**Abstract**

A polarised society is frequently observed among ideological extremes, despite individual and collective efforts to reach a consensual opinion. Human factors, such as the tendency to interact with similar people and the reinforcement of such homophilic interactions or the selective exposure and assimilation to distinct views are some of the mechanisms why opinions might evolve into a more divergent distribution. A complex model in which individuals are exposed to alternating waves of propaganda which fully support different extreme views is considered here within an opinion dynamics model. People exposed to different extreme narratives adopt and share them with their peers based on the persuasiveness of the propaganda and are mixed with their previous opinions based on the volatility of opinions to form a new individual view. Social networks help capture elements such as homophily, whilst persuasiveness and memory capture bias assimilation and the exposure to ideas inside and outside echo chambers. The social levels of homophily and polarisation after iterations of people being exposed to extreme narratives define distinct trajectories of society becoming more or less homophilic and reaching extremism or consensus. There is extreme sensitivity to the parameters so that a small perturbation to the persuasiveness or the memory of a network in which consensus is reached could lead to the polarisation of opinions, but there is also unpredictability of the system since even under the same starting point, a society could follow substantially different trajectories and end with a consensual opinion or with extreme polarising views.

**Keywords:** Opinion dynamics, polarisation, homophily, consensus, diffusion, interaction network

### **1. Introduction**

Modelling some aspects of our society is challenging at an individual and at a collective level. Every idea, every human feeling and every interaction is so unique that measuring and modelling human constructs such as freedom, love, traditions, friendship, power, or fear is defying from its basis. Obtaining a generalisation or an abstraction, such as physical laws, which apply at a social level is frequently not feasible. Two equal drops of water will act the same under similar circumstances, but no two individuals are so similar as to ensure they feel the same, think the same or react the same to some circumstances. Social settings, as opposed to physical

observed ones, often lack of measuring instruments and units, it is almost impossible to repeat experiments and so transforming our knowledge about society into simple, absolute, and universal descriptions is often unimaginable [1]. Social models are inevitably incomplete and inaccurate, because of scientific limitations and a lack of data [2] and because conventional scientific approaches cannot be applied to many of the problems faced by our society [3]. Furthermore, just a few years ago it was impossible to use the right amount of data or to model more than just a few aspects of the individuals, but today we are capable of simulating large human systems [4] with more complex interactions between its members and its environment [5]; to understand the emergence of crowd behaviour in different situations and to challenge and, in some cases, to measure, some of the theories which are frequently applied across some scientific fields [6]. Models of collective human behaviour have gained interest as the need for them grows, their results get more and more applied in policy and decision-making and their implications are spread throughout more widely.

inconclusive evidence or even fake news. Polarised opinions might foster confirmation bias, so that people with more extreme opinions tend to become more certain in their beliefs [13] and therefore, it contributes to the proliferation of fake

an idea and so there are active efforts to reach a consensual opinion. observing opinion dynamics only at a global scale and ignoring individual dynamics often lead opinions to a consensus state [15], in a similar way in which temperature differences tend to vanish. Yet, two or more contrasting ideas might be highly popular, even if all individual efforts try to reach a consensual opinion. Polarisation, or even fragmentation among many opinions, might be one of the emergent states of collective opinion dynamics, where contrasting ideas might co-exist as a steady

Frequently, individuals want to persuade others -even unintentionally- to adopt

Human factors such as the frequency at which we form ties with similar people (homophily), the tendency of having similar opinions as a result of social interactions (social influence), the fact that when presented with mixed evidence, individuals might perceive it as positive feedback for their initial position (biased assimilation), or interpreting the acceptance of an idea as reinforcement when sharing an opinion in a social environment (social feedback) are some of the causal mechanisms why the process in which ideas are updated might be polarising, meaning that final opinions are more divergent than initial opinions [11, 16].

Usually, a person interacts with others of similar age, income or other sociodemographic, behavioural, and intrapersonal characteristics, including opinions or views on a certain topic [17, 18]. If a population has polarised opinions, it means that, at a global level, there is a high probability that when two individuals are randomly picked, they share extreme different views. However, little is known with respect to the actual interactions. Individuals from a highly polarised society could almost always interact with people who share similar views if polarised bubbles rarely interact with each other. Yet, a different opinion process within the same polarised society is observed when people frequently interact with others who shared opposite views. On a polarised population, opinions have high *homophily* if most of the individuals interact with people with similar views, and opinions are *not homophilic* if people with different views interact frequently. See **Figure 1**, where

opinions are represented by the intensity of the colour of a node.

when opinions are observed at a global scale, but to detect if opinions are

Polarisation between two opinions -or fragmentation among many- is detected

homophilic, more local information with respect to the interactions is needed. For instance, in the 2016 UK referendum to remain in the European Union, 52% of the votes were to leave (a highly polarised election), but at a more local level, the area which voted most heavily in favour of one of the options was Gibraltar (where nearly 96% of the votes were to remain), whereas in Watford results were evenly distributed among leave and remain. Thus, Gibraltar had the lowest polarisation, where there was a near consensus for one of the options, but Watford had the highest polarisation between the leave and remain options. In Watford, however, with their highly polarised election outcome, interactions could still happen very frequently between people with similar views, if the opinion sharing process is highly homophilic and there are little interactions between the two voter groups. A slightly polarised society does not have homophilic opinions, but a polarised society might have homophilic opinions, or not, depending on how individuals interact and the opinion profile. The relevance of opinion homophily stems from

news, whereby once an idea is adopted, is rarely corrected [14].

*Opinion Dynamics and the Inevitability of a Polarised and Homophilic Society*

*DOI: http://dx.doi.org/10.5772/intechopen.96989*

state in a society.

**1.2 Homophilic opinions**

**27**

Models of social behaviour are complex. Many features observed at a social level are an emergent behaviour that results from interactions at a personal level and feedbacks between society and its individuals. Social behaviours are the result of collective individual actions. People adapt rapidly to new circumstances, transforming society as a whole on that process, for instance, by making it normal to maintain some physical distance with others or by wearing a facemask during the COVID-19 pandemic, but some of these social features synchronise our behaviours as well, by the constant feedback others provide.

Modelling society usually requires a substantial level of simplification at the microscopic, individual level in the hope to resemble the macroscopic, social behaviour [7]. The mathematical approach is usually to study the emergent collective patterns when thousands or millions of people -or events- are considered. For instance, a crime might be regarded as a point on a map, a friendship could be considered as a link in a network, or a driver could be modelled by its position and its speed; however, these simplifications made within a social context have helped us to understand the emergent patterns of criminal hotspots [8], the small-world phenomena observed in many social networks [9] or the formation of traffic jams despite efforts from drivers to avoid them [10].

Opinions and the ways they are updated is a complex social system. In general, individuals have an opinion about a specific topic, which is somehow updated when they are confronted with other ideas. Usually, a person gains some confidence in their views when they are reinforced by exposure to similar ideas or challenges their beliefs when they are exposed to different opinions. The exposure to distinct views is a social process and therefore, updating beliefs is mostly a social process as well, which happens perhaps during a simple conversation with others, when listening to what others say on the news, or what they publish on social media. And, as with other complex social systems, individuals transform their society with their opinion, but society transforms individuals as well. There are feedbacks between individual opinions and their collective perceptions and ideas.

#### **1.1 Polarised opinions**

Polarisation and the way it emerges is one of the key questions in opinion dynamics models [11]. An increasingly polarised society is observed in attitudes towards the COVID-19 pandemic, views in favour or against a vaccine [12], the consumption of media outlets, opinions on social media and many more. Increased exposure to ideas within an homogeneous community intensifies their tendency to be credulous, whether it is to scientific evidence, unsubstantiated rumours,

#### *Opinion Dynamics and the Inevitability of a Polarised and Homophilic Society DOI: http://dx.doi.org/10.5772/intechopen.96989*

inconclusive evidence or even fake news. Polarised opinions might foster confirmation bias, so that people with more extreme opinions tend to become more certain in their beliefs [13] and therefore, it contributes to the proliferation of fake news, whereby once an idea is adopted, is rarely corrected [14].

Frequently, individuals want to persuade others -even unintentionally- to adopt an idea and so there are active efforts to reach a consensual opinion. observing opinion dynamics only at a global scale and ignoring individual dynamics often lead opinions to a consensus state [15], in a similar way in which temperature differences tend to vanish. Yet, two or more contrasting ideas might be highly popular, even if all individual efforts try to reach a consensual opinion. Polarisation, or even fragmentation among many opinions, might be one of the emergent states of collective opinion dynamics, where contrasting ideas might co-exist as a steady state in a society.

Human factors such as the frequency at which we form ties with similar people (homophily), the tendency of having similar opinions as a result of social interactions (social influence), the fact that when presented with mixed evidence, individuals might perceive it as positive feedback for their initial position (biased assimilation), or interpreting the acceptance of an idea as reinforcement when sharing an opinion in a social environment (social feedback) are some of the causal mechanisms why the process in which ideas are updated might be polarising, meaning that final opinions are more divergent than initial opinions [11, 16].

#### **1.2 Homophilic opinions**

observed ones, often lack of measuring instruments and units, it is almost impossible to repeat experiments and so transforming our knowledge about society into simple, absolute, and universal descriptions is often unimaginable [1]. Social models are inevitably incomplete and inaccurate, because of scientific limitations and a lack of data [2] and because conventional scientific approaches cannot be applied to many of the problems faced by our society [3]. Furthermore, just a few years ago it was impossible to use the right amount of data or to model more than just a few aspects of the individuals, but today we are capable of simulating large human systems [4] with more complex interactions between its members and its environment [5]; to understand the emergence of crowd behaviour in different situations and to challenge and, in some cases, to measure, some of the theories which are frequently applied across some scientific fields [6]. Models of collective human behaviour have gained interest as the need for them grows, their results get more and more applied in policy and decision-making and their implications are spread

Models of social behaviour are complex. Many features observed at a social level are an emergent behaviour that results from interactions at a personal level and feedbacks between society and its individuals. Social behaviours are the result of

transforming society as a whole on that process, for instance, by making it normal to maintain some physical distance with others or by wearing a facemask during the COVID-19 pandemic, but some of these social features synchronise our behaviours

Modelling society usually requires a substantial level of simplification at the microscopic, individual level in the hope to resemble the macroscopic, social behaviour [7]. The mathematical approach is usually to study the emergent collective patterns when thousands or millions of people -or events- are considered. For instance, a crime might be regarded as a point on a map, a friendship could be considered as a link in a network, or a driver could be modelled by its position and its speed; however, these simplifications made within a social context have helped us to understand the emergent patterns of criminal hotspots [8], the small-world phenomena observed in many social networks [9] or the formation of traffic jams

Opinions and the ways they are updated is a complex social system. In general, individuals have an opinion about a specific topic, which is somehow updated when they are confronted with other ideas. Usually, a person gains some confidence in their views when they are reinforced by exposure to similar ideas or challenges their beliefs when they are exposed to different opinions. The exposure to distinct views is a social process and therefore, updating beliefs is mostly a social process as well, which happens perhaps during a simple conversation with others, when listening to what others say on the news, or what they publish on social media. And, as with other complex social systems, individuals transform their society with their opinion, but society transforms individuals as well. There are feedbacks between indi-

Polarisation and the way it emerges is one of the key questions in opinion dynamics models [11]. An increasingly polarised society is observed in attitudes towards the COVID-19 pandemic, views in favour or against a vaccine [12], the consumption of media outlets, opinions on social media and many more. Increased exposure to ideas within an homogeneous community intensifies their tendency to be credulous, whether it is to scientific evidence, unsubstantiated rumours,

collective individual actions. People adapt rapidly to new circumstances,

as well, by the constant feedback others provide.

*Theory of Complexity - Definitions, Models, and Applications*

despite efforts from drivers to avoid them [10].

vidual opinions and their collective perceptions and ideas.

throughout more widely.

**1.1 Polarised opinions**

**26**

Usually, a person interacts with others of similar age, income or other sociodemographic, behavioural, and intrapersonal characteristics, including opinions or views on a certain topic [17, 18]. If a population has polarised opinions, it means that, at a global level, there is a high probability that when two individuals are randomly picked, they share extreme different views. However, little is known with respect to the actual interactions. Individuals from a highly polarised society could almost always interact with people who share similar views if polarised bubbles rarely interact with each other. Yet, a different opinion process within the same polarised society is observed when people frequently interact with others who shared opposite views. On a polarised population, opinions have high *homophily* if most of the individuals interact with people with similar views, and opinions are *not homophilic* if people with different views interact frequently. See **Figure 1**, where opinions are represented by the intensity of the colour of a node.

Polarisation between two opinions -or fragmentation among many- is detected when opinions are observed at a global scale, but to detect if opinions are homophilic, more local information with respect to the interactions is needed. For instance, in the 2016 UK referendum to remain in the European Union, 52% of the votes were to leave (a highly polarised election), but at a more local level, the area which voted most heavily in favour of one of the options was Gibraltar (where nearly 96% of the votes were to remain), whereas in Watford results were evenly distributed among leave and remain. Thus, Gibraltar had the lowest polarisation, where there was a near consensus for one of the options, but Watford had the highest polarisation between the leave and remain options. In Watford, however, with their highly polarised election outcome, interactions could still happen very frequently between people with similar views, if the opinion sharing process is highly homophilic and there are little interactions between the two voter groups.

A slightly polarised society does not have homophilic opinions, but a polarised society might have homophilic opinions, or not, depending on how individuals interact and the opinion profile. The relevance of opinion homophily stems from

**2. Modelling opinions and its dynamics**

*DOI: http://dx.doi.org/10.5772/intechopen.96989*

*Opinion Dynamics and the Inevitability of a Polarised and Homophilic Society*

**2.1 The key ingredients in opinion dynamics models**

There are four ingredients in opinion dynamics models [30, 31]:

1.**Individual opinions** - Modelled usually as a number, say *si*ð Þ*t* ∈½ � �1, 1 for individual *i* at time *t*, based on the extremes of an interval, �1 and þ1, which are identified as opposing opinions, for instance, the levels of support or opposition for an idea, perceptions of security or insecurity, or left–right leaning political views. Other approaches include multi-dimensional views or

2.**External or individual forces** - External forces such as exposure to news sources [33], or events such as suffering a crime [29] or an accident, and individual forces, such as memory loss may cause an individual to update their

3.**Updating process as interactions with others** - Exposure to different ideas is frequently considered as the updating mechanism of opinions. Frequently, through interactions with others, person *i* finds a distinct opinion, *sj*ð Þ*t* , and might update their own views according to some function based on their opinion *si*ð Þ*<sup>t</sup>* and the "new" one, as *si*ð Þ¼ *<sup>t</sup>* <sup>þ</sup> <sup>1</sup> *f si*ð Þ*<sup>t</sup>* , *sj*ð Þ*<sup>t</sup>* , where usually the function *f* is assumed to get opinion *si* closer to *sj* as a result of some consensus effort. Interactions are frequently modelled on some network, where two connected nodes (individuals) share opinions with (some) of its adjacent nodes. The network structure and whether it is directional thus play a role in

4.**Metrics** - From the collective opinions, or "opinion profile", *S t*ðÞ¼

usually as a long-run behaviour of the dynamics.

ð Þ *s*1ð Þ*t* , *s*2ð Þ*t* , … , *sN*ð Þ*t* , usually its mean *S t*ð Þ and other metrics are frequently analysed, perhaps dividing by some population groups or node attributes,

fake news [14].

discrete opinions.

views about certain topics.

the updating process.

**29**

Opinion formation has been studied from many angles and different mathematical techniques, including mean-field theory and kinetic models of opinion formation [27], or by agents on a social network. Individual opinions on a certain topic are usually modelled as a single-valued number contained in some closed interval which represents extreme (opposing) opinions, for example, left–right leaning voters [28], the level of production of an employee in a plant [7] or perceptions between security and insecurity [29]. The process of opinion updating then is modelled as the result of interaction with other views, a process of self-thinking, some memory loss, or external factors. Interactions between individuals are usually modelled on some social structure, such as a network, considering some spatial proximity, or considering some social aspects, such as the level of influence of one individual to others [30]. A long-term, steady distribution of opinions is usually obtained, either as an analytical solution to some differential equations or through simulations, which reveals among others, the formation of opinion clusters, political segregation [31], vaccine hesitancy [12], the use of certain tools [32], the spread of fear of crime more as a result of opinion dynamics than crime itself [29] or even the diffusion of

#### **Figure 1.**

*Opinions (represented by the different colours of the nodes) are shared between individuals who interact (if there is a link between the nodes). Different states in which opinions are distributed show a small polarisation (left part, where most individuals have similar views) or high polarisation (right part, where opinions are split in half) and might show low homophily (bottom part, where opposite opinions are frequently shared among interacting individuals) or high homophily (top part, where opposite opinions are rarely shared among connected nodes).*

the fact that in a highly polarised population, most individuals might not be aware that so many people with different views even exist, whereas in a polarised society with little levels of homophily, encounters between people with opposite views happen frequently. Furthermore, a highly polarised society might be a steady state of some opinion dynamics but given the right circumstances (parameters) that state could be highly homophilic or a state in which most individuals interact frequently with people with different views.

Social media and other technological changes could increase exposure to diverse perspectives [19], but at the same time facilitate some mechanisms, such as the creation of links or friendships in the network, filter algorithms and rank information which may accelerate the formation of homophilic communities [16, 20]. People frequently aggregate in groups of interest, and those existent communities frequently adopt narratives from different topics, reinforcing polarisation across distinct themes, for instance, political ideology and perceptions with respect to the COVID-19 pandemic [21, 22]. People interacting with homogeneous communities tend to grow more extreme opinions and become more certain in their beliefs [13] which can favour the spread of misinformation from partisan media and increase animosity within the population [23]. For COVID-19, for example, most of the misinformation detected involves reconfigurations, where existing (often true) facts are adjusted to fit different narratives [24] which are then reproduced by large homophilic groups as facts. Massive misinformation is becoming one of the main threats to our society [14, 25, 26] which might be fostered by an increasingly homophilic opinion dynamic process and a polarised society.

*Opinion Dynamics and the Inevitability of a Polarised and Homophilic Society DOI: http://dx.doi.org/10.5772/intechopen.96989*
