Model Outcomes

Three distinct outcomes can be identified by simulating this simple model: a successful revolution in which all policemen are killed by revolutionaries, leading to an overthrow of the central government; a failed revolution followed by a state of anarchy 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 after the uprising.

Fig 1 shows these possible outcomes with three simulations in which the random seed and the value of n (n = 1.2) are the same but 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 = 0.1. All three simulations start with a period of instability characterised by minor 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, meaning that they do not degenerate into a revolution. This politically unstable pre-revolutionary period is a common feature of many historical revolutions: e.g. the strikes and workers’ demonstrations in Russia (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, as documented by Lagi, Bertrand and Bar-Yam [29]), inequality, unemployment, as well as by a small degree of political legitimacy, due to the Russian Tsar’s war defeat or the Shah’s unpopular westernised costumes in the case of Iran.

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larger image TIFF original image Download: Fig 1. The three model outcomes. Time series graph for the different model scenarios: (a) time series of the number of active and jailed citizens in a successful revolution; (b) time 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; (e) 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/journal.pone.0154175.g001

Around time 30 a major riot occurs, and the revolutionaries’ threshold rule is satisfied: this implies that revolutionaries become active and the rebellion, that started as a riot motivated by the poorest citizens’ bad economic conditions, has now the features of a political revolution. The revolutionaries’ threshold n therefore plays an important role because it determines the time at which revolutionaries will become active (in this specific simulation, n = 1.2). When revolutionaries become active, the citizens’ estimated probability of arrest is lowered, creating a surge in the number of active citizens. Moreover, this effect is reinforced by the fact that revolutionaries start killing policemen, again lowering the probability of arrest. What happens next depends on the parameters that regulate the relative strength of the two factions.

In the two upper graphs (p = 0.4 and r = 0.3), once revolutionaries have taken action, a large number of citizens become active, and policemen find more readily active citizens than revolutionaries: this explains why, following the surge, many citizens are arrested and only a few revolutionaries are killed. Hidden among active citizens, revolutionaries shoot policemen; when many are killed, the number of active citizens starts to increase again and, when all policemen have been killed, it reaches its maximum, i.e. all citizens with a degree of grievance exceeding the threshold become active: the revolution is complete and the government is overthrown. Political scientists (see Goldstone [3]) have observed a common feature in all successful revolutions: they only occur when there is a link between mass mobilisation and the revolutionary movements that place themselves at the head of popular revolts, giving them organisation and coherence. This occurred with the Bolsheviks and the workers’ riots in 1917 and with the Ayatollah Khomeini and the protests in the Iran’s bazaars. The model is capable of capturing this link between popular spontaneous riots and organised action by revolutionaries. Examples of successful rebellions are represented by the three major historical revolutions in France (1789), Russia (1917) and Iran (1979), as well as by the recent uprisings in Tunisia (2011). In all these cases, the pre-revolutionary government 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 different agents.

Conversely, in the middle graphs (p = 0.9 and r = 0.3), after the surge of active citizens, the armed conflict between revolutionaries and policemen is won by the latter. Nevertheless, a large number of policemen are killed and the revolution is followed by a period of major, never-ending turmoil: the huge reduction in the state’s legal capacity, caused by the uprising, drives the country towards anarchy. A similar anarchic post-revolutionary situation usually follows a rebellion when the percentage of policemen killed exceeds 40% in the simulations. The anarchic outcome resembles the present civil war scenarios in Syria and Libya, where the 2011 insurrections completely destabilised these countries, reducing their government’s capacity to rule. S2 Video shows the emergence of an anarchic outcome after an uprising.

Finally, in the lower graphs (p = 0.9 and r = 0.1), the difference in the military effectiveness of the two factions is too large, and only a few policemen are killed during the uprising (usually less than 40%). This means that, following a major rebellion, the situation is similar to that in the pre-revolutionary period: 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 only 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 different outcomes of the model vary with the parameters associated with policemen’s and revolutionaries’ precision as well as with the threshold revolutionaries employ in their decision rule, the model was simulated for different values of these parameters: in particular, n takes values in the set {0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4}, whereas the two precision parameters p and r assume values in {0.1, 0.2, …, 0.8, 0.9} and {0.1, 0.2, 0.3, 0.4}, respectively. Finally, for each combination of these parameter values, the model is simulated 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 n). The white and light grey regions represent the cases in which a return to the status quo arises after the uprising: the number of policemen killed is less than 40%. In fact, these areas correspond to a high value for policemen’s precision and a low value for that of revolutionaries. As r increases or p decreases, the outcome of the simulations changes towards anarchy: these outcomes are represented by the darker grey areas, where the percentage of policemen killed is between 40% and 80%. Above a certain 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.

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larger image TIFF original image Download: 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 means 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 order maintenance. This advantage results from the fact that policemen randomly draw one agent from the set of both active citizens and active revolutionaries within their vision radius (see rule P), and not from the set formed by revolutionaries only. This part of the model offers an incentive for revolutionaries to become active only when participation in spontaneous riots exceeds a minimum threshold. It also helps explain why, in the past, revolutionary movements occurred following strikes, protests and riots.

Fig 3 shows the same graph, albeit with the standard deviation of the proportion of policemen killed rather than the mean. First, it is interesting to note that areas characterised by anarchy, in average terms, are also associated with a high variability of policemen killed (the dark grey and black areas). In contrast, the regions corresponding to a return 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 it is easier to observe diverse outcomes.

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larger image TIFF original image Download: 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/journal.pone.0154175.g003

One of the main features shared by 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 [6–8] 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 by Taleb and Treverton [30], who point out that apparently stable regimes may be less well equipped to manage political instability than countries that are often affected by disorder and turmoil, which leads to their decline in the presence of significant and unanticipated shocks.

The model presented in this paper is able to explain the unpredictable nature of revolutions. In fact, Fig 4 shows for three different values of n (n = 0.8, n = 1.1, n = 1.4) how many of the 2,160 simulations result in a revolution and the distribution of the time when rebellion occurs (the simulations employed have different values of p and r, but these parameters do not affect the timing of revolutions). For low and medium values of n, revolutionaries become active in every simulation and the time of activation is concentrated within 50 time steps. By increasing the value of the revolutionaries’ threshold, a larger number of simulations do not result in a revolution, because the number of active citizens never reaches the level required for revolutionaries to become active, and the distribution of the time when rebellion occurs is more widespread. The revolutions generated by the model are therefore random events. In fact, it is impossible to anticipate if and when there will be a riot 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 Spring, opposition elites or defected military officers and most individuals who want to rebel against the government have an incentive to hide their true feelings until the crucial moment arises. It is also impossible to know which episode will lead to mass, rather than local, mobilisation.