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Agreement the Dynamics of Vehement Political Revolutions in an Agent-Based Framework

Agreement the Dynamics of Violent Political Revolutions in an Agent-Based Framework

• Alessandro Moro

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• Published: April 22, 2016
• https://doi.org/10.1371/journal.pone.0154175

Figures

Abstruse

This paper develops an agent-based computational model of violent political revolutions in which a subjugated population of citizens and an armed revolutionary system endeavor to overthrow a central authority and its loyal forces. The model replicates several patterns of rebellion consistent with major historical revolutions, and provides an explanation for the multiplicity of outcomes that tin can arise from an uprising. The relevance of the heterogeneity of scenarios predicted by the model can be understood by considering the recent experience of the Arab Jump involving several rebellions that arose in an obviously similar manner, just resulted in completely different political outcomes: the successful revolution in Tunisia, the failed protests in Saudi Arabia and Bahrain, and civil state of war in Syria and Libya.

Commendation: Moro A (2016) Agreement the Dynamics of Tearing Political Revolutions in an Agent-Based Framework. PLoS Ane 11(4): e0154175. https://doi.org/10.1371/journal.pone.0154175

Editor: Frederic Amblard, Université Toulouse 1 Capitole, French republic

Received: July 19, 2015; Accustomed: April 8, 2016; Published: Apr 22, 2016

Copyright: © 2016 Alessandro Moro. This is an open up access article distributed under the terms of the Creative Eatables Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant information are inside the paper and its Supporting Information files.

Funding: The writer has no support or funding to report.

Competing interests: The author has declared that no competing interests exist.

Introduction

The phenomenon of political revolutions has once again caught the attention of researchers in the wake of the recent wave of uprisings in the Arab World. The primary purpose of this paper is to present an agent-based computational model that outlines the common dynamics of major political revolutions and replicates a number of stylised facts.

The model features three types of amanuensis that interact in a bidimensional torus space: a population of citizens who are oppressed by a central government; members of a revolutionary organization who try to overthrow the government by an armed uprising; and loyal policemen who are tasked with suppressing the rebellion.

This simple model is able to reproduce several patterns of rebellion consistent with major historical revolutions: a pre-revolutionary period characterised by spontaneous riots, motivated mainly by poor economic conditions and social inequality, gives mode to an actual revolutionary rebellion, in which organised elements mobilise popular masses against the central government.

Moreover, the model provides an explanation for the multiplicity of outcomes that can arise from an uprising: a completely successful revolution leading to the overthrow of the central potency; a failed rebellion followed by a return to the condition quo; an intermediate instance where the uprising is unable to change the political organisation, but is sufficiently strong to destabilise the country and drive information technology towards anarchy.

The heterogeneity of scenarios predicted by the model is non highlighted in existing literature, and its importance can be understood by considering the contempo feel of the Arab Spring involving several rebellions that arose in an plainly similar way, only resulted in completely different political outcomes: due east.g. the successful revolution in Tunisia, the failed protests in Saudi Arabia and Bahrain, and civil war in Syria and Libya.

For decades, the most popular conceptualisations of revolution were the Marxian theory and the relative deprivation theory. The former emphasises the role of changes in production methods in generating discontent and rebellion; the latter focuses on the gap between economic expectations and realised economical performances to explain the sense of frustration and, consequently, riot participation. Both theories establish an automated link between the structural weather condition that generate grievance in social club and the likelihood of revolutionary episodes. Moreover, in both theories participation in rebellion is motivated by a collective proficient argument, such as the desire to alter the oppressive social social club. Ii of the nigh influential scholars in this stream of literature are Skocpol [1] with regard to the Marxian theory and Davies [2] concerning the relative deprivation theory. For a complete review of the political science literature about revolutions, see Goldstone [three].

In contrast, Tullock [4] develops an economical approach to explain participation in revolutions: since the benefit of an extra unit of public good is small relative to the cost of obtaining it by participating in a rebellion, individuals decide whether or not to participate based on their private gains or losses. Silver [v] provides a classification of revolutions based on Tullock's theory. Moreover, Kuran [6–viii] criticises the idea of an automatic human relationship betwixt social grievance and revolution, arguing that near historical revolutions were unanticipated. He provides an explanation based on the ascertainment that people who dislike their government tend to muffle their political preferences equally long equally the opposition seems weak. For this reason, regimes that appear to be admittedly stable may experience a sudden loss of support in the event of a minor increase in the size of the opposition, even if triggered by insignificant events.

The economical and political science literature take endeavoured to solve the collective activeness issues inherent in revolutions. For example, in criticism of Tullock, Lichbach [ix–11] identifies a number of solutions based on sanctioning and group identification methods. These solutions include the possibility of imposing community obligations, establishing institutional mechanisms, arranging contracts and using say-so. For an example of an institutional kind of solution in the context of 18th century merchant sailors, run into Leeson [12].

Furthermore, in line with Kuran's theory, Rubin [13] argues that cascades of preference revelation are more likely to occur post-obit a major shock in highly centralised regimes. This is because citizens in such political systems have a greater incentive to muffle their true political opinions in order to avert economic or legal sanctions being imposed by the central authority. Makowsky and Rubin [14] extend the previous piece of work by developing an agent-based model to study how social network technology favours preference revelation in centralised societies.

A number of game theoretic papers have also been produced that analyse the economical causes of political change: for instance, following Acemoglu and Robinson's [15] model of the economic origins of democracy, Ellis and Fender [xvi] derive conditions nether which democracy arises peacefully, when information technology occurs after a revolution, and when oligarchic governments persist. An alternative view is represented by the paper of Gard-Murray and Bar-Yam [17], who argue that democracies are more systemically complex than autocracies and, since violent revolutions are likely to disrupt existing evolved complexity, dictatorships have higher chances of emerging after uprisings.

Finally, this paper is also influenced to a bang-up extent past Granovetter's [eighteen] theory about threshold models of collective behaviours and by Epstein's [xix] agent-based model of civil violence. According to Granovetter, individuals face many situations with multiple alternatives, and the costs and benefits associated with these alternatives depend on how many other individuals have called the various options in the past. For this reason, each individual has a personal threshold, and decides to join collective activeness, such as a riot or a strike, if the number of people participating at that time exceeds this threshold. Following this thought, Epstein develops an agent-based model of civil violence involving ii types of role player, agents and cops, interacting in a bidimensional torus infinite. In this model the agents decide to insubordinate against the authorities if their level of grievance corrected by the risk of existence arrested by the cops exceeds their activation threshold. 1 of the main findings of this model is that intermittent outbursts of violence occur, distributed irregularly over fourth dimension and space. Another study that explores the temporal and spatial improvidence of civil unrest is that produced by Braha [20]. In particular, his newspaper demonstrates that the distribution of real episodes of ceremonious violence tin can be replicated using a spatially extended dynamical model that incorporates the effects of social and communication networks.

The remainder of the paper is organised equally follows: the adjacent department describes the model; in the Results section, the three outcomes generated by the model are presented and their dependence on the model parameters is analysed using graphical and statistical tools; the terminal section discusses the results and their relevance for analysing gimmicky revolutions.

Methods

In the agent-based computational model presented in this paper, there are three types of agent that interact in a bidimensional torus space: citizens, policemen and revolutionaries. Citizens are members of a population subjugated to a primal authority who decide whether or non to rebel confronting the regime based on their degree of economic and political grievance. Revolutionaries are members of an organised opposition group that seeks to overthrow the fundamental authorities by an armed insurgence. Policemen are the forces loyal to the primal authority that have been tasked to suppress any kind of defection by arresting rebellious citizens and killing revolutionaries.

In this department, the features of each agent are described in particular, beginning with the citizen specification. Every bit in Epstein [xix], social grievance represents the motivation that potentially leads citizens to revolt; for each denizen i the grievance is assumed to be the product of an index of economic hardship H and a measure of government illegitimacy, defined as one − l, where l is a parameter measuring the legitimacy of the central authorisation: (1) In contrast to Epstein's specification, the perceived hardship, and consequently grievance, is a function of citizens' income y _i . In fact, each citizen is endowed with an income drawn from a lognormal distribution, whose density office is: (2) The functional form chosen for the hardship index is: (3) This function allows each citizen'south economic condition to be mapped to a value in the (0, ane) interval. This alphabetize is a logistic transformation of the difference between citizens' income and the expected income in the population . Given this monotonic transformation, hardship is a decreasing function of citizens' income. This expression is similar to the definition of grievance employed past Kim and Hanneman [21]. The main difference with respect to their specification is that the two authors utilize a local mensurate of inequality, i.e. the altitude betwixt each amanuensis'due south wage and the boilerplate wage in the agent'due south neighbourhood; conversely, in this model a global measure of inequality is preferred.

On the other hand, the price of participating in a rebellion is defined as the production of the estimated probability of being arrested A _i and the opportunity toll of joining a revolt J: (4) In fact, each citizen estimates the probability of being arrested before actively joining a rebellion. This estimated probability is defined as in Epstein [19]: it is an increasing function of the ratio of policemen to already rebellious agents inside the citizen's vision radius. In particular, in this model rebel agents can either be citizens and revolutionaries: (v) where , and represent the number of policemen, rebellious citizens and agile revolutionaries inside the citizen's vision, respectively. The vision, a circular neighbourhood with centre located in the citizen's position and a radius equal to v, represents the set of lattice positions probed by the denizen. The ane in the previous formula makes explicit that, before participating in a riot, a denizen will count himself as an active agent: thus the ratio is e'er well defined. In practice, the flooring operator is applied to the ratio of policemen to rebel agents, every bit in Wilensky'south [22] version of Epstein's model.

If an agile citizen is arrested by a policeman, he remains in jail for a number of periods drawn from a uniform distribution on the (0, j _max ) interval. For this reason, the opportunity toll of rebelling is divers as a function of the maximum number of periods in jail j _max , multiplied by income loss whilst in jail: (6) Since the inner argument of the logistic transformation is positive, given that income assumes merely positive values, the logistic function is rescaled in order to define a cost function J on the (0, 1) interval. Expression (vi) is also consistent with the literature on political violence, which finds a negative relationship between income and participation in ceremonious violence phenomena. For example, Collier and Hoeffler [23, 24] and Fearon and Laitin [25], using cross-country regressions, find that economical growth and per capita income correlate negatively with the risk of civil conflict. Moreover, Miguel, Satyanath and Sergenti [26] place a causal negative upshot between positive income shocks and civil state of war incidence in Sub-Saharan African countries employing an instrumental variable approach.

Having defined the incentives and the costs underlying participation in riot activities, it is now possible to specify citizens' rule of activation. Citizens particularly become active, pregnant that they determine to rebel against the government, if the difference between their social grievance and the expected opportunity cost of joining a riot exceeds a stock-still threshold; otherwise, they will proceed tranquillity. The citizens' rule is therefore:

Rule C: if Chiliad(y _i ) − N(y _i ) > f exist active; otherwise, keep serenity.

This inequality can be interpreted using Kuran's [6] theory: the left-hand side represents the expected utility of expressing opposition to the primal authority in public; the right-hand side f is the constant utility of keeping tranquility and concealing private political preferences.

The revolutionaries' behaviour is simpler. Revolutionaries are members of an organised group that attempts to overthrow the regime by an armed conflict. This kind of amanuensis can be interpreted as a proper revolutionary group or as defected elements from the military that decide to side with the population in revolt. Historical examples of the outset type of organisation include the Bourgeois Militia of Paris in the French Revolution (1789); the Bolsheviks and Carmine Guards in the Russian Revolution (1917); the leftist revolutionaries of the System of Iranian People's Fedai Guerrillas in the Iranian Revolution (1979); the Muslim Brotherhood in the Egyptian Revolution (2011); the jihadist group of the Islamic State of Iraq and the Levant in the Syrian Civil War (2011), and many others. Defections from the military are also very mutual in all revolutions: a typical case is the pro-Khomeini members of the Iranian Air Forcefulness who fought against the loyal Immortal Guards during the 1979 uprisings.

Information technology is assumed that revolutionaries behave co-ordinate to the following rule:

Rule R: if be active and kill a randomly selected policeman inside vision radius 5 with a probability equal to r; otherwise, remain subconscious.

Here R, C and P are the total number of revolutionaries, the total number of active citizens and the full number of policemen, respectively. Rule R means that revolutionaries determine to become active when the ratio of rebel forces to policemen loyal to the government exceeds a given threshold n. In this respect, revolutionaries are unlike from citizens: citizens cull how to behave according to local information available inside their vision radius. In contrast, revolutionaries human action on the basis of global information and make up one's mind when to start a revolution by employing a threshold-based dominion involving the total number of active citizens in the population. In fact, information technology is causeless that the revolutionary organisation is spread across the country, enabling it to obtain an guess of the total number of agile agents in the population.

When a revolutionary is active, he kills a randomly selected policeman in his vision radius with a probability equal to r. Otherwise, when the ratio is less than the stock-still threshold, all revolutionaries volition remain hidden among quiet citizens and policemen will be unable to identify them.

As far as policemen are concerned, they simply audit the lattice positions within their vision radius and randomly cull an active citizen or active revolutionary: if the randomly selected amanuensis is a denizen, the policeman will arrest him, or will kill him if he is an active revolutionary with a probability equal to p. The policemen's rule is therefore:

Dominion P: randomly select an agent from the agile citizens and active revolutionaries inside vision radius v. If the randomly selected amanuensis is a citizen, abort him; if he is a revolutionary, impale him with a probability equal to p.

The aforementioned vision radius v is assumed for citizens, revolutionaries and policemen. Furthermore, parameters r and p tin also be interpreted in terms of weapon precision or, more broadly, in terms of effectiveness in the military chapters of the conflicting parties. Once killed, revolutionaries and policemen are simply removed from the bidimensional space.

Finally, citizens who are not in jail, revolutionaries and policemen who are non killed tin can move in the lattice infinite to a random site without agents or in which there are only jailed citizens following this simple rule:

Rule M: within vision radius five, randomly move to an empty site or to a site in which there are only jailed citizens.

Table 1 presents the parameter values that are kept constant in all model simulations: the values assigned to the lognormal parameters (a, b) and the price function parameter w ₂ are selected in lodge to obtain a widespread distribution of hardship and opportunity costs on the (0, 1) interval, fugitive concentration at the extremes of that interval; the other values are assigned according to those selected by Epstein [19]. The side by side section of the paper investigates the effects of the new parameters introduced past the present model, i.e. the armed services effectiveness of the two factions (p, r) and the revolutionaries' threshold north.

At the get-go of each model simulation, the random values y _i are fatigued from the lognormal distribution and the different agents are randomly situated on the sites of the lattice. So, an agent is selected at random. Nether rule G, he moves to a random position inside his vision, where he acts according to dominion C if he is a citizen, rule R if he is a revolutionary or rule P if he is a policeman. This procedure is replicated until a given time or a specific status (eastward.g. all revolutionaries or policemen are killed) is reached. The model was written using NetLogo (Wilensky [27]), whereas the statistical analysis was performed using R (R Core Team [28]): details of implementation and the code are in the S1 Code file, in the supplementary material.

Results

Model Outcomes

3 distinct outcomes can exist identified past simulating this simple model: a successful revolution in which all policemen are killed by revolutionaries, leading to an overthrow of the cardinal government; a failed revolution followed by a state of chaos due to the large number of policemen killed; a completely failed revolution with only a few policemen killed, signifying a return to the status quo afterwards the uprising.

Fig 1 shows these possible outcomes with iii simulations in which the random seed and the value of n (northward = 1.2) are the same only the two precision parameters take different values: in particular, in the two upper graphs p = 0.4 and r = 0.3; in the middle pictures p = 0.9 and r = 0.3; finally, in the lower graphs p = 0.9 and r = 0.i. All 3 simulations start with a period of instability characterised by pocket-size revolts where the poorest component of the population, made up of citizens with the greatest degree of grievance and the lowest opportunity cost, decides to rebel. However, these riots are too small, pregnant that they practise not degenerate into a revolution. This politically unstable pre-revolutionary period is a common characteristic of many historical revolutions: e.yard. the strikes and workers' demonstrations in Russian federation (1917), Iran (1977–1978) and the Arab World (2011), motivated to a great extent by poor economic conditions such as low wages, high inflation (especially high food prices, equally documented by Lagi, Bertrand and Bar-Yam [29]), inequality, unemployment, likewise as by a minor caste of political legitimacy, due to the Russian Tsar's state of war defeat or the Shah'due south unpopular westernised costumes in the case of Iran.

Fig 1. The three model outcomes.

Time series graph for the unlike model scenarios: (a) time series of the number of agile and jailed citizens in a successful revolution; (b) fourth dimension series of the number of revolutionaries and policemen who have survived a successful revolution; (c) time series of the number of active and jailed citizens in an anarchic scenario; (d) time series of the number of revolutionaries and policemen who have survived an anarchic scenario; (due east) time series of the number of active and jailed citizens in a failed revolution; (f) time series of the number of revolutionaries and policemen who have survived a failed revolution.

https://doi.org/10.1371/periodical.pone.0154175.g001

Around time thirty a major anarchism occurs, and the revolutionaries' threshold dominion is satisfied: this implies that revolutionaries go active and the rebellion, that started equally a riot motivated past the poorest citizens' bad economic atmospheric condition, has now the features of a political revolution. The revolutionaries' threshold n therefore plays an important part because it determines the time at which revolutionaries will become active (in this specific simulation, due north = ane.2). When revolutionaries become active, the citizens' estimated probability of abort is lowered, creating a surge in the number of agile citizens. Moreover, this result is reinforced by the fact that revolutionaries showtime killing policemen, once again lowering the probability of arrest. What happens next depends on the parameters that regulate the relative strength of the 2 factions.

In the 2 upper graphs (p = 0.4 and r = 0.3), once revolutionaries take taken activity, a large number of citizens become agile, and policemen find more than readily agile citizens than revolutionaries: this explains why, following the surge, many citizens are arrested and only a few revolutionaries are killed. Subconscious among active citizens, revolutionaries shoot policemen; when many are killed, the number of active citizens starts to increment over again and, when all policemen accept been killed, information technology reaches its maximum, i.due east. all citizens with a degree of grievance exceeding the threshold go active: the revolution is complete and the authorities is overthrown. Political scientists (see Goldstone [three]) have observed a common feature in all successful revolutions: they only occur when in that location is a link between mass mobilisation and the revolutionary movements that place themselves at the caput of popular revolts, giving them organization and coherence. This occurred with the Bolsheviks and the workers' riots in 1917 and with the Ayatollah Khomeini and the protests in the Islamic republic of iran's bazaars. The model is capable of capturing this link betwixt popular spontaneous riots and organised activity by revolutionaries. Examples of successful rebellions are represented by the 3 major historical revolutions in France (1789), Russia (1917) and Iran (1979), besides as by the recent uprisings in Tunisia (2011). In all these cases, the pre-revolutionary regime is overthrown and a new order is established. S1 Video presents the evolution of a successful revolution showing the bidimensional space and the interactions between dissimilar agents.

Conversely, in the middle graphs (p = 0.nine and r = 0.iii), after the surge of active citizens, the armed conflict betwixt revolutionaries and policemen is won by the latter. Nonetheless, a large number of policemen are killed and the revolution is followed by a period of major, never-catastrophe turmoil: the huge reduction in the state's legal capacity, caused by the uprising, drives the state towards anarchy. A similar anarchic post-revolutionary state of affairs normally follows a rebellion when the percentage of policemen killed exceeds forty% in the simulations. The anarchic outcome resembles the present civil war scenarios in Syrian arab republic and Libya, where the 2011 insurrections completely destabilised these countries, reducing their government's capacity to dominion. S2 Video shows the emergence of an anarchic outcome after an insurgence.

Finally, in the lower graphs (p = 0.nine and r = 0.one), the difference in the military effectiveness of the two factions is too large, and only a few policemen are killed during the uprising (ordinarily less than xl%). This means that, following a major rebellion, the state of affairs is similar to that in the pre-revolutionary menses: the status quo is maintained. Here the analogy is with the 2011 riots in Saudi Arabia and Bahrain, where opposition groups were very weak from a military perspective, and merely a few police officers were killed in the street violence episodes. A simulated example of a failed revolution is presented in S3 Video.

In order to explore how the unlike outcomes of the model vary with the parameters associated with policemen's and revolutionaries' precision as well as with the threshold revolutionaries apply in their determination rule, the model was simulated for different values of these parameters: in detail, due north takes values in the set up {0.seven, 0.8, 0.9, one.0, 1.ane, 1.two, 1.3, one.4}, whereas the two precision parameters p and r assume values in {0.1, 0.2, …, 0.8, 0.9} and {0.1, 0.2, 0.iii, 0.4}, respectively. Finally, for each combination of these parameter values, the model is fake 60 times, for a total of 17,280 simulations (S1 Dataset file contains all of the simulations performed). Each simulation is halted after 300 time steps.

Fig 2 shows the average proportion of policemen killed in the simulations for different combinations of p and r (each mean is calculated employing 480 simulations, averaging over different values of northward). The white and light greyness regions represent the cases in which a return to the status quo arises after the insurgence: the number of policemen killed is less than xl%. In fact, these areas correspond to a loftier value for policemen'due south precision and a low value for that of revolutionaries. As r increases or p decreases, the consequence of the simulations changes towards chaos: these outcomes are represented by the darker greyness areas, where the percentage of policemen killed is between 40% and 80%. Above a sure level for the two precision parameters, the situation changes from anarchy to successful revolution: the regions for successful revolutions, where the average percentage of policemen killed exceeds 80%, are coloured black.

Fig 2. Average proportion of policemen killed for different values of the two precision parameters.

For each combination of p and r, the average proportion of policemen killed is calculated employing 480 simulations.

https://doi.org/10.1371/journal.pone.0154175.g002

An important feature of the figure is that the white and light grey areas are well below the 45 degree line: this ways that policemen need a very high level of precision compared to that of revolutionaries in order to win the armed conflict. This is due to the revolutionaries' strong advantage: in fact, they can hide among active citizens and attack when government forces are engaged in public society maintenance. This advantage results from the fact that policemen randomly describe one amanuensis from the fix of both active citizens and agile revolutionaries within their vision radius (meet rule P), and not from the gear up formed by revolutionaries but. This role of the model offers an incentive for revolutionaries to become agile just when participation in spontaneous riots exceeds a minimum threshold. It also helps explicate why, in the past, revolutionary movements occurred post-obit strikes, protests and riots.

Fig three shows the same graph, albeit with the standard deviation of the proportion of policemen killed rather than the mean. Starting time, it is interesting to note that areas characterised past anarchy, in boilerplate terms, are also associated with a loftier variability of policemen killed (the dark grey and black areas). In contrast, the regions corresponding to a render to the status quo and the regions of successful revolutions display much lower levels of volatility: this means that, in these areas, the same outcome is often observed, while in the regions where anarchy, on average, is observed information technology is easier to observe diverse outcomes.

Fig 3. Variability of the proportion of policemen killed for different values of the two precision parameters.

For each combination of p and r, the standard deviation of the proportion of policemen killed is calculated employing 480 simulations.

https://doi.org/10.1371/periodical.pone.0154175.g003

One of the main features shared past many revolutions in history is that they were not anticipated, neither by the government nor by the opposition. This pattern was first observed by Kuran [half dozen–eight] in the dynamics of the French, Russian and Iranian revolutions and in the fall of communist regimes in Eastern Europe. A related interpretation was provided recently past Taleb and Treverton [30], who point out that obviously stable regimes may exist less well equipped to manage political instability than countries that are often affected by disorder and turmoil, which leads to their reject in the presence of meaning and unanticipated shocks.

The model presented in this paper is able to explicate the unpredictable nature of revolutions. In fact, Fig iv shows for three different values of n (north = 0.8, n = 1.1, due north = 1.4) how many of the 2,160 simulations upshot in a revolution and the distribution of the time when rebellion occurs (the simulations employed have different values of p and r, simply these parameters do non affect the timing of revolutions). For depression and medium values of northward, revolutionaries become active in every simulation and the fourth dimension of activation is concentrated inside 50 time steps. By increasing the value of the revolutionaries' threshold, a larger number of simulations practice not result in a revolution, because the number of agile citizens never reaches the level required for revolutionaries to go active, and the distribution of the fourth dimension when rebellion occurs is more widespread. The revolutions generated past the model are therefore random events. In fact, information technology is impossible to conceptualize if and when at that place will exist a anarchism involving enough active citizens to activate the revolutionaries and generate an uprising. This behaviour of the model mimics real revolutionary events in which, as stressed by Goldstone [31] in the context of the Arab Leap, opposition elites or defected armed services officers and most individuals who want to rebel against the government have an incentive to hibernate their true feelings until the crucial moment arises. It is too incommunicable to know which episode volition lead to mass, rather than local, mobilisation.

Fig 4. The unpredictability of revolutions.

The graphs show how many simulations result in the occurrence of a revolution and the distribution of the time when rebellion occurs: (a) histogram of the number of revolutions that have place in 2,160 simulations for n = 0.viii; (b) histogram of the time when revolutions occur for n = 0.viii; (c) histogram of the number of revolutions that take place in ii,160 simulations for northward = 1.1; (d) histogram of the fourth dimension when revolutions occur for northward = 1.i; (e) histogram of the number of revolutions that have identify in two,160 simulations for n = ane.4; (f) histogram of the fourth dimension when revolutions occur for due north = 1.4.

https://doi.org/10.1371/journal.pone.0154175.g004

Statistical Analysis

Using the aforementioned simulated data described in the previous subsection, several statistical models are estimated so every bit to help empathise how the 3 outcomes of the model depend on the two precision parameters and the revolutionaries' intervention threshold.

In each simulation s a binomial distribution is assumed for the number of policemen killed z _s . The two parameters of this distribution are the number of policemen P and the probability of killing a policeman k, respectively. This last quantity, which can likewise be interpreted as a measure of the probability of a successful revolution, is assumed to be a role of the three well-nigh important parameters of the model, i.e. the precision of policemen p _s , the precision of revolutionaries r _{due south} , the revolutionaries' activation threshold due north _s . The probability part of the number of policemen killed is therefore: (7) The model is estimated with different link functions for probability k, and the issue of northward is included with a third-degree polynomial: (eight) where g(.) can be the linear, logit, probit or complementary log-log link function.

The results are presented in Table two: in the kickoff column, the linear probability model (LPM) is estimated using the ordinary to the lowest degree squares figurer; in the other three columns, a different generalised linear model is estimated using the maximum likelihood estimator, assuming the link role of the logit, probit and complementary log-log model, respectively.

In all models, the two precision parameters have the expected signs: the policemen's precision has a significant and negative touch on the probability of killing a policeman because the higher the precision of governmental forces, the larger the number of revolutionaries killed and, consequently, the lower the effectiveness of revolutionaries in killing policemen; on the other manus, every bit expected, the revolutionaries' precision has a significant and positive upshot on the probability of killing a policeman.

In order to analyse the issue of the revolutionaries' threshold n on the probability of killing a policeman, function k(0.nine, 0.three, due north) is plotted in Fig 5 (p = 0.9 and r = 0.iii are plausible values for the two precision parameters) for the linear, logit, probit and complementary log-log model. In all specifications, information technology is evident that the probability of killing a policeman slightly increases in northward up to a given value; and then, the probability decreases markedly if n increases. A third-caste polynomial is preferred to a second-degree ane because it allows this asymmetry to be captured. The intuition behind this shape is the following: for a revolutionary organisation, it is not optimal to outset a revolution too early, when popular riots are small-scaled (small value of n), because it would hands come up nether burn from policemen. At the aforementioned time, notwithstanding, revolutions may not occur if the revolutionary system waits besides long (high value of northward). According to these estimates, if the revolutionary arrangement's objective is to maximise the probability of a successful revolution, the optimal behaviour is to choose n in [1.0, one.1], which suggests starting the insurgence when the number of active agents is equal to that of governmental forces or exceeds it by about 10%.

Discussion

Although the agent-based model presented in this paper is simple and makes no claim of incorporating all of the complex aspects involved in historical revolutions, it nevertheless captures several relevant stylised facts that are common to most revolutionary episodes in the existent globe.

The about important of these facts is represented by the multiplicity of dissimilar scenarios that tin arise from a rebellion, i.due east. a successful revolution, an anarchic scenario and the return to the condition quo. The relevance of this last aspect can be understood past because contempo feel in the Arab Spring, where many rebellions, that seemed to start in 2011 in a similar way, resulted in completely unlike political outcomes.

Moreover, this model highlights a plausible dynamics, coherent with major political revolutions, that can exist summarised equally follows: a pre-revolutionary period characterised by spontaneous riots motivated mainly by poor economic conditions and social inequality, followed by a proper revolutionary rebellion where organised and politically oriented elements mobilise popular masses against the cardinal potency. This dynamics mimics the sequence of events of almost historical revolutions, and is consistent with the political scientific discipline literature, which stresses the role played past revolutionary elites in the organization of successful revolutions.

Furthermore, this newspaper examines the trade-off that revolutionaries face up in deciding when to go active: if they beginning an uprising too early, when popular riots are minor, they will directly come under fire from policemen; on the other hand, if they wait as well long, the revolution may not occur at all. If the revolutionary arrangement's objective is to maximise the probability of a successful revolution, the optimal threshold should balance these 2 contrary forces, and riots that practice not exceed this minimum level of rebels volition not degenerate into revolutions.

This paper too stresses the random nature of revolutions, pointing out that rebellions arise from interactions between many agents, determining their unpredictability: it is impossible to predict with certainty when and which riot will degenerate into a revolution. This consideration implies that like countries, in terms of institutions and political systems, may experience revolutionary events at unlike points in time, or that some may not experience revolutions at all.

A policy implication that can be derived from the model is as follows. Let united states suppose that a foreign land wants to intervene in another country to support a revolutionary grouping by providing more than effective weapons in order to overthrow the existing government. In the framework of the model, this is translated into an increase in the revolutionaries' effectiveness captured by parameter r. It is also assumed that, without external intervention, the initial configuration of precision parameters would have led to a rebellion followed by a return to the status quo. If the increase in revolutionaries' precision is not sufficiently big, as shown in the graph in Fig two, the political situation may degenerate from a relatively stable situation, the return to the condition quo (the white and light gray areas in the figure), to an unstable one, characterised by a rebellion resulting in anarchy (the darker grey expanse in the effigy). This implies that the foreign government should provide enough support in order to deliver a successful revolution as the concluding consequence (the blackness area in the effigy). Mistakes in the calibration of this support may precipitate a country towards a land of persistent turmoil and civil state of war.

Supporting Data

S1 Lawmaking. The lawmaking that implements the model described in the paper.

The model was written using NetLogo. The file allows users to alter the parameter values and visualise the results both in the bidimensional space and the time serial graphs. The simulated data employed in the analysis were generated using the BehaviorSpace tool in NetLogo; the statistical assay was performed using R.

https://doi.org/x.1371/journal.pone.0154175.s001

(NLOGO)

S1 Video. The video of a successful revolution.

The greenish circles correspond quiet citizens, the orange squares are revolutionaries and the bluish triangles are policemen. When a circumvolve turns scarlet, it ways that the citizen has decided to become active; a black circumvolve implies that the agent has been arrested. This video shows a revolution where all policemen are killed past revolutionaries: in fact, later on the massive activation of citizens, the blue triangles disappear.

https://doi.org/10.1371/periodical.pone.0154175.s002

(MOV)

S2 Video. The video of an anarchic scenario.

This video shows a rebellion where all revolutionaries are killed past policemen, simply where a high proportion of policemen also die: this implies that, even after the uprising, at that place is a persistent level of rebellion activity represented by the numerous red circles.

https://doi.org/10.1371/journal.pone.0154175.s003

(MOV)

S3 Video. The video of a failed revolution.

This video shows a rebellion where all revolutionaries are killed by policemen and very few policemen dice: this means that, later on the uprising, there are very few red circles, representing active citizens, which immediately turn black considering they are arrested past policemen.

https://doi.org/x.1371/journal.pone.0154175.s004

(MOV)

S1 Dataset. This file contains all of the simulations performed in this paper.

Information are organised as a matrix in which each row corresponds to a simulation and each column represents a variable. In detail, the starting time column, called id, reports a progressive number that identifies each simulation. The other columns study the precision of policemen (p), the precision of revolutionaries (r), the activation threshold (north), the number of policemen who survive 300 time steps (called policemen), the number of revolutionaries who survive 300 time steps (called revolutionaries), and the time when the revolution occurs (called t _rev ). If t _rev assumes a value equal to 999, it means that no revolution occurs within 300 time steps.

https://doi.org/10.1371/journal.pone.0154175.s005

(TXT)

Acknowledgments

I am grateful to Professor Paolo Pellizzari, Clairissa D. Breen and an anonymous referee for their extremely useful comments and suggestions. I also thank all the participants in the RODEO seminar in Venice, the 8th Ruhr Graduate School Doctoral Conference in Essen and the 20th Spring Meeting of Young Economists in Ghent for their interesting critical discussions.

Author Contributions

Conceived and designed the experiments: AM. Performed the experiments: AM. Analyzed the data: AM. Contributed reagents/materials/analysis tools: AM. Wrote the paper: AM.

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