Communication Technology and Protest∗
Andrew T. Little†
February 2014
Draft version, comments greatly appreciated
Abstract
Recent anti-regime protests throughout the world have been publicized, and arguably facilitated, by social media and other communication technologies. I present
a game-theoretic argument that examines how communication technology generates
information about two distinct factors: (1) the level of dissatisfaction with the regime,
and (2) logistical information about when, where, and how potential protests will occur. Making grievances against the regime more public has an ambiguous effect on
protest levels as citizens can learn it is more or less popular than expected. Even
when making complaints against the regime easier does increase average protest levels, much of the observed correlation between anti-regime content and protest is not
causal. In contrast, providing information about logistics almost always lowers the
effective cost of protest, leading to more (and potentially more cohesive) anti-regime
action. The model is consistent with a wide range of stylized facts as well as more
systematic empirical analyses of communication technology, protest, and censorship.
∗
A previous version of this paper was presented at the 2013 European Political Science Association meeting. Many thanks to audience members and Dominik Duell for comments.
†
Department of Government, Cornell University. andrew.little@cornell.edu.
Nearly every revolution or large scale protest over the past decade has been accompanied by a spirited debate both within and outside academia over the role of the latest
communication technology. The most recent iteration of this argument, inspired by the
Arab Spring, the Occupy movement, and massive protests in Russia, Turkey, and Ukraine
(among others), has largely focused on social media such as Twitter and Facebook (e.g.,
Aday et al., 2010, 2012; Shirky, 2011; Reuter and Szakonyi, 2013; Hale, 2013). More broadly,
these debates speak to the question of how improved technologies of communication –
from the printing press to radio to the internet – make anti-regime action against autocrats or political action in general more likely (Tarrow, 1994; Farrell, 2012; Bennett and
Segerberg, 2013).
Strong intuitions underlie the idea that communication technology helps facilitate political action. During the Arab Spring, use of social media was so prominent that countless commentators dubbed the events some permutation of “The Twitter/Facebook Uprisings/Protests/Revolutions” (Shirky, 2011; Farrell, 2012). Examples abound of participants
in the revolutions crediting social media, such as an Egyptian activist’s description of the
strategy to “use Facebook to schedule the protests, Twitter to coordinate, and YouTube to
tell the world” (quoted in Howard, 2011).
Others have argued that social media gets more attention from Western observers than
actual participants (Aday et al., 2012; Starbird and Palen, 2012),1 that the emphasis on
the spread of information over social media distracts attention away from those who take
the more risky action of actually taking to the streets (Morozov, 2009; Comunello and
Anzera, 2012), or that the spike in anti-regime content during protests simply reflects the
underlying discontent with the regime that is the true cause of mobilization (Shirky, 2011).
1
Starbird and Palen (2012) find that 30% of the most-retweeted accounts during the height of the Tahrir
Square protests originated in Cairo.
1
Further, better communication technology may be more effective as a tool for regimes to
monitor, influence, or control their citizens than the other way around (Morozov, 2009;
Aday et al., 2010; Gehlbach and Sonin, 2012; Shadmehr and Bernhardt, 2013; Warren, 2013).
The question of whether social media and other technology helps overthrow or bolster unsavory regimes has major practical implications. If new technologies do help fight
repressive regimes, they (for good or ill) provide an opportunity for international actors
– whether governments, companies, advocacy groups, or even individuals – to influence
the politics of the kinds of closed regimes that are hardest to affect through other means.
This paper uses a series of formal models to provide insight into the role of communication technology in organizing political action. I argue that citizens considering antiregime action are faced with two inter-related but distinct coordination problems that are
heavily affected by uncertainty. First, citizens must decide whether to take anti-regime action in the first place without knowing how many others dislike the regime enough to join.
I call this coordinating on action. Second, conditional on participating, citizens must decide
when, where, and how to protest against the regime; again, with uncertainty about what
tactics their fellow protesters will select. I call this coordinating on tactics. Communication
technology can provide information about both whether other citizens dislike the regime
and what tactics protesters will choose.
Formalizing this distinction generates the following results. First, making it easier to
air grievances against the regime with better communication technology has an ambiguous effect protest levels. This is because better information must sometimes reveal the
regime is more popular than expected, though most international focus will be on the
attention-grabbing cases where protests are spurred by revelation of the regime’s unpopularity. Further, much of the observed association between anti-regime content and protest
levels is not causal but merely reflects the fact that citizens are willing to protest independent of the fact that their grievances are publicized broadly.
2
In contrast, with only a minor exception communication technology has a positive
causal effect of mobilization through increasing information about protest tactics. Generating this public information is also a particularly good way to increase protest size, as
it can make protests more cohesive by inducing participants choose tactics more in line
with others.
In sum, the main theoretical contributions of the paper are (1) highlighting the conceptual distinction between coordinating on action versus coordination on tactics, and (2)
demonstrating that better tactical information has a more straightforward positive effect
on political mobilization than better information about the level of dissatisfaction with the
regime. The model’s predictions are also consistent with a wide range of empirical findings linking communication technology, anti-regime beliefs and action, and censorship
(Kern and Hainmueller, 2009; Pierskalla and Hollenbach, 2013; King, Pan and Roberts,
2013a,b; Reuter and Szakonyi, 2013), which are discussed in more detail below.
1
Extant Work
There are many potential links between social media and protest, let alone commu-
nication technology and contentious politics more generally (Tarrow, 1994; Aday et al.,
2010; Comunello and Anzera, 2012; Farrell, 2012; Bennett and Segerberg, 2013).2 To use
the classification of Aday et al. (2010), the models here directly examine how communication technology affects political behavior through individual transformation (in particular,
learning information about the regime), intergroup relations, and collective action, and
also provide informal insights into the effects on regime policies (i.e., censorship, monitoring citizens) and external attention.
Perhaps the most common argument about this relationship is that better communica2
Others have used social media to analyze conflict dynamics (Zeitzoff, 2011), polarization or ideological
networks (Barberá and Rivero, 2012).
3
tion technology facilitates protest by helping publicize grievances agains the government
and coordinate anti-regime actions; forcefully articulated in Rupert Murdoch’s claim that
“advances in the technology of telecommunications have proved an unambiguous threat
to totalitarian regimes everywhere.” (quoted in Morozov, 2009). However, as many have
pointed out, this argument is generally made with anecdotes rather than rigorous theory
or systematic data (Aday et al., 2010, 2012; Comunello and Anzera, 2012). Past writing has
also emphasized two strategic objections to the notion that social media helps facilitative
protest. First, in addition to aiding opposition groups, authoritarian leaders can use social
media to monitor citizens more effectively (Morozov, 2009; Comunello and Anzera, 2012).3
Second, better communication technology may prevent citizens from taking to the streets
to acquire information (Howard et al., 2011; Hassanpour, 2013).
Even those relatively amenable towards the idea that technology and political action
share meaningful links often dither on the question of whether this relationship is causal,
e.g., (Shirky, 2011) warns that “communications tools during the Cold War did not cause
governments to collapse, but they helped the people take power from the state when it was
weak.”4 While theory alone can not tell us when the various relationships between communication technologies and political action are causal, the models here highlight some
issues of causal inference that are particularly difficult when the “treatment” (e.g., better
communication technology) generates information that is observed by both outsiders and
participants in coordinated political action.
The models of coordination under uncertainty draws from large literature on “global
games” (e.g., Carlsson and van Damme, 1993; Morris and Shin, 2003), which have recently
3
For clarity I do not consider censorship or even model the incumbent regime as a strategic actor (see
Shadmehr and Bernhardt, 2011; Gehlbach and Sonin, 2012; Lorentzen, 2013).
4
See also “The major challenge in understanding the relationship between democracy and the Internet—
aside from developing good measures of democratic improvement—has been to distinguish cause and effect” (Morozov, 2009); BBC Correspondent Paul Mason “I don’t say [social media] caused [the Arab Uprisings], any more than the printing press caused the English revolution of the 17th century” (quoted in Else
2012)
4
been applied to a wide variety of political phenomena.5 The argument here brings together two branches of this literature. The first analyzes binary decisions where the actors
either “participate” or do not. The canonical examples of this type of model analyze bank
runs and investment decisions (Morris and Shin, 2001, 2003), and have been applied to
participation in protests and revolutions as well (e.g., Bueno De Mesquita, 2010; Shadmehr and Bernhardt, 2011; Little, 2012; Tyson and Smith, 2013; Hollyer, Rosendorff and
Vreeland, 2013). The second branch analyzes models where the actors make a continuous
choice where they want their actions to be close to others, often called “beauty contests”
(Morris and Shin, 2002; Angeletos and Pavan, 2007). This type of model has seen fewer
applications in political science, with the exception of Dewan and Myatt (2008, 2012), who
analyze policy advocacy within parties. Here I model the interaction between the bankrun-like problem of choosing whether or not to participate in protests (again, coordinating
on action) and the beauty-contest-like problem of choosing how to protest (again, coordinating on tactics) among those who do participate.
In addition to the theoretical contribution on the different ways better information
affects different kinds of coordination problems, the results provide an explanation for
multiple stylized facts as well as more rigorous empirical studies on communication technology, protest, and censorship. The distinction between coordinating on action and coordinating on tactics closely parallels the classification used in (King, Pan and Roberts,
2013a,b), who analyze what types of internet posts are censored in contemporary China.
They find that posts complaining about the regime are not censored, while those related
to information about or calls for collective action are heavily censored. While the for5
The models take as given that better communication technology leads to more information about the
preferences of others. Further I do not examine what kinds of communication technologies and network
structures are best at aggregating information (Galeotti et al., 2010; Calvó-Armengol, De Martı and Prat,
2011; Dahleh et al., 2012). Of course a more micro-founded model where communication is endogenous
could provide additional insight, but for simplicity I focus here on how the different levels of information
affect political action.
5
mal analysis does not explicitly consider the regime’s decision to censor, these results are
consistent with the theoretical findings that better information about the preferred tactics
of others (and, informally, the tactics of ongoing protests) has a stronger and less ambiguously positive impact on protest levels than making it easier to complain about the regime.
Still, the model predicts that censoring grievances against the regime would reduce average protest levels for some sets parameters, highlighting the danger of inferring from the
case of China that this form of censorship is less effective in general.
The theoretical predictions are also consistent with recent findings that cell phone coverage is associated with more violence in Sub-Saharan Africa (Pierskalla and Hollenbach,
2013) and Kern and Hainmueller (2009)’s result that better access to West German television did not lead to more dis-satisfaction with the East German regime. While it may be
intuitive to think that providing more information about life outside a repressive regime
would make citizens less satisfied their government, the models would only predict a such
a relationship if such television portrayed the regime as worse than commonly thought.
On the other hand, (Reuter and Szakonyi, 2013) show that in the wake of the 2011 Russian
Parliamentary elections – plausibly more fraudulent than expected – citizens that actively
used Facebook and Twitter had higher beliefs about the degree of fraud. The general point
highlighted by the model is that the effects if introducing new politically relevant information must always be considered relative to expectations.
The theory also sheds light on the descriptive observation that recent anti-regime movements have been accompanied by spikes in social media activity, and in particular antiregime content (Barberá and Metzger, 2014). However, this observations requires two
caveats. First, when focusing on examples where revolution failed or never started in the
first place, it would generally be the case that new technology either didn’t generate information that the regime was weaker than expected or led citizens to believe the regime
was in fact stronger. Second, some of the correlation that “outsiders” observe between the
6
amount of anti-regime content on social media and the internet and successful protest is
not causal, but confounded by the fact that this kind of content happens when citizens are
willing to take anti-regime action independent of what they learn from the public information. Further, if social media is more visible to outsiders or if participants have better
sources of information than those observed by outsiders, most of the correlation between
what shows up on the internet (among other media) and protest size is not causal.
The rest of the paper proceeds as follows. Section 2 presents a single-actor model that
derives many of the main results in a relatively simple fashion. Sections 3-4 present models
where multiple citizens with heterogenous preferences over the optimal tactics and assessments of the regime decide whether and how to protest, providing richer results about of
how communication technology affects these coordination problems. Section 5 informally
considers some major aspects of communication technology not explicitly modeled in the
formal analysis, and section 6 concludes.
2
Single Actor Model
In the first model, a single citizen first chooses whether to take an anti-regime action
a. This action is binary, where a = 1 means choosing the anti-regime action (e.g., taking
to the streets, joining a rebel movement) and a = 0 means not participating. The model
is meant to describe anti-regime action at a high level of abstraction, capturing any activity that citizens are more apt to participate in when the regime is weak or unpopular
(and, in following section, when other citizens participate as well). Most of the motivating examples involve major revolutionary activity that could lead to the downfall of the
regime, but the formalization could also include protests that partly or primarily aim for
policy changes such as the Occupy movement and recent protests in Spain and Greece
(Theocharis et al., 2013). To strike a balance between generality and concreteness, I gen-
7
erally refer to the anti-regime action as “protesting” and not taking the action as “staying
home.”
If the citizen chooses to protest, she also chooses a tactic t. The tactics are meant to
capture a variety of logistical details, such as when and where to protest, what concessions
to demand, how to respond to the police, etc. Let the tactical decision be a unidimensional
choice on the real line (i.e., t ∈ R).6
The citizen wants to protest against a weak or unpopular regime but not a strong
regime. Let ω ∈ R denote the level of dissatisfaction with the regime (or anti-regime sentiment), and the payoff to protesting with tactic t be
u1 (t) = ω − k(t − θ)2 .
The payoff to protest is increasing in ω, capturing the idea that the citizen is more apt to
protest against a “bad” regime, or because she expects the protests to be larger if others join
(as will happen in the model in section 4). The θ parameter reflects the “average” tactics
chosen by other protesters. That is, the cost of protest is increasing in distance between
the citizen’s choice t and the actions taken by others.7 The k ≥ 0 term scales the general
costliness of protest. Normalize the payoff for staying home to 0.
The citizen is uncertain about the amount of dissatisfaction with the regime (ω) and the
tactics chosen by others (θ). Let the prior belief about ω be normally distributed with mean
µω and precision α0 (i.e., variance 1/α0 ). Similarly, the prior on the tactics θ is normally
distributed with a mean normalized to 0 and precision β0 . (In general, precisions related
to the anti-regime sentiment will be denoted with α terms and precisions related to the
tactics with β terms.)
6
The analysis trivially extends to the multi-dimensional case, albeit with more notation.
The fact that the cost of protest can be zero does not affect any of the qualitative patterns described, and
the expected cost of protest will always be strictly positive.
7
8
Before taking her action, the citizen observes a noisy signal of both parameters of uncertainty. The signal of the tactics is given by:
st = θ + θ ,
where θ is normally distributed with mean 0 and precision βs . When interpreting the
model, I assume that one effect of better communication technology is increasing βs , i.e.,
giving the citizen more information about how others will protest. As several models
examine the how technology and networks affect communication and information aggregation in related models (e.g., Galeotti et al., 2010; Calvó-Armengol, De Martı and Prat,
2011; Dahleh et al., 2012) I do not provide a microfoundation for this assumption here.8
The signal of the regime’s (un)popularity has two components. First, it contains a fraction ρ ∈ (0, 1) of the anti-regime sentiment, which can be loosely interpreted as the proportion of grievances against the regime that are publicized.9 Second, there is a noise
term ω that is normally distributed with mean 0 and precision αs . These components are
additive, so the signal is:
sω = ρω + ω .
(1)
Upon observing st and sω , the citizen forms her beliefs about θ and ω via Bayes’ rule
and protests if and only if her expected payoff from protesting when choosing the optimal
tactics is greater than the payoff to staying home, which is again 0.
To solve the model, first consider the optimal tactics should the citizen protest. By
standard Bayesian updating, the citizen’s belief about θ upon observing st is normally
8
See also Reuter and Szakonyi (2013) for empirical evidence that use of certain social networks increased
awareness of electoral fraud in Russia.
9
The “loose” caveat stems from the fact that ω (in addition to sω ) is not precisely the proportion of aggrieved citizens; in fact, to generate clean results it is normally distributed and hence can be negative or
greater than one.
9
distributed with mean and precision:10
µθ = s t
βs
βs + β0
and
β = βs + β0 .
The k(t − θ)2 term is minimized at t = µθ : in words, the citizen chooses the tactic
equal to her average belief about what others will do. Conveniently, the expected value of
(µθ − t)2 is the variance of the belief about θ, which is 1/β. So, the expected cost of protest
when choosing the optimal tactic is k/β.
Determining whether the citizen does in fact protest requires her posterior belief about
the regime’s popularity. How she interprets the signal of anti-regime sentiment sω depends on the proportion of aired grievances ρ.11 A convenient way to represent this mathematically is to divide both sides of equation 1 by ρ, giving:
sω /ρ = ω + ω /ρ.
That is, sω /ρ represents the signal of regime grievances adjusted for the ease of complaining, which is an unbiased estimate of the anti-regime sentiment. When making this
normalization the noise term is divided by ρ as well. So, when ρ is high – corresponding
to a higher information environment – the citizen will be able to form a more precise belief
about the anti-regime sentiment. Formally, her posterior belief about the ω after observing
sω is normally distributed with mean:
µω (sω ) = λµω + (1 − λ)(sω /ρ),
(2)
10
Many derivations throughout the paper utilize the fact that if x is normally distributed with mean µx
and precision τx , and s = x + where is normally distributed with mean 0 and precision τ , the conditional
+τ s
belief about x given s is normal with mean τxτµxx+τ
11
If ω < 0, she will observe a more negative signal, which could be interpreted as more people voicing
support for the regime.
10
where λ =
α0
,
α0 +ρ2 αs
and precision α0 + ρ2 αs . This posterior belief will be greater than the
prior (µω ) if and only if sω /ρ > µω . In words, a higher proportion of aired grievances
(higher ρ) means the citizen must observe a higher signal to believe the regime is less
popular than previously thought.
Combining the information given by the signals sω and sx , the citizen protests if and
only if:
µω (sω ) ≥ k/β.
(3)
The LHS if this equation is linearly increasing in sω , so:
Proposition 1. The citizen protests if and only if the signal of grievances sω is sufficiently high.
Proof Combining equations 2-3 gives the citizen protests if and only if:
sω >
α0 (k/β − µω )
+ ρk/β ≡ ŝω
ραs
One interpretation of this result is that when fixing the communication technology
(i.e., ρ), the citizen is always more apt to take to the streets when she sees more anti-regime
information. So, in this sense, a high level of anti-regime content on social media unambiguously increases the level of anti-regime activity.
However, this does not answer the question of whether making it easier to air grievances
against the government (higher ρ) or a learning more about the tactics used by others
(higher βs ) makes anti-regime action ex ante more likely. This probability is given by
−2
αs ρ
P r(µω (sω ) > k/β), which is normally distributed with mean µω and precision (1−λ)−2 αα00+α
−2 ≡
sρ
11
τµ .12 So, we can write the probability of protest as:
P r(µω (sω ) ≥ k/β) = Φ(τµ1/2 (µω − k/β)),
where Φ(·) is the cumulative density function of a standard normal random variable. The
result about the precision of the tactical signal is straightforward: by giving a more accurate sense of how others will protest, the effective cost of participation is lower and hence
protest is more likely:
Proposition 2. The probability of protest is increasing in the prior precision on the average tactic
(β0 ) and and the precision of the tactical signal (βs ).
Proof Equation 3 implies that the probability of protest is decreasing in k/β. Since β =
β0 + βs , the probability of protest is increasing in both of these terms.
Note that the likelihood of protest is increasing in both the prior precision of where
the protest will be as well as the precision of the signal about where protest would be.13 A
precise prior on the location of protest could be driven by a history of past protest or having
an obvious location – say a public square (Patel, 2013) – or time – say, after friday evening
prayers – that is commonly know to have “prominence and conspicuousness” (Schelling,
1960, pg. 57). This prior precision could reflect information about tactics that succeeded
recently in similar countries, which Patel and Bunce (2012) argue played a central role in
the spread of the Arab Spring.
As alluded above, the precision of the location signal βs could be increased by improved communication technology such as social media, the internet, or cell phones. This
12
This and later derivations are a consequence of the the fact that if x = y + z where y is normally distributed with mean µy and precision τy and z is normally distributed with mean µz and precision τz , then
τz
the unconditional distribution of x is normally distributed with mean µx + µy and precision ττxx+τ
z
13
As shown in section 3, when the actions of others are taken into account (and with a more general
utility function) the analogous result requires caveats. These will be discussed further in the exposition of
that model and the discussion.
12
is consistent with the results in Pierskalla and Hollenbach (2013), albeit through a somewhat different mechanism than what this paper emphasizes. By reducing the logistical
costs of various types of coordinated anti-regime action, cell phone coverage can make
the effective cost of violent action against the regime lower, and hence such action more
likely.
The effect of increasing the proportion of aired grievances is less straightforward. Differentiating with respect to ρ gives that this expression is increasing in ρ if and only if
µω < k/β. That is:
Proposition 3. The probability of anti-regime action is increasing in the ease of airing grievances
(ρ) if and only if the prior on the anti-regime sentiment is less than the expected cost of protest
(µω < k/β).
Proof See the appendix.
To see the intuition behind this result, consider the limiting case as ρ → 0, in which case
the signal is pure noise. If this is true, the citizen posterior belief about the anti-regime
sentiment is always equal to µω , and hence she always protests if µω > k/β and never
protests if µω < k/β. So making the signal informative can only make protest more likely
if µω < k/β and can only make protest less likely if µω > k/β.
Figure 2 illustrates propositions 2 and 3. Both curves trace the probability of protest as
a function of how precise the tactical signal is for a case where the ability to air grievances
against the regime is relatively low (grey curve) and high (black curve). For both curves,
increasing the citizens’ knowledge of the tactics used by others – i.e., increasing the quality
of the tactical signal – leads to a higher probability of protest.
The difference between the two curves illustrates the more nuanced relationship between the ease of airing grievances about the regime and the probability of protest. When
the prior probability of protest is low – rearranging the inequality in proposition 3, βs <
13
0.5
High ρ
Low ρ
0.0
Probability of Protest
1.0
Figure 1: Probability of protest with poor communication technology (ρ = 1/2, black
curve) and better communication technology (ρ = 1, grey curve) as a function of the precision of the tactical signal (βs ) for k = µω = α0 = αs = 1 and β0 = 1/2. Protest is more
likely with better information about tactics, and is more likely with better communication
technology when protest is unlikely to happen in general.
0
k µω − β0
Precision of Tactical Signal (βs)
k/µω − β0 – there is a higher probability of protest when airing grievances against the
regime is easier (higher ρ, represented by the gray curve). However, when the tactical signal is more precise and protest is generally likely, improving the ability to air grievances
lowers the probability of protest.
The final formal result in this section links the communication technology to the difference between the true regime popularity and the prior mean. To see this, write the
difference between the true anti-regime sentiment and the prior as:
νω = ω − µ ω ,
which by the distributional assumptions made above is normally distributed with mean 0
and precision α0 . When νω is positive, the regime is less popular than expected and better
14
communication technology will help reveal this:
Proposition 4. The relationship between the communication technology and the probability of
protest is positive when the regime is sufficiently less popular than indicated by the prior and negative when the regime is sufficiently more popular than in the prior.
Proof See the appendix.
Regimes that are weaker than is commonly known are hurt by improved communication technology, as this makes their weakness more widely known. So, when we restrict
attention to cases where protest was successful – where regimes generally are weaker than
was known – it will generally be true that better communication technology increased the
protest sizes.14
However, this can not always be the case: in fact, by construction it is ex ante unknowable whether the regime is more or less popular than expected. Sometimes the regime is
more popular than is commonly known, in which case better communication technology
will make protest less likely. Outside observers are tempted to focus on the cases where
new technology is flushed with anti-regime (and, in some contexts, progressive and liberal) content, but should they “dig a bit deeper, they might find ample material to run
articles with headlines like ‘Iranian bloggers: major challenge to democratic change’ and
‘Saudi Arabia: bloggers hate women’s rights” (Morozov, 2009). This indeterminacy provides a potential explanation of why Kern and Hainmueller (2009) do not find that exposure to Western German television made Eastern German’s more pessimistic about their
own regime, but Reuter and Szakonyi (2013) do find that some forms of social media use
are associated with higher beliefs about the amount of fraud in recent Russian elections.
14
This selection effect can extend to more systematic studies: e.g., (Yanagizawa-Drott, 2012) finds that
radio broadcasts may have increased the intensity of the Rwandan genocide, but we should not infer from
this that radio connectivity spurs conflict in general, as the broadcasts in question were about as extremely
pro-violence as one can imagine.
15
Censorship
While the model does not treat the regime as a strategic actor, it does provide insight
into when regimes would prefer to restrict different types of information. Recall the two
variables interpreted as measuring the effectiveness of communication technology are ρ –
which is the ease of expressing anti-regime beliefs – and βs – which captures the amount
of public information about protest tactics. All things equal, regimes that do not want to
face protest would always want to reduce βs , but only regimes that face an ex ante low
chance of protest would want to decrease ρ. In principal, regimes should be able to affect
these parameters separately.
This distinction is consistent with the main empirical findings in King, Pan and Roberts
(2013a,b), who find that China aggressively censors references to planned or ongoing collective action, which is best interpreted as decreasing βs , but does not censor complaints
about the regime, which would correspond to reducing ρ. However, the model also warns
against extrapolating from the contemporary Chinese case to general theories of what
types of communication will be censored. For regimes in a different part of the parameter space, reducing the ability for citizens to air grievances could make citizens less apt
to protest. In addition, censoring complaints against the regime can have effects outside
of those modeled here, such as signaling the ability to do so (Huang and Li, 2013) are
gathering information about the performance of local officials (Lorentzen, 2013).
3
Coordination on Tactics
While the model in the previous section highlights many of the central arguments of
the paper, the focus on a single actor means it can not directly address how public information affects coordination among citizens. To address this, the following two sections
contain models where a large number citizens decide whether and how to protest. Do16
ing so demonstrates that the conclusions from the single-actor model only require minor
caveats when endogenizing coordination and also generates additional results.
In this section I assume citizens share a common belief about the anti-regime sentiment
(ω), but are heterogenous both in their preferred tactical choice and their knowledge about
the preferred tactics of others. The game is now played among a continuum of citizens
mass 1, indexed by i. Each citizen observes a private signal which is also her ideal or
“preferred” tactic xi , given by:
xi = θ + νi ,
where each νi is normally distributed with mean 0 and precision βx . The θ parameter now
represents the average preferred tactic, and νi whether citizen i prefers a “higher” (e.g.,
later in the day, at a location further north, demanding more from the government) protest
strategy than average. As in the single actor model, citizens share a common prior on θ
that this is normally distributed with mean normalized to 0 and precision β0 .
Also as before, the citizens observe a common (or public) signal of θ given by:
st = θ + s ,
where s is normally distributed with mean 0 and precision βs , which again measures the
quality of communication technology. Assume that θ, and the noise terms (s , and the νi ’s)
are independent.
Let the payoff to protesting and choosing tactic ti be
u1 (ti ; xi ) = ω + f (A, R) − k[r(ti − xi )2 − (1 − r)(ti − θ)2 ]
(4)
and normalize the payoff to staying home to 0. The benefit to protest is a increasing in the
17
anti-regime sentiment ω, and also potentially a function of the size of the protest A and
the range of the tactics chosen by protesters R (as defined below). The k term scales the
general cost of protesting, which is comprised of two components. First protesting citizens pay a cost that is increasing in the distance between their chosen tactic and preferred
tactic. Second, they pay a cost that is increasing in the distance between their chosen tactic and the average preferred tactic, which captures the idea that citizens want to choose a
similar tactic as others.15 The r ∈ (0, 1) parameter scales the relative importance of the two
components of the cost: i.e., when r is small, citizens care more about this coordination
motive, and when r is large citizens put more weight on their own preferred tactic.
Citizens observe s and xi , and then choose whether or not to protest, followed by the
protesters choosing their preferred tactic. I solve for Perfect Bayesian equilibria that are
symmetric in the sense that all citizens use the same strategy, and in a stronger sense
elaborated below.
To develop intuitions I first analyze the case where f (A, R) = 0, and then consider how
citizens beliefs about the expected size and cohesion of the protest affect their decision
when these factors affect the payoff to participation.
Regardless of the strategies of others, the optimal protest tactic for citizen i (if joining) is
a weighted average of her preferred tactic and her expectation about the average preferred
tactic of others: t∗i = rxi + (1 − r)E[θ|s, xi ]. Plugging this into the cost term and simplifying
15
It would be more natural to make this component the difference between the chosen tactic and the actual
average tactic chosen by protesters. This formulation is tractable in models like Morris and Shin (2002),
Angeletos and Pavan (2007) and Dewan and Myatt (2008, 2012), since the expectation of the preferred tactic
of others is linear in xi , and hence if all others use strategy that is linear in xj , the best response for citizen
i is to use a linear strategy as well. Unfortunately, if not all citizens participate, the average preferred tactic
of other participants is not linear in xi , so there is no linear equilibrium. Analyzing such a model could
prove interesting, but as it would require a substantially more complex solution I use the more tractable
formulation here.
18
gives the expected payoff of protesting is:
E[u1 (t∗i ; xi )] = E[ω] − k(1 − r) (β0 + βs + βx )−1 + r(xi − E[θ|s, xi ])2 .
(5)
As I assume in this section that all citizens share the same belief about the anti-regime
sentiment, all that matters for the protest decision is the expectation of this variable E[ω].
One component of the expected cost – the (β0 + βs + βx )−1 term – is the variance of the
citizen’s belief about θ upon observing the public signal and her own tactic. As above, this
term is decreasing in the amount of information the citizen has about θ, reflecting the fact
that more information – including from the public signal – helps make a better informed
tactical choice.
However the citizen also cares about choosing a tactic that is close to her own ideal.
When making the optimal choice, this is captured by the (xi − E[θ|s, xi ])2 term, i.e., is
the squared distance between citizen i’s ideal tactic and her expectation of the average
preferred tactic of others. One way to write this term is:
2
(xi − E[θ|st , xi ]) =
where di ≡ |xi −µθ | and µθ ≡
βs s
β0 +βs
β0 + βs
β0 + βs + βx
2
d2i ,
is the public mean belief about the average preferred tac-
tic conditional on the common tactical signal s not the private signal. That is, the expected
cost of protest for citizen i is (1) increasing in the distance between the public average belief about the preferred tactic her ideal tactic, and (2) symmetric in the sense that the cost
is the same for a citizen with ideal tactic µθ − a as a citizen with ideal tactic µθ + a for any
a ≥ 0.
The amount of information citizens have about the preferred tactics of others – including the information gleaned from the public signal – increases this aspect of the cost
to protest. In particular, citizens who have preferred tactics that are far from the pub19
lic mean will be even more certain that true average ideal tactic is far from theirs, which
makes protest less attractive. Combining the two effects described above, increasing the
precision of public information about preferred tactics makes protest more attractive for
those with a preferred tactic close to the public mean while making it less attractive to
those with a more extreme preferred tactic.
Formally, rearranging equation 5 gives that the distribution of the expected benefit to
protest can be written as a − bχi , where:
a = ω − k(1 − r)(β0 + βx + βs )−1 ,
b = kr(1 − r)(β0 + βs )/(βx (β0 + βs + βx )),
and χi is a chi-square random variable with one degree of freedom. So, letting F be the
cdf of this chi-square distribution, the probability that citizen i protest is given by protest
and hence the expected size of protest is given by:
E[A] = P r(a − bχi ≥ 0) = F (a/b).
This generates the following comparative static:
Proposition 5. If f (A, R) = 0, then the expected size of protest is increasing in the precision of
the tactical signal (βs ) if and only if E[A] < F (1/r).
Proof See the appendix.
That is, the effect of increasing the amount of public information about the preferred
tactics of others depends on the expected size of protest. Figure 3 illustrates the result.
When the cost of protest is low (top curve), nearly all citizens participate, and increasing the level of public information about tactics slightly decreases the amount of protest.
20
Expected Level of Protest
F(1 r) 1
0
Figure 2: The expected size of protest as a function of the precision of the tactical signal
for low (bottom curve), medium (middle curve), and high (top curve) costs of protest. For
all curves, µ0 = 0, β0 = 1, βx = 1, r = .5, E[ω] = .5, and the costs of protest are 0.8, 1.5, and
2.
Low Cost
Medium Cost
High Cost
0
1
2
3
Precision of tactical Signal (βs)
4
5
However, as long as the cost of protest (and other parameters) are such that the expected
protest size is less than F (1/r), increasing the precision of public information about tactics
leads to more protest. When the cost of protest is high, this effect can be dramatic: as the
bottom curve shows, there is nearly no protest when the public signal is uninformative,
but rapidly increases as citizens learn more about the tactics of otters
The intuition be behind this result is that increasing the amount of public information has two effects. First, increasing βs makes all citizens more certain about θ, which
lowers the expected cost of participation. This is particularly beneficial for citizens with
a preferred tactic close to the public mean, as they become more certain that the average
preferred tactic is close to their own. However, citizens with relatively extreme preferred
tactics become even more confident that their preferred tactic is unusual when βs is high,
which makes participation less attractive. So, when the expected level of protest is small,
21
the marginal citizen indifferent between protesting or not is one with a preferred tactic
that is close to the public mean belief (µx ), and hence increasing βs leads to more protest.
However, when the protest is large enough that the only citizens not participating are
those with very extreme private signals, increasing βs will decrease the level of protest.
Surprisingly, the critical level of protest that determines whether more public information helps or hurts protest has a simple form: the cumulative density function of a
chi-square random variable with one degree of freedom evaluated at 1/r. Since r < 1, a
sufficient condition for the probability of protest to be increasing is E[A] < F (1) ≈ 0.68.
That is, unless over 2/3 of citizens are protesting, better public information leads to more
protest even if citizens place almost no weight on the coordination motive. When citizens
place more weight on coordination this threshold becomes even higher, e.g., if citizens
place an equal weight on their individual and coordination motives, then better public
information makes protest more likely if E[A] < F (2) ≈ 0.84.
This potential negative effect of more public information could be interesting in some
contexts: say, where there are a finite number of actors and the action must be unanimous
to succeed. However, when applied to anti-regime protest – where much lower levels of
participation are required for success – better information about the preferred tactics of
others generally will increase the size of protests.
Further, the analyses of the remainder of this section shows that increasing the size
of protest with better public information is a particularly effective way to do so when the
payoff to protest depends on both it’s size and cohesion.16 To formalize this, now let the
payoff for protesting be:
u1 (ti ; xi ) = ω + vA A − g(R) − k[r(ti − xi )2 − (1 − r)(ti − θ)2 ],
(6)
16
There are many potential incentives to model here: citizens may be more apt to join protests that are
large, cohesive, or choose tactics that are close to the citizen in question’s ideal point or objectively good. As
it proves tractable and generates additional insight, here I model the first two incentives.
22
where vA ≥ 0 and g is a continuous and increasing function with g(0) = 0 and limR→∞ g(R) =
g for some finite g < vA . So a high vA means the protest size has a large impact on the benefit of joining, and the g function captures how much the effectiveness of protest decreases
as citizens choose a less cohesive set of tactics. The g < vA assumption implies that this
effect is never so large that full participation is less effective than no protest, though the
formal analysis only requires that g is finite.
Motivated by the analysis of the cost function, I search for equilibria where citizens
protest if and only if their tactic is sufficiently close to the public mean tactic µx , i.e.,
ˆ It will follow that if all other citizens use such a strat“protest if and only if di < d”.
egy, the best response for citizen i is to select a strategy of this form as well, for now I set
aside the question of whether other equilibria exist.
If all other citizens use this strategy, then the protest size as a function of θ is:
ˆ = P r(µ − dˆ < xj < µ + d)
ˆ = Φ(β 1/2 (µ + dˆ − θ)) − Φ(β 1/2 (µ − dˆ − θ)).
A(θ; d)
θ
θ
θ
θ
x
x
A citizen observing xi ’s belief about θ is normal with mean µθ (xi ) =
βx xi +βs st
β0 +βs +βx
and precision
β0 + βx + βs , so the expected protest level for such a citizen is given by:
βx (µθ − xi )
βx (µθ − xi )
1/2
1/2
ˆ
ˆ
ˆ
+d
− Φ βA
−d
,
E[A|xi ; d] = Φ βA
β0 + βx + βs
β0 + βx + βs
where βA =
βx (β0 +βs +βx )
.
β0 +βs +2βx
By the symmetry of the normal distribution, this expectation,
like the cost function, is symmetric around µθ , and hence can be written as a function of
the distance from the public mean di . Finally, what matters for the equilibrium condition
is the expected protest size for the marginal citizen, given by:
β0 + βs + 2βx
β0 + βs
1/2
1/2
ˆ
ˆ
ˆ
ˆ
E[A|di = d; d] = Φ βA
+ Φ βA
− 1.
d
d
β0 + βx + βs
β0 + βx + βs
23
(Again, see the appendix for a full derivation.)
The derivation of the range term is more straightforward, which is why I use this statistic rather than some transformation of the variance, which requires a much more involved
ˆ µθ + d]
ˆ will protest
calculation. It is common knowledge that citizens between xi ∈ [µθ − d,
and common knowledge what tactic they will select. Substituting the tactic chosen by the
citizens at this endpoint gives the range of tactics as:
(1 − r)βx
R=2 r+
β0 + βs + βx
ˆ
d,
ˆ
which by inspection is increasing in dˆ and decreasing in βs (for a fixed d).
To complete the derivation of the equilibrium condition, recall we can write the cost of
protest for a citizen with di as:
"
K(di ) = k r(1 − r)
β0 + βs
β0 + βs + βx
2
#
d2i + (1 − r)(β0 + βs + βx )−1 .
Summarizing, an equilibrium dˆ solves:
(1 − r)βx
ˆ = 0.
ˆ
ˆ
ˆ
dˆ − K(d)
U (d) ≡ E[ω] + vA E[A|di = d; d] + g 2 r +
β0 + βs + βx
1
(7)
The equilibrium condition has the following properties:
Lemma 6. If (1) E[ω] >
(1−r)
,
β0 +βs +βx
then all equilibria have a positive amount of protest and there
is at least one dˆ > 0 meeting equation 7. Let g 0 < 0 be the minimum slope of g: if (2) vA and −g 0
are sufficiently small, this intersection is unique.
If condition 1 does not hold there is always an equilibrium with no protest, though in
ˆ solving equation 7 and
this case (or if condition 2 does not hold) there maybe multiple d’s
hence multiple equilibria. When this is the case I restrict attention to the equilibrium with
24
the highest level of protest, though later I informally discuss the possibility that communication technology can generate focal points that get citizens to switch to a higher protest
equilibrium.
Similar calculations as those described above give that expected size of protest is:
s
ˆ = 2Φ
E[A] = P r(ai = 1|d)
!
βx (β0 + βs ) ˆ
d − 1.
β0 + βx + βs
ˆ Taking comparative statics:
Which is increasing in d.
Proposition 7. With the citizen utility function given by equation 6, The expected size of protest
is:
i) decreasing in k,
ii) increasing in E[ω], and
iii) increasing in βs if E[A] < F (1/r) (and sometimes increasing even if this does not hold).
Proof See the appendix
Parts i-ii are intuitive: fewer citizens protest when it is costly and more protest when the
regime is more unpopular. Part iii follows from a similar logic outlined above: better
information leads to more protest unless participation is so massive that the marginal
citizen considering joining has extreme tactical preferences.
Similarly, we can take comparative statics on the range of tactics selected by protesters:
Proposition 8. The range of tactics selected by protesters is:
i) decreasing in k,
ii) increasing in E[ω], and
iii) potentially increasing or decreasing in βs
ˆ The indeterProof The first two parts follow directly from the comparative statics on d.
minacy of the comparative static with respect to βs will be shown by example.
25
Size
0
Cohesion
2
4
0.8
Size
Cohesion
0.2
Protest Size/Cohesion
Protest Size/Cohesion
1
Figure 3: Effect of increasing the cost of participation (left panel) and precision of public
information about tacts (right panel) on the size and cohesion of protests.
0
General Costliness of Protest (k)
5
Precision of Tactical Signal (βs)
Combining the first two parts of propositions 7-8 formalizes the size-cohesion tradeoff :
making protest cheaper or increasing the exogenous benefit will make protests larger, but
since the marginal citizen added is always one with relatively extreme tactical preferences
(relative to the “core” protester with exactly xi = µθ ), this will increase the range of tactics and make the protest less cohesive. (Similar results can be derived when measuring
cohesion with the inverse of the variance of chosen tactics or similar measures.)
This tradeoff is illustrated in the left panel of figure 3. As the general cost of protest
(k) increases, the expected size of protest drops and eventually reaches zero. This makes
protest more cohesive – measured by the inverse of the range of tactics chosen – as only
those with preferred tactics very close to µθ participate. Conversely, as the cost of protest
decreases, protests become and less cohesive.
This tradeoff is at least partially mitigated when increasing the size of protests by increasing the precision of public information about the preferred tactics. This is because
26
better public information results in citizens putting a higher weight on the public information when choosing their tactic. So, for a fixed protest size, better information about
how the protest will occur will always make protests more cohesive. This effect may be
outweighed by the fact that a more diverse group of protesters participate, as occurs for
a low range of βs in the right panel of figure 3: as βs increases, the size of protest rapidly
increases and cohesion rapidly drops. However, when there is a high degree of public
information available about the preferred tactics of others – certainly plausible when organizers can broadcast plans across social media and the internet – further increasing this
amount of public information leads to both larger and more cohesive protests. Further,
even if better information means fewer citizens participate, the increase in cohesion may
make the protest more effective.
4
Coordination on Action
The final model abstracts from the issues of tactical coordination above to derive more
results about how better public information about the popularity of the regime (and heterogeneity assessments of the regime) affects protest behavior. As in the previous section,
allowing for citizens to vary in their approval of the regime largely reinforces the conclusions from the single actor model, but also generates more nuanced predictions, in particular about whether the correlation between anti-regime content on social media and
anti-regime activity is causal.
The actors in the model are again a continuum of citizens mass 1, but rather than differing in preferred tactics each citizen is characterized by a personal level of anti-regime
sentiment ωi , which can be written:
ωi = ω + i ,
27
(8)
where ω is the average level of dissatisfaction with the regime and the i ’s are independent
and normally distributed with mean 0 and precision αω . Assume the citizens share a
common prior on the average anti-regime sentiment that is again normally distributed
with mean µω and precision α0 .
To model the level of communication technology, I assume that n ≥ 1 citizen’s signals are commonly observed. This technical structure best captures public communication
technology like television and social media, but not private communication facilitated by
cell phones, email and the like.17
Citizens also observe a common tactical signal:
st = θ + s ,
with the distributional assumptions above.
Again, normalize the payoff to staying home to 0. Let the payoff for protesting and
choosing tactic ti be:
u1 (ti ; ωi ) = ωi + vA A − k(ti − θ)2 .
The strategy for a citizen is a mapping of her anti-regime sentiment (ωi ) and the public
signals to a decision whether or not to protest, and the tactic to choose if protesting cons
,
ditional on these signals. By sequential rationality, citizens all choose tactic t∗i = st β0β+β
s
giving an expected cost of protest k/β. Further, given this tactical choice, citizens with
ωi > k/β have a dominant strategy to protest (i.e., regardless of the protest size), and citizens with ωi < k/β − vA have a dominant strategy to stay home. So, it is natural to search
17
A previous version of the paper also allows for citizens to receive private signals about the anti-regime
sentiment of other citizens, though with a different payoff structure that makes some of the main results
more difficult to interpret. Giving more private information has similar effects as giving more public information.
28
for equilibrium of the form “protest if and only if ωi > ω̂(s)”
In particular, I search for symmetric Perfect Bayesian Equilibria that are monotone in
the individual level of dis-satisfaction with the regime. This means that (1) all citizens
use the same strategy, (2) citizens protest if and only if they sufficiently dislike the regime,
and (3) citizens’ beliefs about the regime strength and level of protest are consistent with
Bayes’ rule and the other citizens’ strategy profile.
Let s be the average of the public signals. This average – which represents the amount
of anti-regime content on the internet and social media – is normally distributed with
mean ω and precision nαω ≡ αs .
The intuition behind the solution is to find a critical level of dissatisfaction with the
regime for each public signal ω̂(s) such that citizens protest if and only if the average of
their private signals is greater than this threshold when the public signal is s. The key
equilibrium condition is that for every possible public signal, the marginal citizen – i.e.,
the citizen observe exactly the cutoff strategy – is indifferent between protesting and not
given all other citizens use this strategy. By a standard calculation this is given by:
ω̂(s) + vA Φ α̃
where µω ≡
α0 µ0 +αs s
α0 +αs
α0 + αs
(µ − ω̂(s)) = k/β,
α0 + αs + αω ω
(9)
is the average posterior belief about the incumbent unpopularity
conditional on the public information.
Since the second term is decreasing in ω̂(s), there can be multiple intersections if equation 9 and hence multiple equilibria if vA is sufficiently large. I informally consider the multiple equilibrium case in the discussion, but for now assume that the solution is unique.
Also, implicitly differentiating gives that in any unique equilibrium the critical threshold
ω̂(s) is decreasing in s. That is, the more citizens believe that others dislike the regime, the
more willing they are to protest.
29
The expected size of protest given the realization of the public signals is then:
1/2
E[A|s] = P r(ωi > ω̂(s)|s) = P r(ω + νj > ω̂(s)|s) = Φ αA (µω − ω̂(s)) ,
where αA =
(α0 +αs )αω
.
α0 +αs +αω
Differentiating with respect to s and simplifying gives this deriva-
tive is proportional to:
∂E[A|s]
∝
∂s
∂µω
∂s
|{z}
−
Confounding
The
∂µω
∂s
term is positive and
∂ ω̂(s)
∂s
∂ ω̂(s)
.
∂s
| {z }
Strategic
is negative, so the expected protest size is increas-
ing in the public signal. So, there will be a positive relationship between the amount of
observed complaints about the regime and protest levels.
More interesting, this expression highlights how we can decompose the effect of the
public signal on the size of protest into two components. The
∂µω
∂s
term captures the fact
that for a fixed citizen strategy, a higher public signal means that the average anti-regime
sentiment is higher, and hence more citizens will be willing to protest. The
∂ ω̂(s)
∂s
term
captures the fact that a higher public signal lowers the citizen threshold to protest: i.e., for
a fixed distaste for the regime, citizens are more apt to protest if they think others will join.
Notably, the first effect is not causal, in the sense that if an outside observer could control for the true average unpopularity of the incumbent, observing the public signal would
not provide any new information and hence would have no effect through this channel.
However, even when controlling for the true ω the public signal still changes the citizen
strategy, so the second effect can be deemed causal. So, unless an outside observer can
perfect control for the average popularity of the regime, some of the association between
anti-regime media and protest levels is not causal.
Further, in the case of social media, much of what is observed by outsiders is written in
30
a language that most participants can’t read (Starbird and Palen, 2012), is censored by the
regime being attacked, or simply replicates information already available to participants
in the protest. All of these pieces of information will be correlated with the anti-regime
sentiment and hence protest levels, but unless they provide distinct information to the
actual participants of the protest they will not have a causal effect on mobilization.
Finally, as above we can compute the ex ante effect of increasing the amount of public
information on the expected size of protest, with a similar result to those in Section 3:
Proposition 9. The expected size of protest is:
i) decreasing in k,
ii) increasing in β,
iii) can be increasing or decreasing in αs
Proof Parts i-ii follow from the fact that the size of protest is decreasing in ω̂(s) and implicitly differentiating equation 9. See the appendix for more detail on part iii.
Again, the first two comparative statics are straightforward: when protest is more
costly fewer participate and when the tactical information is more precise citizens are more
apt to protest.
The comparative static on the number or public signals revealed (and the amount public information about the anti-regime sentiment) is difficult to sign, though extensive numerical analysis indicates that as in section 2 the expected size of protest is increasing in
αs when the probability of protest is low and decreasing in αs when the probability of
protest is high. See Little (2012) for a similar result in a related model.
5
Discussion
With the formal analysis in hand, I highlight three things not directly addressed by the
models that are particularly important to the central questions of the paper. First, protests
31
unfold over time and much of the information generated by communication technology
is about past protest levels and tactics. Second, the regime can use these technologies to
monitor citizens and manipulate the information available to them via censorship and
propaganda. Third, the models have multiple equilibria for some sets of parameters, and
one role of communication technology may be creating “focal points” getting citizens to
choose equilibria with more protest
Dynamics and Learning
A common argument not captured perfectly in the coordination models is that social
media spreads information about how many citizens have already take to the streets and
what tactics they are using. In the words of a BBC correspondent, “if you follow second
by second some of the accounts coming from Cairo’s Tahrir Square, you can almost see
when activists realized they had broken through, that it wasn’t just a few hundred people
turning up but tens of thousands.”18
Capturing this idea requires a dynamic model, which prove complex when combined
with incomplete information coordination games (Angeletos, Hellwig and Pavan, 2007;
Little, 2013). Still, analogous to the argument made repeatedly here, if communication
technology can provide information that many people are on the streets, it will also make
it more clear when they aren’t on the streets. That is, Twitter can help spread the word that
protests are growing, but it can also spread the word that protesters are going home. So,
conditional on successful revolution, will have seen lots of positive messages spreading
on social media, but in failed cases there generally won’t be, potentially resulting in the
same ambiguous average effect found repeatedly in the formal analysis. On the other
hand, providing better information about the tactics protesters are using should have an
unambiguously positive effect on protest levels
18
http://www.newscientist.com/article/mg21328500.400-the-revolution-will-be-tweeted.html
32
Strategic Leaders
An important omission from the models is the role of the incumbent leadership. Two
important arguments that are not directly modeled as a result are that autocrats (and
democrats) can (1) use social media to identify and target dissidents, and (2) use censorship to control the flow of information.
The first point is certainly valid, though without formalizing the argument it seems
plausible that citizens with an interest in attacking unpopular regimes would avoid using
social media if it helped with repression. The information generated by social media can
also serve as a substitute for taking to the streets, as the regime can learn more easily the
type and magnitude of concessions that would appease citizens without them taking the
more costly route of protesting.
While censorship certainly plays a key role in the relationship between any media and
protest, the types of arguments made here suggest it may not have a large impact on average levels of protest. As better information can not make citizens systematically believe the
regime is weaker or stronger, changing the distribution of what citizens learn from social
media via censorship can not systematically change average beliefs either. In other words,
just as better communication technology led citizens to discount the observed grievances
in the individual model, citizens will react to anti-regime media more strongly in an environment with heavy censorship. As a result, it is not clear that heavy censorship will lead
to less protest on average.19
19
A potential exception to this point is if censorship is not about manipulating information per se, but about
signaling that the incumbent leadership can get away with manipulating information easily (Huang and Li,
2013). In this case, regimes that can successfully censor effectively may be particularly strong regimes that
will be hard to topple.
33
Multiple Equilibria and Focal Points
Both of the coordination models have multiple equilibria for some parts of the parameter space, which are not analyzed in detail as the equilibrium can be unique and all of the
comparative statics hold within the equilibrium with the highest level of protest. However, when there are multiple equilibria, better communication technology can make it
easier for high levels of complaints about the regime – or a particularly salient complaint
about the regime – to act as a focal point spurring larger protests. For example, a single
vendor lighting himself on fire (as in Tunisia in 2010) likely does not dramatically change
citizens’ beliefs about the performance of the regime, but could provide a publicly observable “spark” to get citizens to switch to an equilibrium with more protest. More generally,
a natural equilibrium to analyze in this context is one where the citizens play the highest
protest equilibrium if and only if the public signals of discontent are sufficiently high (see
Little, Tucker and LaGatta 2012 for an analogous argument about electoral rules).
6
Conclusion
As communication technology continues to improve and assume a more central role
in politics and our lives more generally, debates about how exactly new technology affects
politics are not likely to go away. New data will certainly lead to a deeper understanding
of this process, but without a good theoretical structure it is difficult to know how we
should interpret the rapidly increasing glut of data. The models here provide structure
for how we should do so, making a conceptual distinction between different ways more
information affects various types of political coordination.
34
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Appendix
Proof of Proposition 3
Writing out the probability of protest and simplifying gives:
P r(s > ŝ) = Φ (k − µω )
Since
√
ραs
α0
−1
ρ2 α−1
0 +αs
α0
ραs
!
p
ρ2 α0−1 + αs−1
is decreasing in ρ, the probability is increasing in ρ if and only if µω <
k.
Proof of Proposition 4
Write the protest condition as:
ρ(µω + νω ) + ω > ŝ
νω > (k − µω )(1 = α0 /(ρ2 αs )) − ρµω
As long as ρ > 0, this threshold is always decreasing (and hence the probability of protest
increasing) if νω is sufficiently high and increasing (and hence the probability of protest
decreasing) if νω is sufficiently low.
Proof of Proposition 5
The sign of
∂E[A]
∂βs
b
is given by the sign of:
∂a
∂b
−a
∂βs
∂βs
k(1 − r)
kr(1 − r)
βx
=b
−a
2
(β0 + βs + βx )
βx
(β0 + βs + βx )2
= k(1 − r)(β0 + βs + βx )2 [b − rα]
41
That is, the sign is determined by the sign of b − ra. So the probability of protest
is increasing in the level of public information if b − ra > 0, or, a/b < 1/r. Since the
probability of protest is F (a/b), this will hold if the prior probability of protest is less than
F (1/r).
Proof of Lemma 6
The condition for an equilibrium with no protest is that a citizen observing exactly
xi = µθ is not willing to protest when A = 1 and R = 1, which simplifies to condition
ˆ So if (1) and
(1). If condition 2 holds, the equilibrium condition is always increasing in d.
ˆ is positive for dˆ = 0, continuous and decreasing in d,
ˆ and approaches
(2) hold, then U 1 (d)
−∞ as dˆ is sufficiently large, which guarantees a unique intersection and hence a unique
equilibrium. If not there may be multiple equilibria, though at the largest intersection
∂U 1
∂ dˆ
< 0, which is all that matters for the sign of the comparative statics.
Proof of Proposition 7
For part i, the sign of
∂E[A]
k
is equal to the sign of
∂ dˆ
.
∂k
Implicitly differentiating gives:
1
∂ dˆ − ∂U
= ∂U∂k1
∂k
ˆ
∂d
The denominator is positive and the denominator is negative in the largest (or unique)
ˆ = 0, so the expression is negative. Part ii follows from an analogous
dˆ such that U 1 (d)
calculation.
For part iii:
∂E[A]
= 2φ
∂βs
s
!" #
−1/2 2 s
ˆ
βx (β0 + βs ) ˆ
β
(β
+
β
)
1
β
(β
+
β
)
β
+
β
∂
d
x
0
s
x
0
s
0
s
d
dˆ
+
β0 + βx + βs
2 β0 + βx + βs
β0 + βs + βx
β0 + βx + βs ∂βs
42
Where
∗
− ∂U
∂ dˆ
∂β
= ∂U ∗s
∂βs
ˆ
∂d
ˆ d],
ˆ R(d),
ˆ and −K(d)
ˆ are all increasing in βs ) , so
The numerator is negative (as E[A|di = d;
the expression is positive. Finally:
∂E[A]
= 2φ
∂βs
s
!" #
−1/2 2 s
ˆ
βx (β0 + βs ) ˆ
1
β
(β
+
β
)
β
β
(β
+
β
)
∂
d
x
0
s
x
x
0
s
d
+
dˆ
β0 + βx + βs
2 β0 + βx + βs
β0 + βs + βx
β0 + βx + βs ∂βs
Where
∗
− ∂U
∂ dˆ
∂β
= ∂U ∗s
∂βs
ˆ
∂d
ˆ d]
ˆ is increasing in βs and R(d)
ˆ is decreasing in βs . As shown above,
Further, E[A|di = d;
ˆ is increasing in βs if E[A] < F (1/r), where F is the cdf of a chi-square random variable
K(d)
with one degree of freedom. So E[A] < F (1/r) is a sufficient but not necessary condition
for the protest level to be increasing in βs
Derivation of Equilibrium Condition in Section 4
A citizen with regime sentiment’s belief about ω is normal with mean:
µω (ωi ) =
α0 µ0 + sαs + ωi αω
α0 + αs + αω
And precision α0 +αs +αω . So, from the perspective of a citizen with anti-regime sentiment
ωi , the probability of citizen j protesting is:
P r(ωj > ω̂(s)) = P r(ω + νj > ω̂(s)) = Φ α̃1/2 (αs (ωi ) − ω̂(s))
43
Where α̃ =
(α0 +αs +αω )αω
α0 +αs +2αω
The equilibrium condition is that the marginal citizen is indiffer-
ent between protesting and not, or:
ω̂(s) + vA Φ α̃
where µω =
α0 µ0 +αs s
α0 +αs
1/2
α0 + αs
(µ − ω̂(s)) = k/β
α0 + αs + αω ω
is the public mean belief about ω.
Proof of Proposition 9
The ex ante expected size of protest is given by
Z
∞
E[A] =
P r(ωi > ω̂(s)|s)φ(s; µ0 , αs )
s=∞
Which is decreasing in ω̂(s). Implicitly differentiating equation 9 implies the level of
protest is decreasing in k/β, proving parts i-ii.
The level of protest is a complicated function of αs , but extensive numerical analysis
indicates that a result similar to proposition 3 applies, i.e., the level of protest is increasing
in αs when protest is ex ante unlikely and decreasing in αs otherwise.
44