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Of Social Networks and Popular Rebellion
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ten periods. This removal limit is governed by a single parameter, and all the results in this section vary this parameter from 0 to 25, using a base population of 500
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.
While I could assign removal an additional psychological effect, and will explore
this in future work, for simplicity I choose to rely upon the impact already present by virtue of the behavioral assumptions of the base model. This is not inconsiderable, and in fact contains both a direct and an indirect effect. The direct one is the simple act of removal, which immediately lessens the percentage of people in rebellion. The indirect one involves learning: removing someone with ties means that those linked to her are less likely to rebel in the future. While the direct mechanism should act equally across network types, since in each case one or more people are removed, the indirect mechanism should not. A well-known example of this is the weakness of scale-free networks—internet hubs, for example—to targeted attack (Strogatz 2001). If a few hubs are taken down, the network could fail. However, if random nodes are targeted instead, the network is fairly stable.
This leads into a final specification. While an oppressive state clearly desires to
remove as many rebellious citizens as possible, nothing has yet been said about its skill at doing so. Assuming that only the rebellious are at risk of being removed
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, a completely
inefficient government might remove citizens at random, while a maximally efficient state—working from our earlier results—would remove those with a greater number of links first. Because it is likely that this choice matters for the rebellion dynamic, I try each extreme case, under the logic that middling techniques would result in outcomes somewhere between the extremes.
There are thus two questions to explore in this section: how much does removal
decrease the amount of rebellion, and how does removal differ among different forms of society? To answer these, I present a series of plots, each containing a direct comparison of removal under each regime—random and targeted—across a range of removal values for each of the network types. Whenever possible I have chosen parameters that yield equal mean connectivity; the sole exception to this is the scale-free network, in which I chose parameters so as to have a maximal level of rebellion. A limit of zero, corresponding to no removal, has been included in each graph as a baseline, to account for the increased population—and its greater level of rebellion—used in this section.
Most runs eventually equilibrate to zero rebellion, implying that the state will
squash any unrest given sufficient time, and making the equilibrium value of rebellion a poor measure. Since what we want to know, given the bimodal nature of the model’s outcomes, is whether that zero occurred after relative peace or only after substantial unrest, I choose instead to use the maximum level of rebellion achieved during the thousand-period run as a summary statistic, though the total number of citizens removed would work just as well. Results
7
Removal happens every ten periods rather than continuously so as to probe the limit parameter more
sensitively. This is necessitated by the inability of the state to remove partial people. Removing people stochastically is one way to get around this, at the cost of additional parameterization; this tack was taken in an earlier version of this model.
8
This assumption is easily removed, and presents an avenue for further study.
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ten periods. This removal limit is governed by a single parameter, and all the results in
this section vary this parameter from 0 to 25, using a base population of 500
While I could assign removal an additional psychological effect, and will explore
this in future work, for simplicity I choose to rely upon the impact already present by
virtue of the behavioral assumptions of the base model. This is not inconsiderable, and in
fact contains both a direct and an indirect effect. The direct one is the simple act of
removal, which immediately lessens the percentage of people in rebellion. The indirect
one involves learning: removing someone with ties means that those linked to her are less
likely to rebel in the future. While the direct mechanism should act equally across
network types, since in each case one or more people are removed, the indirect
mechanism should not. A well-known example of this is the weakness of scale-free
networks—internet hubs, for example—to targeted attack (Strogatz 2001). If a few hubs
are taken down, the network could fail. However, if random nodes are targeted instead,
the network is fairly stable.
This leads into a final specification. While an oppressive state clearly desires to
remove as many rebellious citizens as possible, nothing has yet been said about its skill at
doing so. Assuming that only the rebellious are at risk of being removed
inefficient government might remove citizens at random, while a maximally efficient
state—working from our earlier results—would remove those with a greater number of
links first. Because it is likely that this choice matters for the rebellion dynamic, I try
each extreme case, under the logic that middling techniques would result in outcomes
somewhere between the extremes.
There are thus two questions to explore in this section: how much does removal
decrease the amount of rebellion, and how does removal differ among different forms of
society? To answer these, I present a series of plots, each containing a direct comparison
of removal under each regime—random and targeted—across a range of removal values
for each of the network types. Whenever possible I have chosen parameters that yield
equal mean connectivity; the sole exception to this is the scale-free network, in which I
chose parameters so as to have a maximal level of rebellion. A limit of zero,
corresponding to no removal, has been included in each graph as a baseline, to account
for the increased population—and its greater level of rebellion—used in this section.
Most runs eventually equilibrate to zero rebellion, implying that the state will
squash any unrest given sufficient time, and making the equilibrium value of rebellion a
poor measure. Since what we want to know, given the bimodal nature of the model’s
outcomes, is whether that zero occurred after relative peace or only after substantial
unrest, I choose instead to use the maximum level of rebellion achieved during the
thousand-period run as a summary statistic, though the total number of citizens removed
would work just as well.
Results
7
Removal happens every ten periods rather than continuously so as to probe the limit parameter more
sensitively. This is necessitated by the inability of the state to remove partial people. Removing people
stochastically is one way to get around this, at the cost of additional parameterization; this tack was taken in
an earlier version of this model.
8
This assumption is easily removed, and presents an avenue for further study.
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