Universita Ca Foscari Venezia Department of Applied Mathematics Prof. Paolo Pellizzari A Dynamical Simulation of Riots: Social Stress, Upper Bounds and Governmental Intervention Handed in on 23.12.2006 by: Krzysztof Olszewski (olszewski@unive.it) ABSTRACT In this paper I present a dynamic model of rioting. It is based on Granovetters model of social thresholds and allows for dynamics in the riot process. I study, via computer simulations, different factors that affect riots and their interplay. First, I introduce social stress that rises over time. Secondly, I consider the possibility of an upper bound of rioters, that lets the whole system collapses. Finally, I introduce governmental intervention that is applied randomly in order to prevent riots. The findings of the paper can be used by both politicians and sociologist for further research. My results show that governmental interventions can stop the emergence of riots, but in order to be successful, they have to be applied often and on a large scale. Keywords: Agent based model, social modeling, riots, thresholds.
1 1 Introduction Sociologist and politicians are concerned about riots that occour from time to time in every population. Some of them are rather small and local, thus neglegible. Others, like in the case of France spread among the whole country and lead to significant damages. During the Paris riots students and demonstrants burned cars and destroyed windows, leading to huge economical losses and creating fear among the population. Thus riots can create a enormous negative externality for the whole economy and should be studied carefully. Among different approaches, the seminal contribution comes from Mark Granovetter (1978), who studies social thresholds and the rise of riots. He looks at a population in which thresholds for riot participation are normally distributed. Granovetter finds out, that groups of people with quite equal average preferences generate very different results. What makes the difference is the variance of the distribution: For a range of different variances only few agents riot, while by passing a specific variance the system explodes and everybody is rioting. Nowadays, we are able to simulate economical and sociological behaviour by the use of Agent-Based-Models (AB). One important contribution is the paper by Arthur (1994), in which he simulates inductive reasoning. In his example people have to decide whether to go to a bar, which is only a nice place if it is not to crowded. A more general overview on ABmodels in social sciences can be found in the article by Rauch (2002). He presents Schellings segregation model, Hammonds corruption model and Epsteins artificial genocide. What we learn, is that micro-behaviour can lead to a totally different macro-behaviour. Moreover, thresholds are responsible for the macro-behaviour and crossing the threshold can trigger unexpected and dramatic results. For example non-racist agents turn out to behave in a racist way, once they are taken as a whole group. In my paper we see that changing thresholds slightly, leads to extreme reactions of the whole society and we discuss the dynamics on rioting. Explaining riots and their emergence is an often touched topic in sociology. Upton (1985) gives a wide presentation on different explanation approaches to the emergence of riots. Also more recent literature deals with the problem of finding out, why a riot emerges. For example Bergensen and Herman (1998) analyze the L.A. riots of 1992 in which around 40 people died and conclude, that they are based on races and immigration. Both papers deal with the pure theory behind human behaviour in large groups, but do not attempt to simulate or predict it. Predictions can be only based on simulations, because it is quite difficult to collect a data set on riots and perform regressions that tell us the exact parameters and their sig-
2 nificance. Having parameters would help a lot to prevent riots, as those tell what kind of preventive measures can be effective. What both politicians and sociologist can do, is to assume some parameters and to simulate possible future behaviour of rioters. This task requires adequate computational tools. While AB-models are used extensively in artificial markets, they are not so common in sociology. Bhat and Maciejewski (2006) state that only few simulations have been performed so far on riots. Nowadays their application becomes more and more important, as we see in the following examples: One very important problem is the right tactic in order to prevent riots at international summits, which are partially secured by the police and sometimes even by the military. Suzić and Wallenius (2005) from the Swedish defence research agency propose a simulation model, which allows the commander to evaluate different anti-riot strategies in real time. Bhat and Maciejewski (2006) apply physics models in order to study the implications of riots on traffic, looking on the case of the L.A. riots in 1992. They find out that in order to start a widely spreading riot, a catalyst is needed, who then triggers the behaviour of the whole group. The most recent application of simulation models is that to riots in prisons. Pabjan and Pekalski (2007) study riots in prisons where different cells, thus different kinds of inmates are perfectly separated. Similar to Bhat and Maciejewski (2006) they find out, that recedivists who act as catalysts are necessary to trigger riots. Contrary to usual approaches, they conclude that an open communication in prisons helps to prevent riots between inmates. Basing on Granovetters work, I propose you a dynamical model of riots which allows for both an increasing social stress and governmental intervention. The paper is organized as follows. Section 2 gives some background on riots and social behaviour and I implement the Granovetter model in a Agent-Based-Model. In Section 3, I augment the model: In the first step I introduce dynamics in the behaviour of agents, as the threshold declines over time. In the second step, riots break down when an upper threshold of rioters is reached. The last part deals with randomly applied governmental intervention. Section 4 concludes the paper. 2 Riots and Social Thresholds Collective behaviour may be very different from individual behaviour and recent incidents in France make it sensible to investigate it more detail-fully. Following very close Granovetter (1978), I give you an introduction to collective behaviour and its application to rioting. Basically, models of collective behaviour are used to explain situations, in which agents can make a binary and mutually exclusive decision how to act. Each action leads to consequences which can be either good or bad and may
3 very much depend on the actions of others. It is striking, that groups with people of similar average preferences but slightly different variance in their distribution can generate completely different outcomes. The first thing we assume here is that all participating agents share different norms. We do not ask how people come to those norms, but take them as given. Granovetter (1978) shows, that a small change of the distribution of such norms can trigger extreme behaviour. The main driving force of agents behaviour is their gain from an action and the cost they have to pay when performing it. As Granovetter (1978) points out, Berk (1974) states that the individual cost of joining a riot declines with the size of the rioting group. Individuals are assumed to be rational and want to avoid punishment. As the group size increases, it becomes less likely that the police will capture them. Because people have different levels of risk-aversion or willingness to destroy something, we introduce thresholds which represent this attitude. The threshold represents the proportion of rioters that trigger the agent to participate the riot. Some agents are always willing to fight, while others become heroic only if a large part of the population participates. The diffusion of violence is studied by Myers (2000) who states that the whole process is quite complex, but basically people turn to behave as a collective group and give up their own thinking, after a threshold is reached. Granovetter adopted the idea of thresholds from Schelling and his model of residential segregation. It is the aggregation of agents, that triggers the extreme behaviour. Single agents are unwilling to riot, on average. But once they see enough rioters, they join the mob. We observe a chain reaction. Primarily, the agent with the lowest threshold starts first, then the one with the next higher threshold joins him and so on. We observe a number of rioters that stays low for a long time and then explodes, once a certain level is reached at which everybody wants to participate. The setting of the parameters is chosen according to Granovetter (1978), thus there are 100 agents in the society. This makes calculus quite easy and the number of agents corresponds to the percentage points of rioters. The mean threshold is set to 25 and the thresholds are normally distributed. Normal distribution allows for negative thresholds, which are difficult to interpret, but gives repeatable results. Using a uniform distribution instead, allows for non-negative values, but has a drawback. If we are unlucky, we do not get anyone with zero threshold, thus the rioting never starts. You can find a discussion on this in Granovetters paper. Moreover, I choose different values for the variance in order to achieve meaningful results. The simulations are run in R and the computer code can be found in the appendix.
4 3 Simulations The computer code I wrote in order to simulate Granovetters model can be augmented such that it captures dynamics on the distribution of thresholds and external effects. Doing this, I follow this path: First I introduce dynamics, which allow for a continuously increasing social stress. In the second step, I put an upper bound on the proportion of rioters, which stops all rioting immediately and restarts the system. Finally, I introduce interactions of the government, which are applied randomly in order to prevent riots. 3.1 Dynamics The original model by Granovetter (1978) assumes the threshold distribution to be fixed over time. This assumption leads to two different results, basing on the choice of the variance. Having a mean of 25, there are around 8 rioters on average when the variance is below 12. But once the critical value of 12.2 is crossed, the number of rioters converges quickly to the whole population size, thus everybody is rioting. I think, that this is to simple and moreover, it is counterfactual to assume a constant distribution. It would mean that depending on the distribution we would observe chaotic riots in some places, while in others just a small and constant number of rioters would be observed. To make the model more coherent with reality, let us look at recent history and introduce the term "social stress". Social stress comes from the fact that one observes a bad attitude of the whole economy, friends become unemployed, prices for substantial goods rise, the weather becomes bad and so on. Initially, all people are endowed with different thresholds, but those decrease over time, as social stress increases. When the social stress increases, it makes the agents to react on fewer rioters than they initially would. One can ask why I do not change the variance over time instead of the mean. There are two reasons: First, we know form Granovetter (1978) how increasing the variance affects the outcome. Secondly, it is counterfactual to assume that social stress decreases the willingness of some people to riot. But this is exactly what happens if the variance increases, as then the values become more extreme on both sides. For the initial simulation I set the mean to 25 and the variance to 9. In every time period the social stress grows by 0.1 points, thus decreases the threshold by 0.1 for everybody. When we run the simulation for 200 periods and repeat it 100 times, we get on average the following picture:
3.2 Upper threshold 5 Mean Rioters 0 20 40 60 80 100 0 50 100 150 200 Time Figure 3.1: Simulated riots with an continuously increasing social stress. The plotted average values in figure 3.1 has a S-shape, and we see that it is first quite flat and then after some point it grows rapidly and reaches the 100% level. The more rounds the simulation is performed, the smoother this function becomes. The introduction of social stress is the first step to capture reality in the model. 3.2 Upper threshold The second extension of the model considers an upper threshold, until which the agents are willing to riot. We know already that agents look at the behaviour of others and act according to their behaviour. We call this herd behaviour in general. In the initial model the cost function of rioting declines with a growing proportion of rioters. But it is not wise to assume that the cost function is monotone. Instead, it is much more sensible to assume an U-shaped cost function. This means that after crossing a given threshold, the cost of participating in a riot starts to increase. We can think about many reasons for such an increase. The first that comes into mind is personal safety - a huge rioting crowd can get out of control, leading to serious health damages or even death. Secondly, if a lot of people are occupied with rioting, hardly anyone will deal with the support of daily consumption goods. Thus there will be not enough food or water supply. Moreover, we can think about an external cause of the increased costs, as the police starts to become more violent and uses
3.2 Upper threshold 6 stronger weapons against the rioters. Finally, it could be the government, that calls for the national guard and ends any rioting instantaneously. However the reason is, I assume that reaching an upper threshold leads to a stop of rioting. From this point the very same people are on the street, they observe the others and continue to riot. If we let their thresholds constant, we still get an dynamic over time, but it is quite poor as the same pattern repeats itself. It is more sensible to assume that people make up their mind, once the riots have been stopped. Thus we need to randomly draw new thresholds for the rioters. I decided to chose the same normal distribution and constant parameters. It is possible to allow the variance to decrease or increase over time, in order to model different behaviour. But when we change to many parameters at once, we loose track of what is causing the behaviour we observe. Moreover, changing the variance leads to the problems mentioned before. The value for the upper threshold has to be chosen corresponding to the problem we want to implement. When we consider a football match, this threshold can be set very high. Contrary, in a usual town the police will start to act very quick, so a value around 30-40 seams to be adequate. The graphical representation of a simulation in such a case can be done for a single run. As the thresholds are drawn randomly every time, we get very different patterns every time the riots start from zero. Taking the mean gives us an uninterpretable picture 1. Thus figure 3.2 shows the simulated behaviour for just one arbitrary chosen run, where the upper threshold is set equal to 40. 1 You can find the mean behaviour for the case of 1000 runs in the appendix, figure A.1.
3.3 Governmental intervention 7 Rioters 0 5 10 15 20 0 50 100 150 200 Time Figure 3.2: Simulated riots, upper threshold set equal to 40. Even with very simple parameters we observe an interesting behaviour. As expected, the amount of rioters is first constant over some quite long intervals, then it jumps to another level, as the threshold declines continously. After some time the point is reached, where we observe an enormous increase of rioters and their number quickly exceeds the upper threshold. This stops all of the rioters for a moment and new thresholds are assigned. Thus the system starts from zero and we observe another path, that basically follows a similar pattern. Sometimes it takes more time to see the riots emerge, but this is only due to the small number of agents. If we increase them by the factor 100 and scale up all the other parameters, the thresholds will be normally distributed and the paths should be quite similar. 3.3 Governmental intervention The final extension to the model incorporates the fact, that the state may interact and prevent the agents from rioting. Until now, the state did not play any role and accepted the behaviour of the agents. The only possible action it could take, was to stop the riots immediately by the use of massive force. A democratic state can interact in a more sophisticated way, namely by fulfilling the agents needs. Riots cause high costs and also negative externalities like bad reputation abroad. On the other hand, too sever actions taken against rioters may harm their human rights and
3.3 Governmental intervention 8 lead to the same bad reputation. This makes it useful for the government to interact with the agents and by this to decrease their willingness of rioting. In the setting of my model the state performs some action that works contrary to the social stress. The effect of the action is an increase in the average threshold, which makes less agents riot. We have to keep in mind, that such actions are costly, too. Thus the state has to consider the trade-off between the costs of rioting on a big scale and the cost of preventive actions. The situation becomes even more problematic, when we consider international summits. Suzić and Wallenius (2005) consider the case, where the whole world looks at an international summit and the national police or military forces have to prevent riots. In this case there is a very strong conflict of interests for the commander who is in charge of preventing the riots. On the one hand, he cannot allow for riots, as the security of international guests is very important and the countries reputation is endangered. On the other hand, he cannot use brutal force against the demonstrants, as those have the freedom of speech and are quite often foreigners. A strong intervention may cause their death, thus an appropriate strategy has to be chosen. Concerning this question, Welch (1975) investigates the expenses that come along with riots. She finds increasing expenditures applied to the fighting and punishing of rioters, instead of preventive measures and fulfilling the needs of the rioters, like increased spendings on schools and the health system. I model this behaviour by implementing a probability with which the state takes the preventive measures. In my setting, the intervention has the same effect on every agent. A possible extension is to consider different effects, which depend on the initial threshold. Primarily, I assume that the probability of taking an action is 10%. I do not show the figure, as it is very much the same as in the initial case. Basically, we have to consider two extreme cases. If the government never reacts, we observe the same behaviour as in section 3.2. The other extreme case is, that the government increases the threshold of the rioters in every period. By this all rioters disappear in a short time. On average, the system behaves in an interesting way, if the government interacts with probability 10%. In this case the positive effect is equal to the negative social stress on average and we observe cyclical emergence of riots. My simulations show, that values from 0-5% have nearly no effect, and we observe the same picture as in the initial model. Values around 6-7% start to make the expected number of rioters increase linearly with the time. Finally values around 8,9,10% decrease the expected value to around some 20% at the end of 200 periods. Increasing the probability of governmental intervention to 15% gives an nearly constant expected number of rioters of 2.5, which is very low. From those observations we can learn some political implications. Namely, governmental interventions have to be performed on a great scale, otherwise they are meaningless.
3.3 Governmental intervention 9 In the last step, I apply all expansions of the model at one time. Initially the social stress increases by 0.1 per period, the government interacts with 10% probability and the upper threshold is set equal to 40. The results obtained on average for 10 runs are shown in the following figure 3.3. We observe a quite realistic pattern. Primarily, the average percentage of rioters is very low. Secondly, there are some discontinuous increases of rioters, which then collapse to zero. From this point the system starts again and shows a similar pattern. In the real world we observe low percentages of rioters, but sometimes riots explode as happened in the case of France. Eventually those enormous riots are stopped, so nobody riots for some time. Indeed I do not consider the time of no riots, as this does not add anything to the explanatory power of my model and the simulations. Average Rioters 0 2 4 6 8 0 50 100 150 200 Time Figure 3.3: Simulation results for 10 runs, with all effects. In the last step two kinds of comparative statics are performed, namely either the probability or the upper threshold is changed, while the other is kept constant. First the upper threshold is fixed at the value of 40. Decreasing the probability of governmental intervention shows a similar result to the one before. As long as the probability is above 8%, the average rioters increase over time, but the highest peak is below 10%. Decreasing the probability to 5% leads to peaks around 15 and at 4% they go up to 25. The average value does not tell us everything about the riots, thus I check, how many times a riot explosion occurs. When the government intervenes
10 with 10% probability, out of 100 simulations only 15 show an extreme riot which reaches the upper threshold. If the probability is decreased only by 2 percent points to 8%, then extreme riots occur every second time, on average. A probability of 6% leads to extreme riots happening in every simulation, and lowering to 5% or below leads to multiple extreme riots in one simulation. We see clearly, that the relation between governmental interventions and its effect is not continuous and thus the proper care of the government has to be chosen wisely. Increasing the probability to values higher than 10% does not lead to any surprising nor interesting results. Keeping the probability constant at 10% and changing the upper threshold does not bring any fruitful insights to our problem. Neither increasing it nor decreasing it by some 10 points changes the results reported before. The only visible effect is, that the peaks of the riots are lower, but neither their probability of occurrence nor their number in a single run changes significantly. 4 Conclusions This paper presents an Agent-Based-model of collective behaviuor, that analyzes the emergence of riots. Due to thresholds and collective behaviour we observe a behaviour that can be hardly predicted basing on individual behaviour. The simulation model augments the Granovetter model by introducing dynamicss, by which it becomes more realistic. The dynamics emerge from three sources, namely an increasing social stress, personal upper bounds until which people participate in riots and finally the probability with which the government takes any preventive measures. My model shows two important things, which should be considered by politicians and sociologist. First and foremost, an increasing social stress leads to extreme riots, even if the initial distribution would not allow for those. Secondly, the government can take effective measures in order to satisfy the needs of the people and by this to prevent extreme riots. It is not the size of the effort, but its proper and repeated application, that allows the government to sustain a calm population. Analyzing social behaviour by the means of simulations and AB-models allows us to understand very complex systems. Moreover, the results can be implemented by the military, police or other law-enforcing forces in order to protect private property, public goods and human life.
11 A Appendix Mean Rioters 1 2 3 4 0 50 100 150 200 Time Figure A.1: Mean simulation results for 1000 runs, with all effects. B R-code for the simulations # Computer code for the paper: "A Dynamic Simulation of Riots: # Social Stress, Upper Bounds and Governmental Intervention" # by Krzysztof Olszewski (olszewski@unive.it) # I am deeply grateful to Paolo Pellizzari who gave me some initial code. # The world is populated by 100 agents numagents <- 100 #The variance can be changed here variancer <- 9 #This is the mean threshold meanr<-25 # The social stress is defined here
12 stress<-0.1 #The world lasts for 200 epochs, which are run for 100 rounds epochs <- 200 rounds<-1 # Upper bound for rioters - if reached, everybody stops. #Setting the value to 101 means, that there is no upper bound. upperbound<-40 #Probability with which the government takes some action; in percent points govvalue<-10 # This matrix will save the data for further analysis testmatrix <-matrix(na,ncol=rounds,nrow=epochs) # # main program starts here # for(j in 1:rounds){ # Initially nobody riots number<-0 # Here I create a vector with randomly drawn thresholds for the 100 inhabitants. thresholdin <- rnorm(numagents,meanr,variancer) threshold<-thresholdin # To see the result of every run, activate this #plot(0,t="n",xlim=c(0,epochs),ylim=c(0,20)) for(i in 1:epochs){ #Count all people whose threshold is below the number of observed rioters, #this are the new rioters. We just add the newcomers to the old rioters #and check, whether the upper bound is reached
13 numbern<-sum(number>=threshold) if(numbern>upperbound) {number<-0 thresholdin<-rnorm(numagents,meanr,variancer) threshold<-thresholdin } else number<-numbern #This is the probability generator for governmental intervention govprob<-runif(1,0,100) threshold[govvalue>govprob]<-threshold+1 # The social stress enters, by which the threshold declines over time threshold<-threshold-stress #The number of current rioters is saved in the matrix testmatrix[i,j]<-numbern # Here we see the outcome #points(i,number) } } # Here we get the mean result meantest <-matrix(na,ncol=1,nrow=epochs) for(i in 1:epochs){ meantest[i,]<-mean(testmatrix[i,]) } #This plots the mean plot(meantest) #testmatrix #threshold
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