Dictators, citizens, networks and revolts : a simulation analysis of the relationship between revolts and the allocation of resources in dictatorships

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DICTATORS, CITIZENS, NETWORKS AND

REVOLTS

A Simulation Analysis of the Relationship between Revolts and the Allocation of Resources in Dictatorships

Master Thesis

Elmar Cloosterman

Student number: 10083499

Master Sociology (general track)

First supervisor: Jesper Rözer

Second supervisor: Jeroen Bruggeman

Date: 10-07-2017

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Abstract

Through history, many cases of revolts by citizens against their dictatorial leaders have been observed, both successful and unsuccessful. This paper focusses on the conditions for a successful revolt and how dictators tend to prevent these. In general, dictators possess two options in preventing collective uprisings: repression and the allocation of resources. Because most previous research on this subject has focussed on the former, this research focusses on the latter. Using a model in which the population is heterogeneous in interests and social influence, this paper demonstrates that the extent to which the allocation of resources reduces participation in revolts depends heavily on the social network in place. More specifically, there is found that a dictator can efficiently lower participation in revolts by targeting individuals with high amounts of social capital. This research therefore provides insight in the dynamics of resource allocation in dictatorial regimes. This paves way for the inclusion of resource allocation when assessing revolts in these regimes.

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1. Introduction

What are the conditions for a successful citizens’ revolt in dictatorial regimes? And how does interaction between citizens affect these conditions? Through history, existence and duration of many historical and current dictatorial governments raise several political and economic questions. Regimes have survived despite disastrous economic policies and great inequalities within society, even when they tend to lack political support from broad constituencies and benefit only a small group of the dictator’s supporters (Acemoglu et al., 2004). Many political and sociological studies have pointed out that dictators do not depend on the direct repression of political and social opposition alone, but also on co-optation, selective repression, and propaganda (Perez-Oviedo, 2015). And while dictators often foster the inability of citizens to generate collective action, revolts have taken place. In recent decades, citizens all over the world took to the streets to protest against autocracies. To name a few cases, protests sparked in Mexico in 1988, in China and East Europe in 1989, in Ukraine, Georgia, Serbia, and Kyrgyzstan in the early 2000s, and most recently a revolutionary wave of both violent and non-violent demonstrations, protests and riots have taken place in North-Africa and the Middle-East, which became known as the ‘Arabic Spring’. Hence, it seems that the collective action problem to viably threaten the regime can be overcome despite the actions dictators take. And while some uprisings had successful reforms as a consequence, a large number of protests are either beat down or diminish over time. For example, an estimated seven and a half million people took it to the streets during the Gezi Park protests in Istanbul to express their dismay on the diminishing freedom of press and expression, and the government’s encroachment on Turkey’s secularism. However, the leader of that time –Recep Tayyip Erdogan- is still in power, and his regime is considered to be more autocratic than ever. These differences between successful and unsuccessful uprisings raise several questions about the conditions of successful revolts.

Political analysis has highlighted the importance of interpersonal networks amidst popular revolts. Opp and Gern (1993) argue that “Social networks are of central importance in explaining social movements and political protests”. This is one of the reasons why repressive regimes throughout history have been very cautious of networks that facilitate communications among citizens or subordinates. Citizens have often been prevented from gaining free access to communication devices such as radio transmitters, photocopiers, and so on. In the recent Arab revolts, challenged regimes have forbidden access to virtual social networks. In this

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context, the structure of the network serves as a foundation to understand the emergence of collective action (Perez-Oviedo, 2015).

The how and why of collective uprisings in repressive regimes has been modelled and studied extensively in recent years (De Mesquita, 2010; Edmond, 2013; Gandhi & Przeworksi, 2006; Ginkel & Smith, 1999; Goh et al., 2006; Kricheli et al., 2011; Shadmehr & Haschke, 2016), but one of the most recent and complete efforts to model under what conditions uprisings are successful, while including communication between citizens and repression tactics by the dictator, is given by Perez-Oviedo (2015). His game theoretic model is formulated as a one-shot, two stage game and is used to formulate a formal proof of Wintrobe’s Dictator’s Dilemma (Wintrobe, 1998). This dilemma describes the consequences of the use of repression by dictators. There is argued that when a dictator uses repression, citizens will be less likely to express their opinion about the dictator. As a consequence, it is unclear for the dictator who is against his regime, and he can no longer observe who to repress. This leads to more repression, even against people who might not be against his regime. Wintrobe argues that dictators therefore cannot stay in power through repression alone, but also have to make use of another mechanism: loyalty. By giving citizens access to resources or power, dictators receive loyalty in return. This makes it possible for dictators to establish a stable coalition of sympathisers, which can reduce the chance of (successful) revolts.

However, Perez-Oviedo makes one questionable assumption in the construction of his model. He assumes that political preferences (i.e. the opinions of the citizens on the regime) are binary and are determined exogenously. While it is often argued that preferences of citizens are systematically dependent (Kricheli, 2011). In reality, it seems implausible that the degrees to which individuals are dissatisfied with the dictator are not dependent on one another. Citizens interact with the same regime; they also interact, socially and politically, with one another, which makes independent political preferences unlikely. With this interaction, citizens form non-binary opinions. When agents have to make important decisions (e.g. participate in a riot) they care to collect many other opinions before taking any decisions and thus can construct opinions that can vary continuously from ‘completely against’ to ‘in complete agreement’.

Therefore, I would like to construct a model that includes dependent and continuous opinions to answer the following research question:

Under what conditions are revolts by citizens against an autocratic regime successful and how is this prevented by the regime?

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The model will be structured in a similar way as the model of Perez-Oviedo: with one dictator and a number of citizens. Because the notion of repression with regards to social networks has been studied quite extensively in recent years (e.g. Siegel, 2011), I will focus on the ‘dynamics of loyalty’ in this paper. That is, I will research the effectiveness of the use bribery (or: the allocation of resources) to prevent uprisings, given certain social network structures. This will increase understanding about the formation and importance of power structures in dictatorial regimes. Insight in this subject might help future empirical research to assess the stability of certain regimes by including network structure and resource allocation into the analysis.

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2. Previous Literature

Because of the complexity of the subject of riots in dictatorial regimes, it relates to several strains of literature. Therefore, the next section is divided into subsections which shortly describe the most important theoretical findings for each of these strains of literature. First, there is described what kind of dictators exist and how they behave. Second, some of the tactics dictators use to stay in power are discussed. Next, the how and of why people revolt is explained, followed by literature on collective action and cascades. Thereafter, the

importance of social networks for collective action is discussed. The last section describes some theoretical models which take all these notions into action in greater detail. There is argued that most models only take one tactic of the dictator to stay in power (i.e. repression) into consideration, while how dictators allocate resources over their citizens (i.e. bribery) is often neglected. Therefore, a model to research the dynamics of bribery is proposed. All aspects of the model relate to the literature discussed in the section.

2.1 The Behaviour of Dictators

Most countries in the world are governed by a form of autocracy. That is some form of individual ruling, either monarchy or dictatorship (Brough, 1986). Dictatorship is a prevalent form of autocracy, with a large part of the world’s population living under this type of rule. However, many questions remain to be answered with regards to the tactics and strategies dictators use to remain in power. Wintrobe (2007) surveys work on authoritarianism which takes an ‘economic’ or rational choice approach. That economic methods are used does not mean that behaviour of dictators is guided by economic goals. Nor does it mean that there is assumed that the economy is the most important aspect of a dictator’s performance. Other goals, such as power of ideology, have been the most important ones for many dictators. Rational choice can be just as useful in understanding the behaviour of people who are motivated by power or ideology rather than wealth.

Wintrobe distinguished four types of dictators. First, he describes dictators that are simply motivated by personal consumption. For which their indulgences often have become legendary. Examples are the palaces of the Shah of Iran, or the luxury cars of the typical African dictator. These type of dictator are called tinpots, which denotes their small-scale aspirations. This is one of the classic images of dictatorship.

At the opposite extreme from tinpots are totalitarian dictators, apparently motivated solely by power or ideology. Examples of regimes with totalitarian dictators, which had

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seemingly unlimited power over their citizens, are Nazi Germany and Russia under Stalin. Somewhat related to these regimes is the third type of dictator: tyranny. A term which was used in ancient times to describe a form of rule in which the leader implements particularly unpopular policies and stays in power through repression. The Pinochet regime in Chile can be recognized as a regime with tyranny behaviours.

The final type of dictator is the benevolent dictator or timocrat: A ‘well-meaning’ and kind dictator, not motivated by wealth, power and/or ideology. There is little evidence that a regime like this ever existed, but economists are particularly vulnerable to this idea because economic theory says there is a right way to run an economy and a timocrat could fulfil this role. A timocrat thus runs a sort of ‘controlled democracy’, in which resources are distributed optimally across society to the likings of the citizens.

2.2 Bribing and repression

The classic view of the difference between democracy and dictatorship in political science is that dictators stay in power through repression and rule by commands and prohibitions. However, this rule by repression alone creates a problem for the autocrat. This is explained in the Dictator’s Dilemma (Wintrobe, 1990, 1998). Which is the problem any ruler faces of not knowing how much support he has among the general population. The use of repression breeds fear on the part of a dictator’s subjects, and this fear breeds a reluctance on the part of the citizenry to signal displeasure with the dictator’s policies. This, in turn, breeds fear on the part of the dictator, since he has no way of knowing what his citizens are planning and thinking. He thus receives no signals whether his citizens are planning and/or thinking to overthrow him. This problem is magnified the more the dictator rules through repression and fear.

To solve this problem, dictators do not rule by repression alone but through loyalty and political exchange. Similar to democratic politicians, they try to implement the policies their people want to obtain support for their rule. However, there is no legal way to enforce these ‘political exchanges’. There is no guarantee that other parties will not cheat in a political exchange. The general solution to this problem of preventing cheating on exchange in product markets is a ‘trust’ or ‘loyalty premium’. Hence, the dictator invests in the loyalty of his supporters by ‘overpaying’ them. In particular, those in position to bring the regime down. This loyalty premium often takes the form of subsidized (‘efficiency’) wages or capital projects, the distribution of goods and services at subsidized prices, and so on. The recipients provide loyal support in return.

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Hence, in order to stay in office, the dictator does not only repress his opponents, he

redistributes to keep his supporters loyal. This means that there is always a class of people who

are repressed under a dictatorship, there is also, in any successful dictatorship, another class:

the overpaid. The ‘middle class’ can side with either group. They may be unhappy that their

civil liberties may be taken away, but other aspects of the regime may compensate for this as far as they are concerned.

Brough & Kimenyi (1986) delve deeper into the why and how dictator redistribute resources and argue that dictatorships are not efficient from both an economic as a social point of view. This is rooted on how dictators generally come to power. Tullock (1974) refutes the common notion of the ‘romantic’ revolution whereby the masses revolt against an evil government and establish a new government whose main purpose is reform. Tullock argues that certain people participating in revolutions can gain more from overthrowing the government than others, especially those who have access to a great deal of resources (economic or social) in the existing government. As power is up for grabs people with high (social) resources have greater opportunity to enrich themselves even more. Hence, participation is partly determined by expected personal gain or loss.

This implicates that those who have the greatest possibility of gaining from a revolution will be those in positions of power. Commonly these are members of the pre-revolution government. Therefore, for existing dictators, the foremost threat is that of coup d’état. On one side or the other, governments officials will be principal actors in case of a revolution. They cannot sit idly on the side-lines because their lives will be heavily affected. Hence, they must choose to join the opposition or support the government. The dictator realizes this and must form a policy of reward and the allocation of power in order to form a stable coalition with which to govern. The dictator thus must rely on granting rents to members of the coalition to ensure the stability of his power. The granting of these rents reduces the efficiency of the regime. A profound strategy to ensure stability for a newly came-to-be dictator might be to keep people with great power or high influence, either in the form of access to resources or in social capital, close to him. Hence, the dictator always has to decide between the trade-off between stability and efficiency. Handing out rents to his coalition partners reduces efficiency while increasing stability, and vice versa.

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2.3 Riots and Rebellion

Riots, rebellion and revolutions have been studied widely in the social sciences the past few decades. The current literature greatly benefitted from Moore & Jaggers landmark study in 1990. In this study, they combined three research traditions: socio-psychological approaches, political conflict approaches, and structural-determinist approaches. For each these approaches leading theoretical treatise are discussed and a synthesis of these conceptual frameworks is presented, including additional hypothesis that it yields. Ted Gurr’s Why Men Rebel (1970) is considered the leading work for socio-psychological approach. This approach focusses on the explanations of violent outbreak by focusing on the individual level of analysis. Gurr argues that relative deprivation (i.e. the discrepancy between what people think they deserve, and what they actually think they can get) is a necessary condition for the outbreak of rebellion. In addition, before individuals join rebellion, citizens must be exposed to appeals to (1) the corporate identity of the group, (2) the identification of the state as responsible, (3) normative justifications for the revolt and beliefs that they can benefit from it, and (4) the utilitarian value of, revolt. Moreover, wider groups in which one feels involved plays an important role in issuing those appeals and channelling collective discontent into positive action.

Furthermore, borrowing from Tilly (1978) with regard to the political conflict approach, Moore & Jaggers argue that resource mobilization is a necessary condition for the manifestation of revolutionary challenges to state power. That is, members of social movements should be able to 1) acquire resources and 2) mobilize people towards accomplishing the movement’s goals. In addition, it is proposed that both developed networks and salient categories must either exist or be constructed by rioting groups. To successfully organize groups thus should consist of, according to Tilly, ‘people who are linked to each other, directly or indirectly, by a specific kind of interpersonal bond’ and should ‘share some common characteristic, be it physical, ideological or psychological’. Moreover, the hypothesis is added that fraternalistic relative deprivation (i.e. relative deprivation on group-level) enhances the mobilization of monetary resources, while individual relative deprivation will enhance the mobilization of human resources.

When considering the structural determinist approach Theda Skocpol’s States and

Social Revolutions (1979) is considered to be the leading treatise. Taking this structural

perspective, Skocpol rejects the position that revolutions can be explained in terms of deliberate actions or carefully planned out strategies. Revolutions cannot be orchestrated, they simply come. Besides the statements that riots and rebellion are more successful in bringing the government down when the state is weakened by its inability to balance its own interest with

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powerful groups within the society it governs (i.e. the trade-off between stability and efficiency), Moore & Jaggers add two more hypotheses: First, appeals must psychologically connect people individuals with a larger category of people experiencing similar types and/or levels of deprivation before they can take advantage of their collective strength. Second, they suggest that the translation of individual into fraternalistic relative deprivation is a necessary condition for revolt.

2.4 Collective Behaviour

An underlying assumption in the literature with regards to riots and rebellion is the assumption that individual actions are interdependent. This interdependence stands central in literature on behavioural cascades (Lohmann, 1994). Classic examples are Mark Granovetter’s (1978) and Thomas Schelling’s (1978) models. Both are relevant to the situation in which individuals can choose between two alternatives, and the net benefit derived from each alternative depend on the number of other individuals choosing that alternative. The individuals are heterogeneous, meaning that each individual has a specific threshold denoting the number of other individuals who must choose an alternative before that individual finds it worthwhile to do so. Hence, one individual’s choice of an alternative has the potential to push another individual over her threshold; the second individual’s action in turn may induce other individuals to follow; up until the cascade comes to a stop.

This model generates several implications: First, the cascade is monotonic. That is, the number of individuals who choose one alternative increases until it stagnates at some point. Second, the actions of extremists characterized by very low thresholds are crucial for the behaviour of moderates with higher thresholds. Third, the triggering and the duration of the cascade depend in a highly sensitive way on the frequency distribution of thresholds.

The model of Granovetter has been enriched and adapted in numerous ways. Kuran (1995) developed a variant which sets one step in the direction of revolution, rather than collective action per se. He models the situation in which a status quo regime is replaced by an alternative regime when public opposition to the status quo exceeds a critical level. Costs of joining political action is assumed to decrease as the size of the protest movement increases. By reducing these costs, one individual’s action may encourage other individuals to express their opposition to the regime publicly. The dynamics of the cascade are thus driven by monotonic changes over time in the external costs of taking action. Extremists turn out in the initial stages of the cascade, while moderates join later on.

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DeNardo’s (2014) model of mass mobilization and political change allows for strategic interaction between the regime and its opponents. The regime can indirectly control the size of the protest movement by implementing political reforms. It can shift its policies toward those demanded by its opponents and thereby reduce the size of the opposition. In a more complex version of his model, DeNardo adds the degree of repression as another variable controlled by the regime. While repression deters and intimidates the opposition (and thus reduces the number of protesters), it also has the potential to produce a political backlash that may endanger the regime’s survival. DeNardo’s model is one example of how dictators can control collective movements by either repressing their citizens or allocate resources. This shows that there is an important relationship between the behaviour of the dictator and the level of collective participation within the country. This relationship is investigated further in this paper.

2.5 Collective Behaviour and social networks

Social networks and their structure are considered to be an important factor for the explanation of conditions for a successful revolt. In general, there is considered that the social environments in which individuals make their decision to participate in revolts enhance the effectiveness of collective action. Oberschall (1973) argues when people are well integrated into the collectively, they are more likely to participate in popular disturbances than when they are socially isolated, atomized, and uprooted. McAdam (1988) identifies ‘micromobilization contexts’ (i.e. interpersonal contacts and personal networks) as crucial for recruitment to high-risk activism.

An important aspect in studying social networks in relation to collective behaviour is the notion that people influence one another if and only if they are connected through their social network. Siegel (2009) focusses on a particular form of influence, in which individuals become more likely to participate the more others do as well. The underlying cause of this influence can vary. In the political participation literature, information transfer plays a major role in the relevance of networks (Huckfeldt, 2001). In general, information exchange allows people to update their beliefs about the costs and benefits related to participation, and so change their decisions. It is also theorized that networks can coordinate and transfer resources, which have an independent effect on one’s willingness to participate (Verba, Schlozman & Henry, 1995).

In sociology the idea that networks transmit direct influence, changing one’s interests in and inherent motivations toward participation, is more persistent (Gould, 1993; Klofstad,

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2007). Closely related are notions of reputation (Kuran, 1995; Mutz, 2002) and fairness (Gould, 1993), in which either negative (being worried about being punished) or positive (being worried about acting unfairly to others) social pressures encourage people to act or not to act. Another explanation for participation in collective movements is the safety in numbers argument; you are safer the more others join the collective action (Kuran, 1991).

Because individuals’ decisions depend strongly on their social contexts, network structure itself is of great importance. This has been noted particularly often in the sociological participation literature (Gould, 1991; Hedström, 1994; Opp & Gern, 1993). It is therefore expected that the structure of people’s connections alters outcomes of collective action. Both the pattern of network connections (Centola & Macy, 2007; Gould, 1993) and the position of individuals within networks play a role in the decision of whether or not to participate (Borgatti & Everett, 1992). Thus, in sum, this shows there is evidence that the structure of networks, in terms of both the patterns of connections and of the way in which individuals are distributed across them, alters aggregate outcomes.

2.6 Modelling Dictator Behaviour and Collective Action

From the above described literature several things can be learned when taking collective uprisings in dictatorial regimes into consideration: First, different types of dictators can be distinguished based on their motivations. Some dictators might be motivated only for the accumulation of personal wealth; others might be motivated by ideology or power. Second, for citizens to take up action against the dictator, some form of relative deprivation should be present. That is, citizens must be dissatisfied by their position in society. This relative deprivation forms negative feelings towards the regime, making people internally motivated to rebel. Third, for these negative feelings towards the regime to be capitalized in the form of participation, heterogeneous threshold exists across the population. Meaning that each individual has a personal number of people that must participate in collective action before he or she will participate. This makes cascades of participation possible. Fourth, social networks are of great importance for collective behaviour. Both the patterns of connections, as the placement of individuals in these networks can alter aggregate participation outcomes. And lastly, dictators generally have two measures to beat down or prevent collective uprisings against their regime: repression and the allocation of resources.

While the how and why of collective uprisings in repressive regimes has been modelled and studied extensively in recent years (De Mesquita, 2010; Edmond, 2013; Gandhi &

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Przeworksi, 2006; Ginkel & Smith, 1999; Goh et al., 2006; Kricheli et al., 2011; Shadmehr & Haschke, 2016), models take all these five notions into consideration are scarce. one of the most recent and complete efforts to model under what conditions uprisings are successful, while including communication between citizens and repression tactics by the dictator, is given by Perez-Oviedo (2015). His model is formulated as a one-shot, two stage game. The model consists of one dictator and a group of citizens. Citizens have utility functions that depend mainly on random assigned (by nature) political sympathies among the citizens. In the first stage, the dictator will bribe and/or eliminate (selective repression) some citizens in order to maximize his expected utility. After that, the citizens will broadcast their political preferences and decide whether to revolt or not. Regimen’s repression originates fear among the citizens. However, the same fear makes it impossible for the dictator to identify his political supporters, he could be overspending in bribing agents who already support the regime or exercise over-repression by eliminating some of his sympathizers. Perez-Oviedo uses this model to formulate a formal proof of Wintrobe’s Dictator’s Dilemma (Wintrobe, 1998). This dilemma describes the consequences of repression for the dictator. There is argued that when a dictator uses repression, citizens will be less likely to express their opinion about the dictator. As a consequence, it is unclear for the dictator who is against his regime, and he can no longer observe who to repress. This leads to more repression, even against people who might not be against his regime.

However, Perez-Oviedo makes one questionable assumption in the construction of his model. He assumes that political preferences (i.e. the opinions of the citizens on the regime) are binary and are determined exogenously. While it is often argued that preferences of citizens are systematically dependent (Kricheli, 2011). In reality, it seems implausible that the degrees to which individuals are dissatisfied with the dictator are not dependent on one another. Citizens interact with the same regime; they also interact, socially and politically, with one another, which makes independent political preferences unlikely. With this interaction, citizens form non-binary opinions. When agents have to make important decisions (e.g. participate in a riot) they care to collect many other opinions before taking any decisions and thus can construct opinions that can vary continuously from ‘completely against’ to ‘in complete agreement’. Also, with the model of Perez-Oviedo being a game theoretical model, perfect and complete information by the dictator is assumed. Meaning that the dictator can take (future) actions of citizens into account for determining his actions. This makes the model highly unrealistic and almost inapplicable to real-life situations.

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A more realistic model is constructed by Siegel (2011), which he uses to determine the effect of repression on collective action in social networks. He simulates his model, consisting of non-binary interdependent motivations, over a typology of networks structures given certain repression tactics of the dictator. He finds that the efficacy of repression depends fundamentally on the structure of the social network of the population.

However, while the notion of repression has been modelled and studied very widely (in addition to Perez-Oviedo and Siegel, see e.g. Escriba-folch, 2013; Guriev & Treisman), literature on the mechanisms and dynamics behind the dictators other ‘weapon’, the allocation of resources (or: bribery), is scarce. Therefore, I will propose a model that is used to investigate the dynamics of this ‘loyalty exchange’ with regards to civil uprisings when taking social network structure into account. The structure of the model lends heavily from Siegel, and thus also includes non-binary interdependent motivations of citizens. Hence, a version of this model is proposed that focusses on how the dictator allocates resources, instead of repression. As this model is not a game theoretical model it does not assume perfect and complete information, making it more realistic and applicable than Perez-Oviedo’s model. The model is explained in detail in the next section.

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3. Model

The model consists of 𝑁 + 1 agents, a dictator and 𝑁 citizens. Each of the citizens operate as a node in a social network. The dictator starts each period with an endowment and observes the structure and motivation of the citizens. These motivations towards participation in a riot (or: revolt) are separated into two disjoint components. The first, termed net internal

motivation, encompasses all factors relating to one’s desire to participate in a collective action

that do not depend on the participation of others. Examples of these factors include general opinion about the regime, moral certainty of the cause and the level of relative deprivation one experiences during his lifetime. These internal motivations are considered to be heterogeneous across the population. In general, information about the nature of the regime is dispersed among the members of its society. In their daily lives citizens have both positive and negative experiences in their interactions with the regime. These interactions differ from person to person and when these interactions form opinions, these opinions are considered relatively stable (e.g. Elder, 1994; Mannheim, 1952). These internal motivations are typically considered to be private; in oppressive regimes people talk little about their private opinions in fear of repercussions, and when they do, often only to a very select core of intimate ties avoiding that their opinions become public (Volker & Flap, 2001). Therefore, it is possible for a society to consist of a majority of people who have negative internal motivations, without having immediate uprisings, as these require some form of cascade initiated by harsh-rabble rousers. Each person 𝑖’s net internal motivation is called 𝑏_& ,with population mean 𝑏_'()* and standard deviation 𝑏+,-(. . As in Siegel (2011), internal motivations are drawn from a normal distribution. Although one’s opinion is relatively stable and to a large extent formed before one reaches adulthood, it can change. However, people are relatively inflexible. Hence their opinions often change little through their life course. The degree to which their opinions can change is thus based on the opinions and actions of others, which is reflected in the second component of the motivation.

The second component of the motivation is one’s net external motivation, which is denoted 𝑐_&,, for each individual 𝑖 at time 𝑡. This covers all factors relating to one’s desire to participate that depend on the actions (i.e. participation) of others within one’s personal social network. It thus captures network effects. It is not assumed that citizens directly observe external motivation of other citizens in their social network, but more that they are influenced by the actions of people surrounding them. That is, 𝑐_&,, is increasing in the observed participation of others. As explained above, the mechanism behind this is considered to be a

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combination of information exchange, influence, and the safety in numbers arguments. Because internal and external motivations are assumed to be disjoint, any change arising from the actions of others in the network only alters external motivations: only 𝑐_&,, responds to the behaviour of others in the network.

It is possible for the dictator to influence citizens’ decision making process by giving out bribes. These bribes resemble either direct monetary transfers, ‘rents’ and/or access to resources or power. These bribes 𝜂 ∈ 0, 1 in periods 1 to n reduce a person willingness to riot. Meaning that the dictator can influence citizens in not participating, even if they have a (slightly) negative opinion about the regime and some of their peers are already participating in a riot. From a rational choice perspective, these added resources increase the marginal losses when one decide to participate in a riot, thus reducing the likelihood that one will riot. Putting these factors together yields the following decision rule: An individual 𝑖 participates at given time 𝑡 if and only if 𝑏& + 𝑐&,,– *,78𝜂&,, > 0, i.e. if and only if the net motivation to participate is positive. Since the left hand side of this inequality is increasing in others’ participation, this rule implies that the more people participate, the more one wants to do so as well. After each period, citizens update their net external motivations according to the information about the participation of others within their local networks during the preceding period. The model assumes that they utilize the ‘linear updating rule’ 𝑐_&,,:8 = 𝜆𝑐_&,,− 1 − 𝜆 1 − 𝑙𝑝𝑟_&,, , where 𝑙𝑝𝑟_&,, ∈ [0,1] is the local participation rate for individual 𝑖 at time 𝑡 . New external motivations are thus functions of both old external motivation and the present social context and are increasing in the proportion of participants in one’s social network. The weight 𝜆 ∈ [0,1] dictates the degree to which individuals use new participation information in their decisions, responding to their fellows’ actions. Higher values indicate less responsiveness to local participation levels. Hence, if lambda is high, citizens are less influenced by the actions of the people in their social networks, and more by their own previous actions, which in turn are mostly influence by their internal motivations. When lambda is low, individual are highly influenced by the actions of their peers, and less so by their own motivations. Initially, external motivations are set at their minimum 𝑐_&,C = −1 to avoid hard-wiring participation into the model. This implies that 𝑐_&,, increases from -1 to a maximum of 0 as 𝑙𝑝𝑟_&,, increases from 0 to a maximum of 1. 𝑏_& is unbounded, which induces that there will be ‘rabble rousers’ (Grannovetter, 1978) with 𝑏_& > 1 who always participate regardless of their fellows and there will be “wet-blankets” with 𝑏_& ≤ 0 who will never participate under any circumstances, absent bribes. This last group can be seen as the ‘coalition’ of the dictator: those who have received a

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great deal of power, prestige, or money from the status quo. These individuals will never riot, even if all individuals they are connected to in the network decide to do so.

The iterative process will start with the dictator selecting who to bribe. The dictator starts by observing the social network and the motivations of the citizens. After the dictator has observed the opinions of its citizens, he hands out bribes. Because the dictator cannot predict how his bribes will affect the outcomes due to stochasticity of some decisions (see below), he has to act according to a strategy set beforehand.

Three strategies are proposed: motivational targeted bribes, influence targeted bribes and random bribes. With the motivational targeted strategy, the dictator gives out bribes to the top X% of citizens who have the most positive attitude towards the regime (i.e. the citizens for which 𝑏_& – * 𝜂_&,,

,78 + 𝑐&,, is the lowest). One can imagine that a dictator does not take power as a sole individual, and that there are people who surround him who are full regime sympathizers. When the dictator takes power, it is likely that these people will be placed in a position of power and thus will have access to a great deal of resources. The level of X is varied between simulations and will be used as the main x-axis variable in the analyses. By varying the level of X between 0 and 100 it can be observed how big of a clique of sympathizers the dictator has to create given variations of the other parameters of the model. The lower X, the lower the number of citizens receiving resources from the regime. This way, something can be said about the relation between resources given out by the regime and participation levels (i.e. riots) in the regime. One would expect that this relationship is linear in a situation where there are only regime haters and where individuals do not influence each other. In this case, the dictator has to single handily bribe every person under his control as there are no network effects that can initiate or halt cascades.

In the targeted ties bribes strategy, the dictator will not target the people who have the most positive opinion towards the regime, but the X% of people with the most (direct) network connections will receive resources. Obviously this strategy is only possible in network structures in which the number of network connection differs between individuals (i.e. there are ‘opinion leaders’). Hence, this strategy resembles the situation in which the dictator targets the people with the highest social capital, expressed in number of ties.

In the last strategy, a random group of X% citizens will receive bribes. This strategy does not directly resemble any real world situation, but serves more as a baseline to test whether the targeted strategy makes any significant difference. The height of the bribes as well as the total number of bribes to be given out will be similar in all strategies. Because ideology and/or

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the dictator’s motivation to possess power is not included in this model, it is closely related Wintrobe’s description of tinpot dictators. As the trade-off between the allocation of resources (bribes) and participation (i.e. riots; the probability that the dictator will stay in power) is researched, there is assumed that the dictator is just interested in staying in power, while having access to as many resources as possible.

With regards to the network structure, a similar approach will be used as Siegel (2011). The used social networks are represented by a typology of qualitative network structures that mirror commonly observed empirical networks. These four types are: The Small World, the Village (or Clique), the Opinion Leader, and the Hierarchical Network. These network structures, together with the reason why this typology is chosen, are explained in greater detail in the next section.

By running this simulation several things can be studied. First, it can be observed whether the strategy to create a close clique of sympathizers based on opinions, number of ties, or randomly is the most fruitful for the dictator in preventing riots. Second, a comparison of the successfulness of this strategy between social network structures can be made. This shows the levels of robustness of participation in different network structures. This thus provides insight in how dictators appoint important positions and allocate resources within their regime.

3.1 Network Typology

In his analysis, Siegel (2009) proposes a network typology for which he states it is not an exhaustive characterization of all network configurations, but rather a listing of commonly observed social structures that may be distinguished on qualitative grounds. Four types of network structures are distinguished: The Small World, the Village (or Clique), the Opinion leader, and the Hierarchical Network. For simplicity there is assumed that all ties between individuals in the networks are symmetric and constant throughout each realization of the model. Meaning that any individual who exerts influence over someone else, is also influenced by this someone, for each iteration. According to Siegel the former is true because most forms of influence regarding costly actions (such as riots) involve reciprocity and are often facilitated by mutual friendship or familial connections (McAdam, 1986; McAdam & Paulsen, 1993). This, however, does not imply symmetric influence in the network. It is easier for an opinion leader to affect the behaviour of one of his many followers than for one follower to influence the leader’s behaviour.

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The Small World network (Travers & Milgram, 1967; Watts, 1999) corresponds to modern, reasonably dense cities and suburbs. In this structure, everyone is either directly or indirectly connected to everyone else, and there are no exceptional citizens who hold an inordinate amount of ‘power’ over their peers. Networks are substantially overlapping, but individuals also have some chance to influence individuals outside their direct environment. This happens when, for instance, people move away from their childhood friends and join new groups of friends. To create this network, individuals are arrayed in a ring, and connected to a number of other individuals to both sides of them equal to the parameter Connection Radius. A Connection Radius of 5 thus indicates a connectivity of 10. Then, each network tie has some change of being severed and reconnected randomly to any other node in the network according to the parameter Rewire Probability. Varying this parameter takes the network from a ring (Rewire Probability 0) to Purely random (Rewire Probability 1), while maintaining the same number average of ties per person.

The Village network is somewhat similar to the Small Work network, but is more tightly clustered. It mimics small towns, villages, and cliques, in which everyone knows one another in the social unit and everyone exerts equal influence on each other. Few people span multiple cliques, acting as a ‘social relay’ (Ohlemacher, 1996). They also possess ‘bridging’, rather than only ‘bonding’ social capital (Putnam, 2000) and are able to exert influence outside the unit. For the village network the population is split up into an array of equally-sized subsets called villages that are of size Village Size. If the population does not divide evenly any left-over individuals are placed into a last, smaller village. Second, every possible connection within each village is made. Finally, each individual has some probability, called Far Probability of being connected to any other individual outside of his or her village. These probabilities are checked twice, so the true probability of any citizen being connected to a particular citizen outside his or her village is equal to twice Far Probability. Individuals in the village network thus might have different degrees of connectivity, though the average connectivity is the same for all.

The next two networks model situations in which social elites are present who have more connections than other individuals. In the Opinion Leader network most people have few connections, while a few ‘opinion leaders’, have many. Simple versions of such networks have also been termed ‘star’ or ‘wheel’ networks (Gould, 1991). First, each individual is assigned a number of ties according to the distribution 𝑝 𝑘 ∝ 𝑘GH_{, where}_{𝑘 is the number of ties a} particular individual has. The parameter 𝛾 thus determines the characteristics of the network, with smaller values corresponding to greater overall connectivity due to presence of a greater

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number of elites (i.e. individuals who are connected to a large number of others). These networks are also known as Scale-Free network in the literature.

While the power of elites in the Opinion Leader network lies in their greater number of network ties, the power of elites within the Hierarchy lies in their privileged placement at its top. As described by Morris (2000), the backbone of the Hierarchy is a series of levels expanding exponentially in width. Each person is connected to one person above them, and a number of people one level below them equal to the rate of expansion of the hierarchy. For example, if the expansion rate is 3, there is one person at the top, three people on the second level, nine on the third, 27 on the fourth, and so on. Those in the second level are all connected to the person on the top and are connected to three people in the third level. Hence, individuals in the top levels exert great (indirect) influence over the individuals in the lower levels of the hierarchy, while individuals in the lower levels exert only small influence over the individuals in the levels above them. The network is created by first creating the ‘skeleton’ of the hierarchy according to the parameter Expansion Rate. One individual is placed at the top, and each individual is connected to a number of individuals below him equal to Expansion Rate, continuing until no more individuals are left in the population. Each level thus contains a number of individuals equal to a power of Expansion Rate. However, the last level might have fewer individuals than this if the population does not divide evenly. Once this skeleton is created, each potential tie between individuals within the same level has a probability equal to parameter Level Connection of being made. Visual representations of these networks are shown in Figure 1.

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3.2 Procedure

Analysis of the model relies on simulation to overcome the problem of varying multiple parameters at once. Each simulation run begins with the creation of a network and the distribution of the citizens’ internal motivations. After initialization, every period the following sequence of actions occurs: 1) The dictator observes the network and, based on the set strategy, chooses the citizens who will receive bribes at each iteration of the model 2) The chosen group of citizens’ receive their bribes1 3) individuals update their external motivations and decide whether or not to participate 4) the total rate of participation is recorded. All elements in this sequence occurs simultaneously for all individuals in the network, continuing until no individual has changed his or her participation status for 50 consecutive iterations. Participation rates reported in this paper are the averages equilibrium participation rates over 100 simulation histories, each with an initial population of 1000 individuals. In other words, each possible parameter combination of the model is run 100 times. This is because, as noted earlier, the model’s dynamics tend to produce either near-cascades or relatively little participation in any given run. Running the model multiple times for all parameter combinations thus reduces the variance in these averages. The procedure and corresponding variables of the model are graphically illustrated in Figure 1. Simulations are run using the Netlogo software package. A version of the code for this model can be found in Appendix C.

1_{There is chosen to hand out bribes before citizens update their participation because often when new} dictatorships arise a ‘clique’ lead by the dictator takes power. Instead of a dictator taking power and then choosing who is close to him.

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4. Analyses

Because of the path-dependent nature of behaviour in the model, I start this section explaining some of the model’s dynamics in order to understand how network structure and dictator strategies alter the efficacy of bribery. First, consider a clique of ten friends (in which each individual in the clique is connected to one another) situated in a ring, attempting to mobilize despite being subjected to bribery. Assume that one of the friends holds a very negative opinion on the regime and can be considered a rabble-rouser. Also assume that every other individual is just slightly more positive about the regime than the friend next to them. At first only this rabble rouser will try to mobilize and participate in a hypothetical riot, but due to his participation two of his friends will also choose to participate. This increases local participation rates of each individual in the network to 0.3 (i.e. 3 out of 10 individuals in the network). Because everyone in this network is connected to one another, the local participation rate of each individual is equal to global participation rate, in this case. This in turn might motivate several other friends to participate as well. The dictator may be able to bombard the initial rabble rouser with bribes, eventually making him a regime sympathiser (reducing the local participation rate for each individual back to 0.2), but the participation of the first two friends who were affected in their participation by the initial rabble-rouser might be sufficient to create a cascade which mobilises the whole group of friends. Hence, given that the learning rate and bribe height are sufficiently balanced, the dictator will need a strategy that prevents the spreading of participation by the initial followers of the rabble-rouser (as he cannot transform the initial rabble rouser into a regime sympathiser immediately as he needs more than one iteration to change the participation level of the rabble-rouser), to prevent collective uprisings. In this situation the dictator only has two strategies: bribes are given out randomly, or bribes are targeted towards individuals with the greatest sympathy for the regime. Targeting individuals based on their social capital (i.e. the number of ties) is not possible, as all individuals have the same number of ties. If the dictator chooses to target individuals based on their opinion, he cannot stop this hypothetical cascade from happening, but rather can halt the cascade to a certain degree by creating a set of ‘wet-blanket’ regime sympathisers. Hence, if the dictator chooses to bribe two individuals, the cascade stops at the two most regime-loving individuals (resulting in a participation rate of 0.8). If the dictator chooses to bribe four individuals, the cascade stops at the four most regime-loving individuals (resulting in a participation rate of 0.6), etc. When the dictator chooses a random strategy, there is a probability that the dictator will target some of the individuals that set the cascade in motion.

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Hence, the dictator can (partly) prevent this cascade, reducing the overall participation. Thus, in this case, handing out bribes randomly is more effective than targeting regime sympathisers.

Now assume a simple version of the opinion leader network, in which 9 individuals are situated in a circle. All individuals in the circle are connected to one other individual who is situated in the middle of this circle, but are not connected to one another. Assume two different situations: First assume that the individual in the centre of the circle is a rabble rouser. Now, the rabble rouser exerts great influence over the network. As each individual in the network has only one tie, the participation of the rabble rouser increases the local participation rate for each individual from zero to one, immediately persuading several others in the network to join the riot. When the dictator targets his sympathisers to allocate bribes to, he does not prevent the rabble-rouser to exert his influence, as in the last example. Again, a random strategy will include the probability that the initial rabble rouser is among the few to be bribed. This will lower the local participation rates of each individual in the network back to zero, greatly reducing the total participation rate. Next, assume the person in the middle of the network is weak sympathiser of the dictator, and one of the individuals in the circle is a rabble rouser. Now the rabble rouser can only exert direct influence over the person in the middle. Increasing this person’s local participation rate by 0.1. To prevent further spreading of the movement, the dictator only has to make sure the individual in the middle of the circle is a strong enough sympathiser that this relatively small increase in his local participation rate will not influence his participation decision. In this situation, bribing sympathisers might thus be more efficient than handing out bribes randomly. However, in the network structure last considered the dictator possesses another strategy, namely: targeting the individuals with the highest amount of ties2_{. When using this strategy, the dictator only has to bribe one person to halt collective} uprisings, which is the individual situated in the middle of the circle.

These two illustrative examples imply several things. First, different strategies of the

dictator applied to different network structures can lead to vastly different outcomes. While

the optimal strategy for the dictator might be easily deducted in these two examples, network structures are much more complex in the typology used for analysis. This increases interdependencies, which reduces the likelihood that the dictator can determine the optimal strategy in advance. However, this does not tell the whole story. Participation levels in any structure to not only depend on gross quantities of interest like network type and the dictator’s

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strategy, but also on the specific location of individuals within the network and which

particular individuals are being bribed. To overcome these specificities and derive general

relationships across network types, there should be averaged over many sample paths. These averages are the comparative statistics used in subsequent sections.

4.1 Sequential Parameter Sweeping

Sequential parameter sweeping is a method for better understanding complex computational models with several parameters, and necessitates building the model in stages (Siegel, 2011). First, only the basic model is analysed, containing only one or two input parameters. These are varied across their full ranges, and the model’s outcome is computed for each set of parameter values. Often one can identify regions of the parameter space in which the outcomes vary similarly in response to variation in the parameters, sometimes with the aid of extant theory. This implies, for example, that increasing parameter A might always increase the outcome variable in one parameter region, but decrease it in another.

When such parameter regions are identified the model can be made more complex, adding one or two parameters. These are sweeped across each of the identified regions. This process is continued until no regions can be identified at some stage of complexity. While it is not guaranteed to discover all possible interactions with this method, it does produce a substantial detail about the functioning of the model.

For the model considered in this paper, a total of four stages are examined: (1) aggregate behaviour absent network structure or bribes (i.e. participation behaviour in a fully connected network with no bribes) (2) behaviour in networks absent bribes (i.e. behaviour in each of the four considered network structures with no bribes) (3) behaviour with bribes absent networks (4) behaviour in networks with bribes. Given previous work of Siegel (2009, 2011) that analysed the first two stages in great detail3, I will rely on these articles their analyses for these stages. Two important facts from that work are relevant for the analysis of the last two stages. First, the parameter space spanned by the trio of parameters {𝑁, 𝑏_'()*, 𝑏_+,-(.} -with 𝑁 being the total number of citizens, 𝑏_'()* the average internal motivation of the population, and 𝑏_+,-(. the standard deviation of these opinions- can be broken up into three regions, within each of the network structures acts similarly. These are denoted motivation classes and called individually weak, intermediate, and strong. Because populations within the weak class participate rarely, only the intermediate and strong classes are considered for this paper.

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Second, network without leaders (Small World and Village) may be described in terms of: (1) their levels of connectivity; and (2) whether their number of weak ties is either less-than-optimal-, optimal, or greater-than-optimal in terms of how well they encourage participation. Optimal is defined as the parameter value that yields the highest level of participation in the intermediate class, all else equal, which may not occur at maximum connectivity.

To understand these optimality levels, consider the following, taken from Siegel (2009, p.130): In a friendship network one’s friends are also friends with each other. These clusters of friends can be thought of as enclaves of participation, since shared experiences encourage a similarity of behaviour within them. If one’s connections are insufficient to spur one to participate, after all, they are less likely to spur another with very similar connections to participate. These small enclaves are necessary for the initial spread of riot behaviour, as they allow rabble-rouser to have a substantial effect on the actions of whom they are tied, as external motivations depend on the local participation rate. Too big an enclave can deteriorate the rabble-rouser’s impact, especially in the intermediate class, in which less of the population on average shares the rabble-rouser’s motivations. Since the ‘weak’ ties are the network structure that determines the behaviour spread (i.e. the size of the ‘enclave’) in a Small World network, the number of weak ties can be optimal, sub-optimal or greater-than-optimal for participation.

Networks with leaders may be described in terms of: (1) the level of influence of their leaders and (2) the level of influence of their followers (only for the Hierarchy network). The influence of followers is determined by the connectivity probability followers have with one another. The next section provides a summary of each network type and the parameters that determine their network structure (see Table 1 below) and discusses how the values for each parameter are determined.

4.2 Parametrization of the Model

As stated above, the first stages of the parameter sweeping procedure have been performed in previous work by Siegel (2011). Thus, for certain parameters fixed parameter spaces have already been defined. This section summarizes these parameter spaces. Definitions of the parameters and a general overview can be found in Table 1. The first considered is the parameter region spanned by {𝑁, 𝑏_'()*, 𝑏_+,-(.}. Siegel (2009) describes the analysis and theoretical support behind splitting this into three regions: weak, intermediate, and strong

motivation classes. Higher values of 𝑏'()* increase participation levels in all regions. In line with limit theorems, increasing 𝑁 reduces randomness in aggregate behaviour, decreasing

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participation when it is unlikely, and increasing it when it is likely. Increasing 𝑏_+,-(. increases participation as long 𝑏_'()* is not too high. Siegel uses the parameter triples {1000, .6, .25} and {1000, .6, .3} for intermediate and strong motivation classes, respectively.

The second stage is networks. Based on Siegel (2009) each of the four network types is characterized according to the regions of the parameter space over which the model behaves similarly. These values are mainly chosen for visualization purposes, as most networks behave similarly over larger parameter spaces. These are:

Small World (Connection Radius, Rewire Probability): in the analysis higher

connectivity and lower connectivity lines correspond to a Connection Radius of 15 and 5

respectively. As individuals are situated in a ring in the Small World network, connection radius thus determines the number of individuals an individual is connected to on both sides. A Connection Radius of 5 thus indicates that any individual is tied with five individuals to his or her left and five individuals to his or her right. The number of weak ties that is optimal depends on the connectivity parameter, so they are used in pairs. For ‘optimal’ Small Network, with Rewire Probability second, these pairs are: (15, .14), (5, .3). For greater-than-optimal the pair is found to be (15, .7). With Rewire Probability corresponding to the probability an individual is randomly tied to any other individual in the network.

Village Network (Village Size, Far Probability): Similar pairs as in the Small World

structure are formed for the Village network. Higher and lower connectivity lines correspond to Village Size (i.e. the number of individuals per tightly clustered ‘village’) of 25 and 5 respectively. For optimal village networks, with Far probability second, the pairs are: (25, .004) and (5, .003). Less-than-optimal village networks correspond to the pair (5, .001). With Far Probability indicating the probability that an individual is connected to any other individual in a different village.

Opinion Leader (𝛾): As the Opinion Leader network is a form of a scale-free network (i.e. a network whose degree distribution follows a power-law), it only has one parameter. Namely, the parameter 𝛾. There is chosen to let 𝛾 = 3 4_{. In this case, the network is constructed} through the preferential attachment algorithm. This means that the more connected an individual is, the more likely it is to receive new ties from newly added individuals in the network, also known as the ‘rich get richer’ mechanism. This algorithm is explained by the

4_{This parameter value does not correspond to chosen parameter in Siegel (2011) (where 𝛾 = 1.4), due to} technical difficulties programming a tuneable parameter value. Real life scale-free networks are often found to have a parameter value close to three (see, for instance, Barabási & Albert, 1999) and thus this structure can be considered more realistic. However, as this value was not considered in the parameter sweeping procedure performed by Siegel, results of analysis should be interpreted with caution.

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following example: let A and B be two individuals that are connected to one another. Let C be an individual new to the network. C will randomly pick one tie available in the network and randomly select one of the individuals at the end of this tie to connect to. At this first stage, only one tie is present in the network. C thus selects this tie and he is randomly paired to individual A. Now let individual D enter the network. He will again randomly select a tie, but this time both ties present in the network are originating from individual A. Thus individual A has a twice as high probability to be connected to D, compared to individuals’ B and C. This algorithm continues up until all N individuals are present in the network.

Hierarchical Network (Expansion Rate, Level Connectivity): As the Hierachical

Network is built up in a ‘tree’ structure. Two parameters determine the network structure. First,

Expansion Rate, determines the number of individuals each individual is connected to in the

level below them. If expansion rate is 4, the individual in the middle of the network is connected to four other individuals, each of these individuals are connected to four more individuals. The network expands up until N is reached. Analysis from Siegel determined an Expansion Rate equal to 10. Two different states of the network are determined: high influence followers and

low influence followers, which are determined by the degree of connectivity within each level

of the tree. This parameter thus indicates the probability that individuals are randomly connected to any other individual in their own ‘branch’ of the tree. The high influence followers state corresponds to the pair (10, .007), while the low influence followers state is determined to be (10, .002)

As part of the third stage of the parameter sweeping procedure, the values of two other variables are determined for analysis. These are 𝜆 (i.e. rate of updating) and the height of the bribes given out by the dictator. For further analysis, rate of updating is fixed at 𝜆 = 0.8 and the height of the bribes are fixed at 0.5 per iteration. As the focus of this paper is on network structure, details of this third stage are relegated to Appendix A. The main lesson here is that the rate of updating has no significant impact on the mean participation rates in equilibrium. That is, because only participation rates are considered when the model is stable (i.e. participation has not changed for fifty consecutive iterations), the rate of updating has no significant effect on these participation rates within the tested range between zero and 0.8. Hence, lambda can be fixed at an arbitrary (but theoretical plausible) value within this range.

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Table 1: Summary of Network structures and parameter pairs used for analysis

Parameters Parameter pairs

Small World Connectivity Radius The number of individuals

an individual is connected to both sides of him in the ring

Higher Connectivity, greater-than-optimal weak ties

(15,.7)

Rewire Probability Probability of randomly being connected to any other individual in the network. Determines number of weak ties.

Higher Connectivity, optimal weak ties

(15,.14) Lower Connectivity,

optimal weak ties

(5,.3)

Village Village size Size of fully connected

clusters (villages)

Higher Connectivity, optimal weak ties

(25,.004)

Far Probability Probability that an individual is randomly connected to someone in another village. Determines number of weak ties.

Lower Connectivity, optimal weak ties

(5,.003) Lower Connectivity,

lower-than-optimal weak ties

(5,.001)

Opinion Leader 𝛾 Parameter determining the

degree distribution according to a power law

𝛾 = 3

Hierarchical Expansion Rate Rate of expansion of the network. Each individual is connected to a number of individuals below them equal to Expansion Rate

High influence followers (10,.007)

Level Connectivity Probability that an individual is connected to any other individual in the same branch of the network

Low influence followers (10,.002)

4.3 The Impact of Bribes Absent Networks

As part of the third stage of the parameter sweeping procedure, this section will discuss the impact of bribes on participation absent networks. These results thus serve the purpose of a sort of baseline for subsequent sections. Results of the simulations are illustrated in Figure 3. Simulations are run on fully connected networks in which each individual is connected to every

Dictators, citizens, networks and revolts : a simulation analysis of the relationship between revolts and the allocation of resources in dictatorships