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

University of Amsterdam

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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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Table of contents

1. Introduction 5 2. Previous Literature 8

2.1 The Behaviour of Dictators 8 2.2 Bribing and repression 9 2.3 Riots and Rebellion 11 2.4 Collective Behaviour 12 2.5 Collective Behaviour and social networks 13 2.6 Modelling Dictator Behaviour and Collective Action 14

3. Model 17 3.1 Network Typology 20 3.2 Procedure 23

4. Analyses 25 4.1 Sequential Parameter Sweeping 27 4.2 Parametrization of the Model 28 4.3 The Impact of Bribes Absent Networks 31 4.4 The Impact of Network Structure 33

1.1.1 Small World 33 1.1.2 Village Network 36 1.1.3 Hierarchical Network 39 1.1.4 Opinion Leader Network 43 1.1.5 Hierarchical and Opinion Leader Networks with Unified Leaders 46

4.5 Summary of results 48 5. Discussion 51 6. Literature 54 Appendix A: Bribe Height and Rate of Updating 57 Appendix B: Additional graphs 61 Appendix C: Netlogo code 66

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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&,,– 𝜂&,,*,78 > 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

19

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

20

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.

21

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 𝛾thus determines the characteristics of the network,

with smaller values corresponding to greater overall connectivity due to presence of a greater

22

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.

Figure 1: Visual representations of network structures

23

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.

24

Figure 2: Flowchart representation of simulation procedure and corresponding parameters

25

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.

26

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

2 As centrality measures are highly correlated with the number of ties used in this paper, the strategy in which the dictator targets the most central individuals is not considered.

27

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 𝑁being

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.

3 See web appendixes of both Siegel articles for detailed results of this parameter sweeping procedures

28

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

29

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 = 34. 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.

30

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 = 0.8and

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.

31

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

32

other individual in the network5. Plots in the left column correspond to a random bribe strategy,

plots in the right column to the strategy in which the dictator targets regime sympathisers.

Simulations ran on the intermediate and strong motivation class are situated in the top and

bottom row, respectively. Figure 3: Effects of bribes on participation behaviour absent networks

The plots illustrate that participation rates are generally higher for the strong motivation class

compared to the intermediate motivation class, as proposed by Siegel. More importantly,

participation rates differ greatly when the two strategies of the dictator are compared. Where

participation under the targeted opinion strategy decreases almost linearly as the percentage of

individuals receiving bribes increases, under the random strategy this relationship is much

more convex. Meaning that returns in terms of lowering the participation rate are marginally

diminishing for the dictator, with the ‘optimal’ trade-off point situated at bribing 40 percent of

the population, approximately. As a result, participation rates are always lower for any given

5 Because of the high number of ties in this random network, creating a network with 1000 individuals was not possible due to lack of computational power. As a compromise, the random network consisted of 100 individuals. In theory, this should generate similar results as in a network with 1000 individuals, but with a slightly higher variance. This explains the non-monotonicity of the results.

33

bribe percentage when the random strategy is used compared to the target regime sympathisers

strategy - except at the extreme values where either no one or everyone receives bribes, then

participation rates are similar- . Note that in this case the linear relationship between

participation and the number of people receiving bribes in the target regime sympathiser

strategy indicates a highly ineffective way of stopping participation for the dictator. It indicates

an almost one-to-one relationship: for every extra citizen the dictator bribes, he receives one

more regime sympathiser. He thus does not benefit from any added network effects. That is,

his bribes (and possible change in participation that it causes) do not ‘spread’ throughout the

network, affecting more than one citizen at a time. Hence, from these results there is concluded

that absent networks the strategy of the dictator significantly affects participations rates, with

the random bribe strategy being more effective in lowering participation rates compared to

strategy in which the dictator targets regime sympathisers. This thus implies that when the

dictator is confronted with citizens in a fully connected network he has to spend less resources

to prevent collective uprisings when distributing these resources randomly over the population

compared to when he targets sympathisers.

4.4 The Impact of Network Structure

Given the above mentioned parameter values, comparative statistics are produced for each

network structure. For each network structure results are discussed briefly below. Thereafter,

results from each network structure are compared.

4.4.1 Small World

For the Small World network structure, Figure 4 illustrates results of the simulation runs. The

x-axis in each plot corresponds to the percentage of individuals that receive bribes from the

dictator, the y-axis to average participation rates. Plots on the top row show results for the

intermediate motivation class (i.e. 𝑏+,-(. = 0.25), while plots on the bottom row show the

strong motivation class (i.e. 𝑏+,-(. = 0.3). Results are divided to situations where the dictator

used a random bribe strategy (left) and where he uses a strategy that targets regime

sympathisers (right). Lines correspond to parameter pairs summarized in Table 1, with either

the connectivity of each individual being varied (i.e. the total number of individuals an

individual is connected to on both sides of him/her in the ring) or the number of weak ties.

34

Figure 4: Simulation results for the Small World network

Firstly, the plots illustrate that participation rates are on average higher in the strong motivation

class compared to the intermediate motivation class. This is due to the higher variance in

internal opinions, which in turn places more rabble-rousing individuals in the network.

Secondly, there is observed that participation absent bribes for the higher connectivity

situations is generally higher. However, in the intermediate class both higher connectivity

classes with either optimal or greater-than-optimal have similar participation rates. This is in

line with Siegel (2009), as the optimality of weak ties was determined by the number of weak

ties needed to reach optimal participation in the intermediate motivation class. Thirdly,

increasing the percentage of individuals who receive bribes decreases participation, as

expected.

When the strategies are compared, it is easily observed that the random strategy is the

most effective strategy for the dictator to reduce participation in this network structure. As in

the fully connected network, bribes have a near linear relationship with participation when a

strategy of targeting regime sympathisers is used. While a steep decline is observed when

bribes increase from zero to twenty percent in the random strategy.

35

Another important thing to notice from these plots is that all connectivity lines converge

towards each other. This means that as the percentage of individuals who receive bribes

increase, the differences between network parameterizations decrease. Handing out sufficient

bribes does not only decrease participation, it will no longer matter what levels of connectivity

are present in the network. This response occurs for both strategies of the dictator; all lines

eventually converge toward one another. However, the dictator’s strategy does influence the

speed of this convergence. With the random strategy, convergence happens relatively fast as

bribes increase compared to the situation in which the dictator targets his sympathisers. Also,

to make this convergence possible, networks with higher connectivity are more vulnerable to

bribes. Again, consider the three lines representing different levels of connectivity. The higher

the level of connectivity and the number of weak ties present in the network, the higher

participation absent bribes. For the above described convergence to be possible, every

additional person bribed should not have the same effect on participation for each connectivity

level. Connectivity levels with higher participation absent bribes should see a steeper decline

in participation for each additional citizen bribed, up to the point of total convergence, for this

convergence to be possible. As a result, the marginal efficacy of bribes increases as

connectivity in the network increases. This is mostly because a great deal of participation in

highly connected network is due to rabble rousers who are highly connected, and thus can

persuade a great deal of non-rabble-rousing types into participation. When highly connected

rabble-rousing types are targeted with bribes, the external motivations of a lot of individuals

are negatively affected. Logically, when a rabble-rouser is less connected the external

motivations of less individuals is affected. Hence, higher connected networks are more prone

to bribery.

Another important measure is the standard deviation of participation rates. As the

participation rates in the above discussed plots are the mean participation rates over 100 runs

of the model, taking standard deviations from these means into account can tell something

about the possibilities of cascades happening. If the variance in results is high, the situation

allows for cascades of participation given the right conditions. Figure 5 shows the range of

participation results and the standard deviation of these results. For illustrative purposes the

parameter pair with higher connectivity and optimal weak is used. Plots corresponding to the

other parameter pairs can be found in Appendix B.

36

Figure 5: Min-max participation and standard deviation of participation. Small World network with higher connectivity and optimal weak ties .

As expected, participation rates are more robust in the higher motivation class compared to the

intermediate motivation class, absent bribes. Where participation rates in the intermediate

participation class absent bribe range from near zero to one, in the higher motivation class rate

vary between 0.5 and one. This is due to the higher number of rabble-rousers who participate

no matter the actions of others. The plots also illustrate that the higher the number of individuals

receiving bribes, the lower the variation in possible participation, as in all plots standard

deviations decline as the percentage of individuals receiving bribes approaches one. Hence, the

more bribes are present in the network, the less likely it is cascades of participation will flow

through the network.

4.4.2 Village Network

For the Village network results are shown in Figure 6. Again, decreasing participation rate is

observed as the percentage of individuals in the network receiving bribes increase. Also, the

37

convergence of participation as bribes increase between parametrizations of the model is

observed, as in the Small World network. Figure 6: Simulation results for the Village network

The Village network and Small World network are similar in their core structure: there exist

highly connected clustered of individuals of which some possess a number of weak ties,

resulting in similar average connectivity for each individual in the network. There are however,

some striking differences to be found in the results. Frist, participation rates are generally lower

in the village network. This is due to the highly clustered nature of the village network. As a

result, behaviour of rabble-rousing types can only spread to individuals they are connected to

directly in their village (assuming the rabble-rousing type has no connections to outside

villages). There is thus often observed that villages start off as fully participating or fully non-

participating. This suppresses possibilities of cascades happening, reducing participation rates.

Second, higher connectivity reduces participation in the village network. This is explained by

the fact that connectivity levels in the village networks are determined by village size. That is,

the number of individuals all tied to one another, creating a village. As village size increases,

the influence of randomly placed rabble-rousing types decreases, due to smaller part of each

38

individuals’ local participation rate the rabble rouser influences. If a village consists of five

individual including one rabble rouser, the local participation rate of each individual in the

village is 8U= 0.2. If the village size is twenty and there is also one rabble-rousers, local

participation rates are equal to 8VC= 0.05. Hence, as the number of rabble rousing types is equal

in both cases, they exert less influence when villages are large, thus reducing participation

rates. As a result, the opposite as in the Small World network is found: the marginal efficacy

of bribes decreases as connectivity in the network increases.

When taking the dictator’s strategies into account, there is observed that under the

random strategy the efficacy of bribes is similar compared to the Small World network. When

the dictator targets regime sympathisers, results are different. In case of higher connectivity

network with optimal weak ties and lower connectivity with lower-than-optimal weak ties, a

near constant participation rate is observed, up to a certain point. After which participation

decreases almost linearly. This is due to the relatively low participation rates absent bribes and

the above explained notion that villages start of either fully participating or fully non-

participating. As participation rates are low, there should be only a few villages in the network

consisting of only individuals who are participating. Also, it is highly unlikely that harsh

regime sympathisers are present in these villages. As the dictator targets regime sympathisers

first, he is likely to target villages with only non-participators first, which has no influence on

participation rates. This situation continues up onto the point he targets individuals in the fully

participating villages. It is thus observed that when the participation rate absent bribes is, for

instance, 0.2 (as in the higher connectivity, optimal weak ties case), participation starts to drop

when the last 20 percent of individuals is targeted with bribes (i.e. 80 percent of individuals

receive bribes).

When comparing the range of participation rates, more differences can be found. Figure

7 shows the range of participation rates in the higher connectivity Village network with an

optimal amount of weak ties. Results from other parametrizations of the network can be found

in Appendix B.

39

Figure 7: Min-Max participation rates and standard deviations of participation. Village network with higher connectivity and optimal weak ties.

When comparing the Village Network with the Small World network, there is again

observed that standard deviations behave in a similar fashion as average participation rates

when taking the percentage of individuals in the network receiving bribes into consideration.

Meaning that: as the number of individuals in the network receiving bribes increases, standard

deviation of participation decreases. Which in turn decreases average participation rates.

Hence, bribes make participation rates more robust, reducing either the minimum and/or

maximum observed values of participation, rather than changing the probability that relatively

high or low participation rates are observed, while keeping the same minimum and maximum

observed participation rates.

4.4.3 Hierarchical Network While both the Village network and Small World networks have a similar core network

structure (i.e. all individuals have, on average, the same number of ties). Subsequent sections

focus on network structures that are significantly different, as both the Hierarchical as the

40

Opinion Leader network have different tie distributions across individuals in the network.

Meaning that some individuals in the network have a more connected (or more ‘central’)

position in the network than others. In case of the Hierarchical Network this is due to network

creation starting from one individual. From this one individual a number of other individuals

are connected equal to parameter Expansion Rate (in this case, expansion rate is equal to ten).

These individuals are situated in the first ‘branch’ of the network. Each individual in this branch

is connected to, again, a number of individuals equal to Expansion Rate. This continues up

until the desired number of individuals is reached. It is not hard to notice that individuals up in

higher branches benefit from their central position and posit more influence than individuals

in lower branches. Figure 8 shows simulation results for this network structure. Solid lines

correspond to ‘high influence followers’, which means that individuals in each ‘branch’ have

a 0.7 percent chance to be randomly connected to any other individual in their branch. For ‘low

influence followers’ this probability is equal to 0.2 percent. This difference in tie distribution

compared to the previously discussed network structures also adds another strategy to the

arsenal of the dictator. Namely, the dictator can also target those individuals with the highest

amount of social capital, measured in the number of ties. Results from this strategy are added

in the column on the right in Figure 8.

41

Figure 8: Simulation results for the Hierarchical network

As in both the Small World and Village networks structures, participation rates decrease (near)

monotonically when the percentage of individuals in the network who receive bribes increases.

Again, participation rates absent bribes are higher in the strong motivation class compared to

the intermediate motivation class. For this Hierarchical network structure, increased

connectivity increases participation. Also, convergence of connectivity lines is again observed

as the bribe percentage increases. Meaning that in the Hierarchical network the marginal

efficacy of bribes increases as connectivity increases.

When comparing strategies, the Hierarchical Network behaves similarly as the Small

World Network when considering both the random and targeted regime sympathiser strategy.

With participation decreasing near linear in the latter and taking a more convex form in the

former. When the dictator uses the strategy in which he targets individuals who have the highest

amount of ties, this strategy greatly reduces participation rates. Especially the first few

individuals bribed yield a very high marginal reduction in participation rate. When looking at

the high influence followers line in plot in the bottom right corner of Figure 8 (targeted ties

strategy, strong class) a drop in participation rate from approximately 0.9 to approximately 0.3

42

is observed as bribes increase from zero to 5 percent. Hence, in the Hierarchical network, the

strategy in which the dictator targets individuals based on the number of ties they possess is

highly effective in reducing participation rates. It is also observed that this strategy is more

effective (i.e. the marginal effectiveness is higher) with high influence followers compared to

low influence followers. The reasoning behind this is as followed: as the dictator targets

individuals with the highest number of ties, he is targeting the most influential individuals in

the network. If there is a rabble-rouser situated in a highly influential position in the network

(that is, in a high branch of the network), he is likely to have influenced a great deal of

individuals into participating. Hence, targeting this rabble-rouser indirectly changes

participation for these followers. When influence of the followers is high, the influence of this

rabble-rouser is even more widespread, thus increasing the efficacy of the bribe.

Figure 9 shows plots for the range of participation rates and standard deviation of these

rates in the Hierarchical network. Plots for the low influence follower situation can be found

in Appendix B. As in previous sections, it is observed that increasing the number of bribes in

the network decreases both the range of participation and the standard deviation of

participation.

43

Figure 9: Min-Max participation rates and standard deviations of participation. Hierarchical network with High influence followers.

The plots illustrate that standard deviation of participation is relatively high in the Hierarchical

network compared to both the Small World and Village Network structure. With standard

deviation being as high as 0.4 in the intermediate class absent bribes. This is significantly

higher than most other observed standard deviations6. In case of the Hierarchical network

structure higher connectivity corresponds to higher standard deviation of participation, as in

the Small World network. With regards to the dictator strategy in which he targets the

individuals with the most ties, a steep decline in standard deviation of participation is observed

for the first few percentages of bribes, as observed in the average participation rates.

4.4.4 Opinion Leader Network

As the Opinion Leader network is generated through the preferential attachment method (as

explained on p. 28) The network consists of multiple individual that can be seen as ‘hubs’ that

6 Except standard deviations in the Small World network with higher connectivity and greater-than-optimal weak ties. See Appendix B

44

possess a large amount of ties, and relatively many individuals that possess relatively little

number of ties. As a result, position in the network matters greatly for the amount of influence

an individual has. How this affects participation rates is illustrated in Figure 10.

Figure 10: Simulation results for the Opinion Leader network

The plots illustrate that participation is relatively low in this network structure compared to the

previously discussed network structures. With participation rates absent bribes being

approximately 0.15 and 0.25 for the intermediate class and strong class, respectively. It is

observed that participation under the random strategy decreases in a slightly convex path as the

bribe percentage increases. More interestingly, an almost step wise decrease in participation is

observed under the strategy in which the dictator targets individuals based on their ties. This is

explained by the fact that the number of ties in the network follows a power law distribution.

As said above, the network consists of a number of hubs with relatively many ties. The more

ties, the more direct influence an individual has. One can image that if one of these hubs is a

rabble rouser, targeting this rabble rouser will result in a steep decline in participation. As more

individuals in the network receive bribes under this strategy the more hubs already have been

45

targeted, and subsequent targeted hubs have less influence over other individuals in the

network. Thus, for every targeted hub participation declines less steep, resulting in an overall

near step-wise decline in participation when the percentage of bribes increase.

When taking participation range and standard deviation of participation into account, it

is observed that standard deviations are relatively low for the Opinion Leader network

compared to the other network structures. This is illustrated in Figure 11. This can, however,

be explained by the relatively low participation rates observed in the network structure.

Figure 11: Min-Max participation rates and standard deviations of participation. Opinion Leader network

It is also observed that standard deviations behave similarly as in other networks: the higher

the percentage of individuals receiving bribes, the lower the standard deviation of participation.

Also, the strategy in which the dictator targets the individuals with the most amount of ties

seems to be the most effective strategy for reducing the standard deviation of participation

rates.

46

However, results discussed for both the Opinion Leader network and the Hierarchical

network do not tell the full story for both participation rates and the efficacy of bribes. As

participation in both networks is highly dependent on the placement of individuals in the

network this should be investigated further. In both cases, one can imagine that the possible

placements of rabble rousers affect outcomes of simulations greatly. Therefore, in the next

section analysis is performed on additionally run simulations in which network position is

either positively or negatively correlated with internal motivations.

4.4.5 Hierarchical and Opinion Leader Networks with Unified Leaders

As participation outcomes in both the Hierarchical and the Opinion Leader Network depend

greatly on the placements of individuals in the network, additional analysis is performed on

situations in which the ‘leaders’ of the network are unified. That is, placement in the network

is correlated (either positively or negatively) with internal motivations 𝑏&. In case of the

Hierarchical network correlation is based on the branch of the network an individual is placed.

When opinions are positively (negatively) correlated, the closer an individual is up to the

individual where the network is originating from, the higher (lower) his/her internal motivation

will be. For the Opinion Leader network this correlation is based on the number of ties. In the

case of positive (negative) correlation, more ties correspond to higher (lower) internal

motivations. Thus, in the case of positive correlation one would expect more rabble rousing

types in the influential positions in the network. When these positions are correlated with

motivation, there is said that leaders are ‘unified’. Results for these simulations are shown in

Figure 12 and 13 for the Hierarchical and Opinion Leader network, respectively.

Each line in the plots correspond to one of the dictator’s strategies, when the

network position is either positively or negatively correlated with motivations. The plots show

that there are big differences in participation rates for both network structures when this

correlation is varied. The following can thus be concluded: when networks consist of a handful

of individuals who exert great influence, the placement of individuals in the network is of great

importance for participation rates. When taking the Hierarchical network (Figure 12) into

consideration, it is observed that participation is almost non-existent when the motivation is

negatively correlated with network position, while the participation rate reaches 1 when there

is positive correlation, absent bribes. When the dictator’s strategies are compared when this

correlation is positive, the plots illustrate that the strategy in which the dictator targets regime

sympathisers is the least effective in reducing participation, followed by the random strategy.

47

The strategy in which the dictator targets individuals with the most amount of ties is most

effective. Figure 12: Simulation results for the Hierarchical network with unified leaders

Figure 13: Simulation results for the Opinion Leader network with unified leaders

48

When the plots in Figure 12 are compared to the plots in Figure 8 (simulation results

for the Hierarchical network absent correlation, p.41), it is observed that under each of the

dictator’s strategies participation decreases more slowly when the percentage of bribes

increases. Hence for the Hierarchical network there can be concluded that unified leaders

reduce the efficacy of bribes. For the Opinion Leader network this notion does not hold. When

comparing plots in Figure 13 and Figure 10 (p. 44) there is observed that the efficacy of the

targeted ties strategy increases when leaders are unified and have positively correlated

motivations. Hence, participation in the Opinion Leader network is vulnerable to a targeted

ties strategy, even when leaders are unified.

When participation in the strong and weak motivation classes is compared, plots for

both the Hierarchical network and the Opinion Leader network illustrate that there a no big

differences between motivation classes. Hence, there is concluded that when leaders are

unified, differences in motivation class have less influence on participation. This means that if

leaders are unified, it matters less whether there are relatively much rabble rousers or relatively

few rabble rousers in the rest of the network. These results also show that the effects of unified

leaders differ between network structures. While in both cases it highly increases participation,

participation reacts differently to different bribe strategies. There is however concluded that in

all cases the dictator is the most efficient when targeting the individuals with the most amount

of ties.

4.5 Summary of results

For previous sections it can be seen that some commonly used metrics of networks –

connectivity, prevalence of weak ties, the presence of elites – have a complex interaction with

participation and the efficacy of bribes on this participation. The list below summarizes the

main results for each of the network structures used in these analyses.

• Small World: This network induces high participation levels absent bribes, which

spreads quickly via a combination of strong and weak ties. In the stronger motivation

class, participation is higher compared to the intermediate motivation class.

Connectivity and the number of weak ties have a positive influence on participation.

However, the higher the connectivity and the greater the number of weak ties, the higher

the efficacy of bribery. The random bribe strategy is more effective in reducing

participation than the strategy in which the dictator targets regime sympathisers. When

49

taking into account standard deviation of participation, the strong motivation class

corresponds to a lower deviation. Also, the higher the number of bribes the lower the

standard deviation of participation.

• Village: participation rates are relatively low in the Village network due to the highly

clustered nature of the network. Also, higher connectivity reduces participation rates

and the marginal efficacy of bribes decrease as connectivity in the network increases.

Participation rates react similar to bribes under the random strategy as compared to the

Small World network. The strategy under which the dictator targets his sympathisers is

much less efficient. Standard deviations behave in similar fashion as in the Small World

network when bribes increase: they decrease as bribes increase.

• Hierarchical: Because the structure of the Hierarchical network allows for the creation

of ‘leaders’ and ‘followers’, the core network structure is significantly different from

both the Small World and Village networks. However, as in the other networks,

participation decreases (near) monotonically when bribes increase. Participation

approaches 100 percent in the strong motivation class, but is significantly lower in the

intermediate class. Results show that increased connectivity increases participation,

while the marginal efficacy of bribes increases as connectivity increases. Participation

behaves similarly as in the Small World network when taking the two original strategies

of the dictator into consideration. The third proposed strategy, the targeting of

individuals with the most amount of ties, is even more effective than the random

strategy. The standard deviation of participation is relatively high in the hierarchical

network. Again, the targeted ties strategy of the dictator is highly effective in reducing

this deviation. When position in the network is correlated to motivations, there is found

that this either highly reduces (negative correlation) or increases (positive correlation)

participation. Also, different motivation classes have less influence on participation.

When correlation is positive participation rates become more robust to bribery, but the

targeted ties strategy is still the most efficient for the dictator.

• Opinion Leader: The Opinion Leader network has relatively low participation and the

stronger motivation class has higher participation compared to the intermediate class.

Again, the targeted ties strategy is highly effective in reducing participation, and does

so in a step-wise fashion. This is due to existence of ‘hubs’ in the network. The range

of participation and standard deviation of participation is relatively low, mostly due to

the relatively low average participation rates. When network position correlates

50

positively with motivations higher participation rates are observed. While in this case

participation seems fairly robust under the random strategy and the regime sympathiser

strategy, the targeted ties strategy still seems very effective in reducing participation.

Hence, participation in the opinion leader network is very prone to a strategy in which

individuals are targeted based on the number of ties they possess.

51

5. Discussion Analyses in this paper have shown that answers to the question “Under what conditions are

revolts by citizens against an autocratic regime successful and how is this prevented by the

regime?” depend fundamentally on the structure of the social network that connects the

population. As this research focussed on the allocation of resources by the dictator (i.e.

bribery), there is found that the network structure interacts with both the distribution of

individuals’ motivations within the network as well as the level and allocation of the said bribes

in producing outcomes of participation in revolts against autocratic regimes. To understand

and predict the levels of participation in revolts one should not just understand on or two of

these notions, but must also consider the conditioning effect of each on the others. While this

leads to a complex causal story, it is necessary for understanding how the allocation of

resources in repressive regimes affects revolts.

As an example, the degree to which the allocation of resources by the dictator handed

out to social leaders attempting to rouse their followers to revolt against the regime is efficient

depends on the interest of these social leaders, their connections to their followers, and the

strategy used by the dictator. When these social leaders are unified in their interests’

participation in revolts is relatively resistant against handed out resources. However, when the

dictator is able to select these social leaders based on the level of their social capital,

participation in revolts is highly affected. Meaning that when a dictator comes to power, his

best strategy to ensure stability of his regime is to allocate resources to the already powerful.

This used example thus relates to theorization of Tullock (1974), who described the trade-off

dictators face between keeping the rich and powerful satisfied and the efficiency of the regime.

Giving insight to this dynamic of this trade-off can be considered the most notable finding of

this paper.

In a more general matter, there is found in that in most cases, the more connected people

are to one another, the higher the chance of successful revolts. Conversely, when citizens are

more connected, each additional distributed resource reduces the probability of successful

revolts more than when citizens are less connected. Exception to this is when citizens live in

highly connected clusters, then the marginal effect of distributed resources reduces as

connectivity increases. Additionally, there is found that given all network structures,

motivation distributions, and connectivity levels, handing out resources reduces variability in

participation numbers. Hence, it can be stated that the more resources a dictator hands out, the

more robust predictions can be made about the possibility of successful revolts.

52

Nonetheless, one should proceed with caution when trying to apply these results to real-

world situations. As per definition the modelling of complex behaviour can only be achieved

by allowing for assumption to be made. Hence, in the model discussed in this paper several

assumptions have been made to achieve workability. Firstly, there is assumed that the dictator

only cares about personal resources and staying in power. Numerous examples can be named

for both current and past dictatorial regimes where the dictators in place were more driven by

either ideology or the sole possession of power. This stylization of the dictator’s behaviour is

put through in the possibilities of his actions. As the model only allows for three simple

strategies the dictator can perform, while real life dictators may have a near infinite set of

possibilities to allocate resources across the population. In addition, dictators in the model are

perfectly informed about both the motivations and placement in the network of individuals.

One could expect that real life dictators generally receive this information including some form

of error.

More importantly, this research has focussed on only the most understudied of the two

‘weapons’ a dictator possesses for staying in power. That is, the allocation of resources rather

than repression. It therefore places itself next to the already existing models and literature more

as a direct ‘expansion’ rather than a more deepening or applicable version. That is, as models

such as the one from Siegel focussed only on repression, it cannot tell the whole story about

collective uprisings in dictatorial regimes. In the same manner, this research is also unable to

tell that complete story. However, if future research does want to make accurate and applicable

predictions about revolts, not only repression and the allocation of resources should be taken

into account, but also their interdepencies. As these interdependencies can only be

distinguished when the effects on revolts for both factors in isolation are known, this research

may be an important stepping stone for future research.

When taking into consideration some real life examples of some of the above

mentioned results, the problem of these interdepencies are also noticeable. With regards to the

finding that the dictator’s best strategy is to keep already powerful people or groups on his side

by giving them access to resources one could point to a few African dictatorships where social

structures remained stable after one dictator was replaced with another. Or even some of the

authorial regimes that existed in the middle-east (such as Iraq), where even though formal

regimes have changed power, the influence of militant ideological groups was not diminished.

On the other hand, numerous regimes can be pointed out where everyone even weakly related

to the old regime was repressed or exterminated, such as Cambodia under the rule of Pol Pot.

Hence, results from these models do not translate directly to explain behaviour of dictatorial

53

regimes. This shows that these interdependencies exist and both tactics of dictatorial leaders

are most often used in conjunction.

Future research should thus first try to model the participation in revolts when the

dictator possesses the power to use a combination of both repression and the allocation of

resources. After which more profound assessments can be made about the stability of current

or future autocratic regimes. Hence, this research’s main contribution is to give insight in the

dynamics of resource allocation in dictatorships in a vacuum, pathing way for other scholars

to assess revolts in dictatorships in a more complete fashion.

54

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Appendix A: Bribe Height and Rate of Updating

As part of the third stage of the parameter sweeping procedure, analysis is needed for the rate

of updating 𝜆 in relation to the height of given bribes. The six graphs in Figure 14 illustrate

the connection between the rate of learning and the height of bribes. Simulations were run on

a fully connected network in which every possible connection between individuals was

made7. The different rows of graphs correspond to the percentage of randomly selected

citizens in the network who received bribes, which are 1, 10 and 50 percent for the top,

middle and bottom row, respectively. Plots on the left correspond to the intermediate

motivation class, plots on the right to the strong motivation class. Figure 14: Learning and bribe height in the Fully-Connected Network

The plots illustrate that participation rates remain relatively stable as bribes increase. For the 1

percent level, participation rates are similar when bribes are non-existent (zero) and very high

7 Because of the high number of ties in this random network, creating a network with 1000 individuals was not possible due to lack of computational power. As a compromise, the random network consisted of 100 individuals. In theory, this should generate similar results as in a network with 1000 individuals, but with a slightly higher variance. This explains the non-monotonicity of the results.

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(near one). Absent bribes all values of 𝜆 seem to yield similar participation rates except when

𝜆 approaches one, then participation rates are significantly lower. As expected, participation

rates are higher for the strong motivation class compared to the low motivation class. In the

cases where 10 or 50 percent of the individuals in the network receive bribes, a steep decline

is observed in participation when bribes jump from zero to 0.1. This indicates that bribing

citizens does affect participation rates. However, whether participation rates are 0.1 or at the

maximum of 1 (or somewhere in between) does not seem to matter for overall participation.

When half of the population receive bribes, participation rates drop close zero. This is a logical

result within a fully connected network where every individual is connect to each other

individual. Because at least half of the individuals in the network are very likely not participate

due to bribes, local participation rates will not be greater than 0.5 for each individual in the

network, reducing the probability that non-bribed individuals will participate. This in turn

reduces local participation rates. This process continues up until only harsh rabble rousers (with

relatively low internal motivations) decide to participate in a riot. In sum, the level of both 𝜆

and the height of the bribes do not influence average participation rates as might be intuitively

expected. This is due to that the recorded participation rates are the averages of the participation

rates for each run in the model ‘in equilibrium’. That is, participation rates were recorded and

stored when none of the individuals in the model changed their participation for fifty

consecutive iterations. To further explain this relation, I take one step back in the parameter

sweeping procedure to investigate how the updating rates affects participation absent network

and bribes. Results are shown in Figure 15. Plots in the top row show how the updating rate

(x-axis) affects average participation rates (y-axis). For the plots in the bottom row updating

rate is plotted against the total number of iterations the model needed to store the ‘equilibrium’

participation rate. As the model was programmed to run for an 50 iterations to check if no

individual would update their participation, minimum value of the number of iterations is 49

(50 minus the first iteration).

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Figure 15: Effects of updating rate on both participation and iterations of the model

There is observed that the updating rate has no significant effect on participation in the

fully connected network as long as it falls in the range between 0 and 0.9. When the updating

rate is larger than 0.9, participation rates steeply decline. As expected, participation rates are

generally higher in the strong motivation class. When looking at the number of iterations the

model needs to reach equilibrium, the model behaves as expected. The higher the updating

rate, the higher the number of iterations needed. As higher values of lambda correspond to a

slower updating procedure this is logical. When a person in the network changes its opinion it

takes more time for others to be influenced by this change and to update their participation.

When the updating rate is equal to one, the number of iterations drops to its minimum as no

updating is possible because no individual can change their external motivations (and thus their

participation).

As the rate of updating is, per definition, a rate and the bribes (and their corresponding

height) are a constant the non-significant relationship is as followed: as long as there is some

form of updating, participation of some individuals will change in a fully connected network,

as long as sufficient individuals in the network are participating. The speed of this process is

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determined by the updating rate. However, if bribes are allocated in the network they either

target individuals who are not participating or individuals who are participating. In the former,

nothing will happen to participation rates as the local participation rates by individuals tied to

this individual will see no change. If the bribes target individuals that are participating,

participation rates will eventually change as long as the dictator persists in handing out bribes

long enough to this individual to change his/her participation. When this happens, individuals

tied to this bribed individual will see a drop in their local participation rates which may in turn

change their participation. However, the speed in which this happens is, again, dependent on

the updating rate 𝜆. Hence, the speed of both positive and negative changes in participation are

determined by this updating rate. As long as it takes less than fifty iterations for an individual

to update his/her opinion, bribes will always have the full effect on the network as long as there

is some form of updating, irrespective of their height. Therefore, the rate of updating and the

height of bribes have no significant effect on equilibrium participation rates, as long as there is

some form of updating that ensures the updating of participation within fifty iterations.

As the value of 𝜆 has no effect on participation rates as long as it falls in the (tested)

range between zero and 0.8, it can be set as a fixed value within this range for further analysis.

Because internal motivations are considered the leading factor in deciding to participate in

revolt, and theory dictates that people are at least somewhat influenced in their actions by others

in one way or another (Grannovetter, 1978; Mutz, 2002), I fix lambda at the highest possible

value which falls in this range, namely 𝜆 = 0.8, as in Siegel (2011). For this value of lambda

participation rates remain stable over the whole range of analysed bribe-heights. Hence, also

this value can be fixed for further analysis. There is chosen to fix bribes at 0.5 in all the analyses

of this paper.

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Appendix B: Additional graphs

Small World Network Figure 16: Min-Max participation rates and standard deviations of participation. Small World network with higher connectivity and greater-than optimal weak ties.

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Figure 17: Min-Max participation rates and standard deviations of participation. Small World network with lower connectivity and optimal weak ties

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Village network Figure 18: Min-Max participation rates and standard deviations of participation. Village network with lower connectivity and optimal weak ties

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Figure 19: Min-Max participation rates and standard deviations of participation. Village network with lower connectivity and lower-than-optimal weak ties

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Hierarchical network Figure 20: Min-Max participation rates and standard deviations of participation. Hierarchical network with low influence followers

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Appendix C: Netlogo code

extensions [ network ] turtles-own [group-membership] globals [ connected? ; stores true if network connected clustering-coeff ; stores average clustering coeff ave-path-length ; stores average path length infinity ; an arbitrary large number used by calc-ave-path-length height-of-bribes ; random-group ; group of randomly selected nodes used by the random strategy global-participation-rate ;overall participation rate count-global-participation-rate ;used to count the number of ticks participation rate is stable number-of-cliques ticker ] breed [nodes node] ; create a turtle breed called nodes undirected-link-breed [edges edge] ; create a link bread called edges nodes-own [ internal-motivation external-motivation new-external-motivation bribes participation total-motivation branch leader groupid ] ; ====== CREATE-NEW-NODES ; clear-all and creates some new nodes. Hence they will be numbered from 0 upward. ; most of the network creation procedures call this first. to create-new-nodes [n] clear-all ask patches [ set pcolor white ] create-nodes n [ set color red set shape "circle" ] ask nodes [set bribes 0 set internal-motivation random-normal b-mean b-std.dev. set external-motivation -1 set total-motivation (internal-motivation + external-motivation - bribes) ] update-participation update-global-participation-rate bribe-height-chooser if count nodes = num-nodes [ set random-group n-of (num-nodes * percentage-receiving-bribes) nodes] ask nodes [update-look-of-nodes]

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reset-ticks end ; ///// NETWORK CREATION procedures for various topologies (graphs) ; ===== RING graph ; wire nodes into a ring by asking each node to link to ; the next node. use modulo function so that the last node ; wires to the first node to wire-ring create-new-nodes num-nodes ask nodes [ create-edge-with node ( (who + 1) mod (count nodes) ) ] ring-layout calc-stats end ; ===== RANDOM graph ; wire nodes into a random graph where each pair of nodes ; has an edge between them with proabibility p. ; iterate through every pair of nodes once ; do this by asking each node (in who value order) ; to ask other nodes with who value greater than ; themselves to wire-random [p] create-new-nodes num-nodes foreach sort nodes [ ; iterate through each node (sort by who value) ask nodes with [who > [who] of ?] [ ; the "?" contains the current node of the for loop if prob p [ create-edge-with ? ] ] ] random-layout calc-stats end ; report true with probability p to-report prob [p] report (random-float 1 < p) end ; ===== PREFERENTIAL ATTACHMENT graph ; use preferential attachment to create a scale-free network ; this routine is adapted from the netlogo models library ; based on the Barabási–Albert growth model. ; see: sample models > networks > preferential attatchment to wire-pref-attach create-new-nodes 2 ; create the first two nodes (0 and 1) ask node 0 [ create-edge-with node 1] ; link them together create-nodes num-nodes - 2 [ create-edge-with [one-of both-ends] of one-of edges ; pref select old node with more links

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set color red set shape "circle" ask nodes [set bribes 0 set internal-motivation random-normal b-mean b-std.dev. set external-motivation -1 set total-motivation (internal-motivation + external-motivation - bribes) ] ] if count nodes = num-nodes [ set random-group n-of (num-nodes * percentage-receiving-bribes) nodes] update-participation update-global-participation-rate bribe-height-chooser radial-layout ask nodes [update-look-of-nodes] calc-stats end ; ===== STAR graph to wire-star create-new-nodes num-nodes ask node 0 [create-edges-with other nodes] ; node 0 is central in radial layout radial-layout calc-stats end ; ===== TREE graph to wire-tree clear-all ask patches [ set pcolor white ] create-nodes 1 [ ; create root node of tree set shape "circle" set color red set branch 0 expand-network rewire-branches ] ask nodes [set bribes 0 set internal-motivation random-normal b-mean b-std.dev. set external-motivation -1 set total-motivation (internal-motivation + external-motivation - bribes) ] update-participation update-global-participation-rate bribe-height-chooser set random-group n-of (num-nodes * percentage-receiving-bribes) nodes ask nodes [update-look-of-nodes] radial-layout calc-stats reset-ticks end to expand-network

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if expansion-rate = 0 [ stop ] while [count nodes < num-nodes] [ ask nodes with-max [branch] [ hatch min list (num-nodes - count nodes) expansion-rate [ create-edge-with myself set branch branch + 1 ] ] ] end to rewire-branches ask nodes [ ask nodes with [ who > [who] of myself and branch = [branch] of myself] [ if random-float 1.0 < wiring-prob [ create-edge-with myself ] ] ] end ; ===== SMALL-WORLD graph ; Wires a small-world network using a variation of the Watts-Strogatz method ; Here edges are rewired in random order rather than sequentially ; A similar version can be found in the netlogo models library: ; sample models > networks > small worlds to wire-small-world [k p] wire-lattice-1D k ; create 1D lattice with k links per node ask edges [ ; ask all existing (old) edges if prob p [ ; with probability p (rewire) let snode end1 ; we wish to rewire the forward (clockwise) end of the link ; make sure snode contains the start node (deal with looping on the ring) if (([who] of end2) - ([who] of end1)) > k / 2 [ set snode end2 ] ; link snode to a random node that it is not already linked to ask snode [ create-edge-with one-of other nodes with [ not edge-neighbor? myself] ] die ; remove the old edge ] ] ring-layout calc-stats end ; wire nodes into a 1D lattice with each node having k ; links to neighbours (k/2 either side). ; when k = 2 then this is the same as a the simple ring ; implemented in the "wire-ring" procedure to wire-lattice-1D [k]

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if k > num-nodes / 2 [set num-nodes k * 2] ; ensure a min of k * 2 nodes create-new-nodes num-nodes ask nodes [ let c floor (k / 2) ; create k/2 forward links while [c > 0] [ ; iterate for forward links create-edge-with node ( (who + c) mod (num-nodes) ) ; connect set c c - 1 ] ] end ; ==== 2D LATTICE graph ; wire nodes into a 2D lattice with four neighbours (north, sound, east, west) ; nodes on the boundary have less neighbours to wire-lattice-2D [width height] create-new-nodes (width * height) ; wire a node to it's neighbours ask nodes [ if (who + 1) mod width != 0 [create-edge-with node (who + 1)] ; east if who mod width != 0 [create-edge-with node (who - 1)] ; west if (who + width) < count nodes [create-edge-with node (who + width)] ; north if (who - width) >= 0 [create-edge-with node (who - width)] ; south ] grid-layout width height calc-stats end ; ===== Village graph to village clear-all setup-clusters cluster-layout reset-ticks end to setup-clusters create-new-nodes (num-nodes / clique-size) ask nodes [set leader 1] ring-layout ask nodes [set groupid groupid + who] while [count nodes < num-nodes] [ ask nodes with [leader = 1] [ hatch min list 1 (num-nodes - count nodes) [set group-membership groupid] ] ] set random-group n-of (num-nodes * percentage-receiving-bribes) nodes wire-clusters wire-villages end to cluster-layout ask nodes with [group-membership = groupid] [ rt random 360

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lt random 360 fd 3 ] end to wire-clusters ask nodes [ ask nodes with [ who > [who] of myself and groupid = [groupid] of myself] [ create-edge-with myself ] ] end to wire-villages ask nodes [ ask nodes with [ who > [who] of myself and groupid != [groupid] of myself] [ if random-float 1.0 < (far-probability * 2) [ create-edge-with myself ] ] ] end ; ///// LAYOUT PROCEDURES - layout and display related procedures ; do a spring layout to spring-layout repeat 1 [layout-spring nodes edges tautness spring-len repulsion] end ; do a radia layout with node 0 as the root to radial-layout layout-radial nodes edges (node 0) end ; do sorted ring layout to ring-layout layout-circle (sort nodes) max-pxcor - 2 end ; do random layout to random-layout ask nodes [setxy random-xcor random-ycor] end ; do grid layout ; layout in a grid in the "who" (node ID) order to grid-layout [width height] let xinc (world-width / width) let yinc (world-height / height) ask nodes [ set xcor (xinc / 2 ) + min-pxcor + ( who mod width ) * xinc set ycor (yinc / 2 ) + min-pycor + ( floor (who / width) ) * yinc ] end

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; display selected node labels to label-nodes ask nodes [set label ""] ; clear label if node-label = "ID number" [ask nodes [set label who]] if node-label = "local C" [ask nodes [set label precision local-clustering-coeff 2]] if node-label = "local K" [ask nodes [set label count edge-neighbors]] if node-label = "L from node 0" [ if is-list? [distance-from-other-turtles] of node 0 [ ;; check list has been initialised ask nodes [set label first distance-from-other-turtles]] ; first item in list is L to node 0 ] if node-label = "mean L from all" [ if is-list? [distance-from-other-turtles] of node 0 [ ;; check list has been initialised ask nodes [set label precision (mean distance-from-other-turtles) 2]] ; mean of items gives average L ] end ; ///// MAIN PROCEDURE procedures in the iteration process of the model to go handout-bribes include-lpr update-motivation update-participation update-global-participation-rate ask nodes [update-look-of-nodes] tick if stop-ticking? [stop] end ;;; Bribes are handed out either to the top N nodes with the most positive motivation, the top N nodes with the most ties, or randomly to handout-bribes if strategy-of-dictator = "targeted-opinion" [ ask max-n-of (num-nodes * percentage-receiving-bribes) nodes [( - total-motivation) ] [set bribes (bribes + height-of-bribes)]] if strategy-of-dictator = "targeted-ties" [ ask max-n-of (num-nodes * percentage-receiving-bribes) nodes [count my-links] [set bribes (bribes + height-of-bribes)]] if strategy-of-dictator = "random" [ ask random-group [set bribes (bribes + height-of-bribes)]] end ;;update motivations to include bribes to update-motivation ask nodes [ set total-motivation (internal-motivation + external-motivation - bribes)] end ;; Nodes update their 'external motivation' by including the local participation rate. That is, rate of nodes to whom they are connected that have a participation rate > 0.

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to include-lpr ask nodes [ set new-external-motivation (labda * external-motivation - ( 1 - labda ) * ( 1 - lpr)) set external-motivation new-external-motivation] end to update-participation ask nodes [ifelse total-motivation > 0 [set participation 1] [set participation 0] ] end ;; calculate local participation rate to-report lpr ifelse count link-neighbors > 0 [report ( (sum [participation] of link-neighbors) / (count link-neighbors) )] [report 0] end to update-look-of-nodes ifelse participation = 1 [set color red] [set color yellow] end to update-global-participation-rate let old-global-participation-rate global-participation-rate ;store old value set global-participation-rate ((count turtles with [participation = 1]) / (count turtles)) ;get new value ;increment or reset counter; set count-global-participation-rate ifelse-value (global-participation-rate != old-global-participation-rate) [1] [1 + count-global-participation-rate] end to-report stop-ticking? ifelse count-global-participation-rate >= 50 [report true] [report false] end ;;;;;;;;;;;;;;;CHOOSERS;;;;;;;;;;;;;;; to bribe-height-chooser if bribe-height = "low" [ set height-of-bribes 0.1] if bribe-height = "med"[ set height-of-bribes 0.5] if bribe-height = "high" [ set height-of-bribes 1] end