Russia, provocation, Novorossiia, DNR, LNR, berkut, kiberberkut, glory, stopcrimeantatarsgenocide, russiainvadeukraine, russiaviolatedceasefire, stoprussianaggression, weapon, Russian, Medvedev, Moscow, legislation, Yanukovich, truth, Donetsk, Luhansk, Russian march (one word hashtag), Russians, Ukrainians, Non-russians, Navalny, monument, Lenin, western, eastern, geek, Lavrov, grad, humanitarian, anti-Russian, SSSR, Donbass, Bafana, elections, legislator, fire, Mirakova, ukraintsami, radio, Putin supporters (one word hashtag), Ukraine_France, Zakharov, Mironov in Ukrainian and Russian language. Tweets that contained at least one of these keywords were kept in the filtered data, otherwise removed.

Any analysis of Twitter data faces a number of well-known difficulties (Ruths and Pfeffer, 2014). Some of them, e.g. the SPAM tweet problems, we have addressed already above. One potential problem is that the sample only includes public tweets from public Twitter accounts. This does not pose a problem in the context of our study though, since we are interested in the use of Twitter as an instrument of communication in the public sphere. Moreover, Twitter data is not representative, which again is rather unproblematic for our study because all political groups and their supporters are represented on Twittersphere, so the public debate on Twitter does overall mirror the general public debate and public opinions (Stern, 2014; Ronzhyn, 2014). Another potential issue is that the sample is based solely on the 1% of all public tweets, which for instance makes it difficult to use the data as panel data (though we’ve done this to probe opinion changes within individuals, see Supplementary Fig. S3, the number of observations is however drastically reduced). However, other Twitter data samples offered by Twitter (e.g. Gardenhose with 10% of all pubic tweets) have to be purchased, which makes them often unaffordable for research purposes.

One aspect of Twitter data ”richness” is that it is supposedly geo-referenced. However, as already mentioned in the main manuscript quite a large proportion of Twitter users do in fact not provide any geographical information. Frequently, even if ”geo_enabled” was activated by the Twitter user (thus the value was set to ”true”), the actual ”geo” or ”place” ”coordinates” value would be ”null” because the device that was used to post the tweet had no geo-referencing (e.g. GPS) activated. The data that the user provides through the profile ”location” tag is more often available, however, here we have to rely on the accuracy and honesty of the Twitter users. Moreover, if the information provided through ”location” was imprecise, e.g. just ”Ukraine”, we could not use this information for plotting. Did we however have serious and specific information from the user, e.g. ”Kiev”, then we used that information to generate a longitude and a latitude coordinate value that we could then plot on a generated Ukraine map in Fig. 3C,D in the main manuscript. We deliberately ignored another potential geographical information, the ”time_zone”, because it offers only imprecise geographical information. Overall, we could extract form the Twitter data of the last September week 2014 493 Twitter users for whom we had sufficiently precise geographical data. This data along with the calculated West and East scores were used to produce the Figures 3C and D in the main manuscript.

Twitter Data Analysis

In order to understand the empirical polarization dynamic in Ukraine and furthermore in order to make the data usable for model calibration, it was necessary to identify the political opinion of the Twitter users in our data. First, we identified the Twitter users in our Twitter data based on the value of their ”screen_name”. We then compiled two lists of keywords, extracted from the word count analysis of the most common words that contain words associated with either the pro-East political camp or the pro-West political camp: annexion: -2 , annexing: -2, separatism: -2, moskali (meaning Moscow sympathizers): -2, [Russian] official: -2, Putin khuijlo (one word hashtag): -3, Luganda: -3, Lugandon: -3, Daunbas: -3, zrada: -2, insurgents: -2, occupants: -2, MGB: 1, Zakhar: 1, Russian peace (one word hashtag): -2, Putin is murder (one word hashtag): -3, Putler: -3, Putin help (one word hashtag): 2, putinism: -1, freedom fighters (one word): 2, freedom fight (one word): 2, small/so what Russia: 2, Crimea is ours (one word hashtag): 3, At least Crimea is ours (one word hashtag): 3, punitive: 3, ptnpnkh: -3, ptn: -1, pnkh: -3, vata: -3, vatnik: -3, glory to Russia: 3, Russia: 0, Russian: 0, Russians: 0, provocation: 0, separatist: -3, separatism: -3, Novorossiia: 2, DNR: 1, LNR: 1, sanctions: 1, berkut: 1, kiberberkut: 1, stopcrimeantatarsgenocide: -3, russiainvadedukraine: -3, russiaviolatedceasefire: -3, anti-Russian sanctions (one word hashtag): 2, stoprussianaggression: -3, peace: 0, Putin: 0, weapon: 0, Medvedev: 0, Crimea: 0, Moscow: 0, Yanukovich: 0, truth: 0, Donetsk: 0, from Lugansk (one word): 0, Russian march (one word hashtag): 0, Non-Russians: 0, dead/killed: 0, negotiations: 0, politce: 0, rebels: 0, Lugansk: 0, war: 0, duma: 0, Mockva: -1, government: 0, leader: 0, monument: 1, Lenin: 1, warriors: 0, prisonerns: 0, military: 0, East: 0, army: 0, relations: 0, soldier: 0, reconciliations: 0, geek: -2, Lavrov: 0, grad: -1, humanitarian: 1, anti-Russian: 2, SSSR: 1, Donbass: 0, Bafana: 0, elections: 1, referendum: 0, confrontation: 0, fire: 0, crisis: 0, conflict: 0, Putin supporters (one word hashtag): -1, Mironov: 0 were the keywords for the East political camp and mobilization: 1, kiborgi: 2, unity: 1, glory to the heroes (one word hashtag): 3, RNBO: 1, Iaijtheniukh: -3, junta: -2, ukr: -3, ukry: -3, khokhly: -1, okraina: -1, Ruina: -3, raguli: -3, poproshenko: -2, Papashenko: -2, papasha: -3, bacon to the heroes (a wordplay in Russian with glory to the heroes - geroiamsala): -3, civil war (one word hashtag):- 2, visit Kaiarosha (one word hashtag): 2, nazis: -3, Bandera: -3, banderlogi: -3, bandery: -3, banderovtsy: -3, titushki: 2, Ukraine: 0, Euro Maidan (one word hashtag): 1, U_REVOLUTION: 2, peaceful march (one word hashtag): 1, radio freedom (one word hashtag): 1, inforesist: 1, Aronets: 1, avtomaijdan: 1, Ukrainian truth news (one word hashtag): 1, SOS Maidan (one word hashtag): 1, digital Maidan (one word hashtag): 1, Maidan history (one word hashtag): 1, sitemaidan:1, Maidan: 0, freedom:1, government: 1, Ukrainian: 0, Urkrainians: 0, NATO for Ukraine (one word hashtag): 2, will: 2, will: self-determination, against: 2, revolution: 2, anti-Maidan:- 2, ukrop: -3, Poroshenko: 0, Europe: 0, USA: 0, Kiev: 0, weapon: 0, Timoshenko: 0, truth: 0, Cameron: 0, democracy: 0, dead/killed: 0, negotiations: 0, military service: 0, Zakharchenko: 0, opposition: 0, Obama: 0, war: 0, parliament: 0, activists: 0, political action (one word): 0, protest: 0, sector: 0, Azarov: 0, upper: 0, leader: 0, rada: 0, Yatseniuk: 0, Turchinov: 0, Klichko: 0, MID: 0, Nayyem: 0, Briginets: 0, constitution: 0, president: 0, Avakov: 0, MVD: 0, Yushchenko: 0, Kuchma: 0, Kravchuk: 0, Kharkov: 0, Grushevskogo: 0, warriors: 0, Euro: 0, EU: 0, military: 0, Slaviansk: 0, West: 0, western: 0, army: 0, soldier: 0, Mariupol: 0, reconciliations: 0, NATO: 0, ATO: 1, conflict: 0, Medvedchuk: 0, Medvedchukvv: 0, Strasbourg: 0, crisis: 0, Lutsenko: 0 ,Tusk: 0, peace: 0, relations: 0, national: 1, help: 1, glory to Ukraine (one word hashtag): 2, hundred: 2, over: 2, power: 2, BENDERovets: 3, civil war: -2, krimealook: 1, Ukraine_France: 1 were the keywords for the West political camp. These keywords were scored between -3 and 3, with negative scores indicating negative attitudes towards the respective political camp, positive values positive attitudes and a zero a neutral opinion. Some keywords were unambiguously associated with a political affiliation. For instance, the word ”Putler” (scored -3), a composition of Putin and Hitler, is clearly a negatively annotated word referencing the East political camp. Similarly, the word ”banderovtsy” (scored -3) linking the West political camp to Stepan Bandera, leader of the Ukrainian nationalist and independence movement during the Second World War, who cooperated with Nazi Germany, shows clearly a strong disapproval of the West political camp. On the other hand the hashtag #slavarossii (translated: Glory to Russia, scored +3), shows a clear support for the East political camp, while the hashtag #natoforukraine (scored +3) expresses an unequivocal pro-Western political affiliation. A word like ”Putin” (East political camp) or ”Poroshenko” (West political camp) however would be assigned a ”0” because depending on the remaining content of the tweet the names could have been associated with positive or negative attitudes. And for that reason an additional sentiment analysis of the tweets was necessary.

We used the sentiment analysis SentiStrength (http://sentistrength.wlv.ac.uk) approach to determine a sentiment score for each tweet. SentiStrength is a free Java-based automatic sentiment analysis tool, widely used in research, which is also available for the Russian language. We created a comprehensive dictionary for Ukrainian sentiment words (to be shared upon request) based on the SentiStrength sentiment scoring system and we reviewed the sentiment word dictionary that SentiStrength is using for the Russian language and complemented it with other sentiment words (among others offensive words that were missing in SentiStrength) to make it equivalent to the Ukrainian dictionary. The sentiment scores in SentiStrength and thus in our two sentiment words dictionaries range from -5 to +5 with 0 signifying a neutral word, negative values a negative sentiment and positive values a positive sentiment. The higher the absolute value the stronger the sentiment. For each tweet we calculated a sentiment score average based on the identified sentiment words in the tweet. We calculated a separate sentiment score for the East political camp related keywords and one for the West political camp related keywords. The emotional intensity score is averaging these two sentiment scores.

In the case of unequivocal keyword tweets, the tweet score would derive from these keywords. For instance, if a keyword contained the words ”Putler” (scored -3) and the hashtag ”stoprussianaggression” (scored -3), the tweet score would be the average of these two scores, thus -3. Whenever a tweet was scored zero because of neutral keywords, we added to the score the respective sentiment score. Thus if an East political camp related tweet had a zero score (e.g. ”Putin”), and the East political camp related sentiment score was -2 (for instance resulting from the sentiment word ”zachvatil” (translated: grabbed)), then the tweet would get an East political affiliation score of -2. This is based on the assumption that users would express positive sentiments about terms associated with their own camp and/or negative sentiments towards terms associated with the other camp. Since most users would have posted several tweets, users were assigned a set of tweet scores, depending on the number of tweets and from these scores overall average scores, one East score, one West score, were calculated for each user, representing their political affiliation

Automatic classification and sentiment analysis have certainly their limitations, e.g. automatic sentiment analysis often fail to spot irony and classifications do not account for instance for complex inner-fraction dynamics, that is political fractions within political fractions. However, manual classification is becoming increasingly impossible with the growing amount of data and/or limited capacities and resources and thus automatic classification is increasingly applied. It is however important to work on further developing and elaborating these tools and to supervise, critically reflect and where required correct the process of automatic analysis and its outcomes.

Additional Results

We present here some additional results that support our main conclusions in the manuscript. Supplementary Figure S4 shows the skewness and kurtosis of opinions in the Twitter data and computer simulation. These plots show again the discontinuity of political opinions in the Ukrainian Twittersphere, with jumps in February 2014.