The dynamics of revolutions

The dynamics of revolutions
Moti Michaeliy
& Daniel Spiroz
February 6, 2018
Abstract
We study the dynamics of revolutions and mass protests addressing a number of fundamental,
but currently unanswered, questions. Existing theories invariably predict that revolutions will be
initiated by the most extreme opposition to the regime, like in the Iranian Islamic Revolution,
but why do revolutions sometimes start with moderate opponents of the regime, like in the
Egyptian Arab Spring in 2011 and in the USSR in 1989-1991? And how can the implementation
of popular policies, such as Perestroika, trigger a revolution? To address these and related
questions, we develop a uni…ed theoretical framework providing predictions for who –moderates
or extremists –is more likely to start a revolution, what ideology they will express, and which
policy may trigger the revolution. We show how the answers depend on the regime’s sanctioning
structure and on the individuals’costs of deviating from their own ideological convictions. The
results are illustrated by several historic revolutions.
JEL: D74; P2: P5; Z12.
We wish to thank Elias Braunfels, Jean-Paul Carvalho, Sylvain Chassang, Mona El-Sherif, Israel Eruchi-
movitch, Bård Harstad, Moshe Kim, Carl-Henrik Knutsen, Arie Melnik, Anirban Mitra, Kalle Moene, Manuel
Oechslin, Paolo Piacquadio, Debraj Ray, Kjetil Storesletten, Patrick Testa, Arthur van Benthem, Sareh Vosooghi,
Yikai Wang, and seminar participants at George Washington University, University of Oslo, Tilburg University,
Uppsala University, King’s College, EUI and the ASREC, IMEBESS and NCBEE conferences for valuable com-
ments.
y
Department of Economics, University of Haifa, Israel; Department of Economics, European University Insti-
tute, Italy. Email: motimich@gmail.com.
z
Corresponding author, Dept. of Economics, Uppsala University, Sweden; Oslo Business School, Norway.
daniel.spiro.ec@gmail.com.
1

1 Introduction
Throughout history, revolutions have led to fast and massive changes in institutional, economic
and social environments and, as such, most social-science disciplines have been interested in un-
derstanding their causes and dynamics. It is common to divide revolutions against a regime into
two categories (Tanter and Midlarsky, 1967). First, coup detats, performed by military elites or a
competing party to the regime. Second, major revolutions, driven not by a small group of elites
but by popular protest and large social movements. This paper is concerned with the latter cate-
gory, which includes, e.g., the recent Arab Spring, the toppling of the Shah in Iran in 1978-79, the
collapse of the communist regimes in Eastern Europe in 1989 and the Tiananmen-Square protests
in Beijing in 1989. In particular, we contribute to the understanding of who –on an ideological
scale –will participate in a revolution, which stances these individuals will express and what may
spark the revolution.
The workhorse model of revolutions and mass protests is binary.1 I.e., each individual can either
support the regime or protest against it, individuals di¤er in their inclination toward each of these
two alternatives and, importantly, the larger the population share that chooses an alternative is, the
more each individual is inclined to choose so as well. The binary model provides valuable insights
on, e.g., thresholds for regime stability. However, since an individual in that model can only choose
between complete obedience to the regime and full-blown protest, the binary model invariably
predicts that the revolution will be initiated by those who dislike the regime the most. This
prediction is inconsistent with many actual revolutions. Consider, e.g., the Arab Spring in Egypt
in 2011. These protests were initiated by moderate liberals and moderate conservatives (Lesch,
2011), while those most critical to Mubarak’s regime –the Muslim Brotherhood and the Sala¢ s
–were the last to join (BBC, 2013; Al Jazeera 2011). Similarly, many of the communist-regime
collapses in Eastern Europe in 1989-1991 started by moderates (or regime insiders) (Lohmann,
1994, Przeworski 1991, Breslauer 2002). The binary model is furthermore silent about the extent
to which di¤erent individuals will dissent –i.e., which demands each individual will make or what
ideology she will express –and how this will change over the course of the revolution. This means
that it cannot distinguish between a revolution, such as the Iranian in 1979, where dissent was
…erce right from the start (by Khomeini and his followers) while factions joining later dissented
less (Razi 1987, Moaddel 1992, Ghamari-Tabrizi 2008), and protests such as those on Tiananmen
Square in 1989, where the initial dissent was moderate but then got more …erce over time (Zhao
2001).
This paper presents a uni…ed framework that accounts for these di¤erences between revolutions
and whereby three distinct classes of revolutions and mass protests can be explained (the examples
are described more fully in the paper).
1
The binary model was developed by Granovetter (1978) and then discussed and applied in a series of papers
by Kuran (1989, 1991, 1995). Other papers using such, or an adjacent, setup are, e.g., Naylor (1989), Bueno de
Mesquita (2010), Olsson-Yaouzis (2012), Edmond (2013) and Rubin (2014). See the later literature review for more
details.
2

1. A revolution starting with extremists dissenting extremely: those who are the most
critical to the regime initiate the revolution by dissenting intensely, and later less critical
individuals join the protests but dissent less than the initiators. This class can be illustrated
by the Islamic Revolution against the Shah in Iran in 1978-79 and the fall of Madero’s regime
in Mexico in 1911-1913.
2. A revolution starting with moderates dissenting moderately: the revolution starts
with moderates expressing moderate critique, and later less moderate individuals join and
express harsher critique. This class of revolutions can be illustrated by the Arab Spring in
Egypt in 2011 and by the fall of communism in 1989-1991.
3. A revolution starting with extremists dissenting moderately: strong opponents of
the regime stay in the frontline throughout the protests, while gradually increasing their
dissent. This class can be illustrated by the evolution of the Tiananmen-Square protests in
Beijing in 1989 and by the April Revolution that led to the fall of President Rhee in South
Korea in 1960.
Our theory provides predictions for which of the three classes of revolutions will occur, and hence
which individuals –moderates or extremists –will participate in a revolution at various stages and
how extreme their dissent will be. We also provide explanations for other central observations that
the binary model cannot account for.2 E.g., the binary model predicts that only unpopular policies
can start a revolution, while popular policies cannot since they ultimately increase the relative
attractiveness of supporting the regime. However, history shows that sometimes a popular policy
does spark a revolution, e.g., Perestroika in the USSR (Brown 1997, Lane and Ross 1994). That such
policies could ignite a revolution came as a surprise to both experts and academics (as documented
by, e.g., Kuran 1991 and Lipset and Bence 1994). Following this surprise, Przeworski (1991, p.1)
wrote that “[a]ny retrospective explanation of the fall of communism must not only account for
the historical developments but also identify the theoretical assumptions that prevented us from
anticipating these developments”. We do just that, and furthermore provide predictions for when
a popular policy is likely to start a revolution and when not.
Another important characteristic of revolutions about which the binary model is silent is whether
dissent would come only from one side of the political spectrum or from both sides. Our model
accounts for both cases, predicting when dissent will start only on one side (like the radical Muslims
in Iran 1979) and when it will start on both sides, with “strange bedfellows”weakening the regime
simultaneously. E.g., in Egypt in 2011, among the …rst protesters some complained Mubarak was
not su¢ ciently liberal while others complained he was not su¢ ciently conservative. Similarly, in
the USSR in 1987-1991, hardline Communists criticized the extent of Gorbachev’s reforms while
others, like Yeltsin, complained the reforms were not su¢ ciently far reaching.
2
In the literature review and in other relevant parts of the paper we discuss other models, which consider as-
pects orthogonal to ideology (e.g., how individuals overcome the collective-action problem).
3

The theory we develop contains all the core components of the standard binary model with a
seemingly simple extension. Rather than having a binary choice between obeying the regime or
dissenting against it, an individual can choose the extent of her dissent (where not dissenting at all
can be interpreted as staying silent or alternatively supporting the regime). The more an individual
dissents, the more she will be sanctioned. Just like in the binary model, what makes her possibly
dissent despite this sanctioning is that she has a private blisspoint (a political view or an economic
interest) from which it is costly for her to deviate. Hence, each individual trades o¤ the sanctioning
for disobeying the regime against the cost of deviating from her blisspoint. These blisspoints
are heterogenous in the population thus capturing that society consists of di¤erent factions. The
strength of the regime (i.e., how heavily it sanctions dissent) is endogenous –it decreases in the
extent of dissent in society in terms of the number of dissenters and how strongly each one dissents.
Then, since the strength of the regime a¤ects the propensity of individuals to dissent, individuals
who themselves do not dissent discourage others from dissenting as well (basically a collective-action
problem).
We show in the paper that the evolution of dissent largely depends on the sanctioning structure
the regime is using, in particular on whether the cost of sanctioning increases concavely or convexly
in the size of deviation from the regime’s policy. Similarly, the evolution of participation largely
depends on whether the cost of deviating from one’s ideological blisspoint increases concavely or
convexly in the size of such deviation. Then, who starts the revolution and how dissent evolves
during the revolution has implications for whether popular or unpopular policies may trigger a
revolution; when a revolution is more likely to be one-sided and when two-sided; at what stage a
revolution is most likely to fail and what the regime can do to achieve it; and when the revolutionary
momentum will mainly be driven by new recruits versus by gradual increases of dissent of current
participants.
Following a brief literature review, Section 2 outlines the model and presents the main results.
Sections 3-5 analyze the three classes of revolutions, each in turn, and provide more details on the
historic examples brie‡y discussed earlier. In particular, Section 4 analyzes revolutions started by
moderates and by implementation of popular policies. Section 6 concludes. The appendix provides
a detailed and more formal analysis of the three classes of revolutions and also testable predictions
and further implications of our model.
1.1 Relation to previous research
As stated in the introduction, our main contribution is in explaining the dynamics of participation
and statements in di¤erent kinds of revolutions –in particular those initiated by moderates, which
were not explained thus far –and in explaining which regime policies are likely to trigger a revolution
(in particular when it comes to popular reforms). Thus, our main dimension of analysis is the
dimension of ideology. Other dimensions by which revolutions may be analyzed –such as economic3,
3
See, e.g., Davies (1962), Knutsen (2014) and Hegre and Sambanis (2006).
4

collective-action resolution4 and resource-mobilization ability5 –are all relevant in many revolutions
but are largely orthogonal to the current analysis. In Appendix D we mention other explanations
for the revolutions in the USSR and Egypt and discuss their explanatory power.
In order to study the dynamics of participation and statements in revolutions, like we do, a
model has to (1) di¤erentiate between di¤erent extents of revolutionary actions and (2) involve
dynamics, i.e., allow these actions to change over time. Most previous papers analyzing dynamics
of revolutions and mass protests utilize a binary-action model (see, e.g., Granovetter 1978; Kuran
1989; Naylor 1989; Bueno de Mesquita 2010; Olsson-Yaouzis 2012; Edmond 2013; and Rubin 2014),
hence cannot di¤erentiate between di¤erent extents of revolutionary actions.6 Shadmehr (2015a)
does di¤erentiate between di¤erent extents of revolutionary actions and, as such, is able to analyze
how extreme the revolutionary agenda will be. He also studies how a regime’s sanctioning structure
(its curvature) a¤ects participants’ choices, hence is the paper most related to ours. However,
his model has no dynamics – the revolutionary agenda is assumed to be constant throughout
the revolution. This is challenged when considering, e.g., the Arab Spring in Egypt, where the
revolutionary agenda shifted greatly during the revolution (from liberal to extremely conservative).
Furthermore, and most importantly, his model predicts (along with the binary models) that the
most extreme factions will under all circumstances be part of the revolution hence it cannot account
for cases where they join last.
More broadly, obeying a regime and conforming to a social norm are theoretically quite similar
and in the literature on social norms some non-binary models exist (Bernheim 1994, Kuran and
Sandholm 2008, Manski and Mayshar 2003, Michaeli and Spiro 2015, 2017). The structure of
the individual trade o¤ – between obeying a regime or norm and following one’s heart – is thus
shared by these papers and the current paper. However, Bernheim (1994), Manski and Mayshar
(2003) and Michaeli and Spiro (2015) are concerned with static equilibria hence are silent about
the dynamics; and in Kuran and Sandholm (2008) and Michaeli and Spiro (2017) there exists no
regime and instead the sanctioning (i.e., social pressure) is decentralized to groups and individuals.
Granovetter (1978), Kuran (1989) and many subsequent papers o¤er a dynamic setting in
which individuals take the actions of others as given. This kind of analysis, which abstracts from
strategic considerations on the individual level, seems adequate for analyzing major revolutions
and mass protests whereby, literally, millions of individuals may participate. We therefore adopt
this approach in our paper too. We want to emphasize that adding strategic considerations would
not change our main results.7 Strategic considerations by revolutionary participants are analyzed
4
See, e.g., Tullock (1971), Esteban and Ray (2001) and Chwe (1999).
5
See Jenkins (1983) and Edwards and Gillham (2013) for summaries.
6
In Rubin (2014) the regime can choose its policy from a continuum but the individual’s decision whether or
not to support the regime is binary.
7
We have also solved a version of our model with a small number of strategic agents. The main results remain
the same, in particular the prediction that moderates may be the ones initiating the revolution. In that version
of the model, a moderate agent takes into account that, if she does not revolt, an extremist may initiate the rev-
olution instead, which would save her the need to be the …rst one revolting and facing the regime when it is still
strong. However, the same mechanism of our main model makes the extremist reluctant to be the …rst to protest,
while the moderate is better o¤ initiating a revolution and getting the extremist’s support in the next stage than
5

by Lohmann (1994), Bueno de Mesquita (2010), Edmond (2013), Shadmehr (2015a) and Chen and
Suen (2016). However, to the extent that individuals di¤er in these models, they predict that
under all circumstances the most extreme factions will be part of the protests at all stages of the
revolution. Hence, these theories cannot explain revolutions in which moderates lead the way and
extremists join only later, nor do they allow for revolutions triggered by popular policies.8
Two other main concerns of many papers on revolutions are coordinated protests and the
collective-action problem, often in conjunction. Coordination is not a central issue in our setup,
because people in an uncoordinated fashion gradually (dynamically) best respond to the revealed
choices of others. The collective-action problem (see Olson 1971 and Tullock 1971 for early treat-
ments and, e.g., Oliver and Marwell 1988; Chwe 1999; and Esteban and Ray 2001 for more recent
work) is re‡ected in our model by the fact that individuals who do not dissent discourage others
from dissenting as well, implying that agents dissent too little. What makes individuals in our
model partly overcome the problem and dissent against the regime is that they wish to express
their own ideology (ideological disagreement has indeed been identi…ed as an important determi-
nant of revolutions, see e.g. Goldstone 2001). We do not, however, directly contribute to the full
solution of the collective-action problem nor to, e.g., the analysis of which group sizes are more
likely to overcome it (like, e.g., Esteban and Ray 2001 do). On the other hand, one way of viewing
our contribution is that our model predicts which ideological groups have the strongest incentives
to overcome their internal collective-action problem (holding other di¤erences between the groups
…xed).
2 The model
We start by describing a static version of the model and then add a dynamic structure to it. Society
consists of a continuum of in…nitesimal individuals of mass 1 and of a political regime. The regime
has a policy R 2 [ 1; 1] which can be thought of as a point on a left-to-right political scale. Focusing
on revolutions and mass protests against a given regime, we let R be exogenous (capturing the
regime’s ideology). Each individual takes a stance s 2 R, with the distribution of stances denoted
by S. The regime sanctions dissent, i.e., stances that deviate from its policy (s 6= R), with larger
deviations representing harsher critique of the regime, which in turn is sanctioned more heavily.
s = R can be interpreted as the individual staying silent. The sanctioning is represented by the
following punishment function:
P (s; R; K) = K js Rj ; > 0. (2.1)
not revolting at all. Such a model is, however, not tractable for obtaining our further results, so we do not pursue
it further in this paper.
8
See also Karos (2016) for an analysis of how regime repression a¤ects the scale and probability of anti-
government protests and Knutsen (2011) for an analysis of what policies (one of which is repression) are optimal
for the regime depending on whether the threat is internal or external.
6

Figure 2.1: Regime sanctioning for di¤erent values of .
The overall severity of punishment (sanctioning), to which we also refer as the strength of the
regime, is represented by K in (2.1). It is endogenously determined by
K = KA
where K is a parameter capturing the force of the regime and A 2 [0; 1] is the approval of the
regime, which in itself is determined by the overall dissent in society. K could represent, e.g., the
per capita law-enforcement forces used by the regime to sanction dissent. A, the approval of the
regime, is simply assumed to be decreasing the more dissenting each individual stance is.9 Hence,
the overall severity of punishment K decreases in total dissent, capturing the notion that the more
dissent there is, the less likely it is for an individual dissenter to get caught. Alternatively, A could
indirectly represent the proportion of law enforcement forces that stay loyal to the regime when
asked to use force against dissenting civilians.
The parameter captures the curvature of the sanctioning system, which will be important for
the analysis. It is illustrated in Figure 2.1. A regime with a large (> 1) uses convex sanctioning
and hence is tolerant towards dissent as long as it is not too extreme. A regime with a small
(< 1) uses concave sanctioning whereby it punishes rather heavily even small dissent but does not
9
More precisely, A has the property that for any non-zero mass of individuals, if these individuals strictly in-
crease their dissent (while holding the dissent of the rest …xed) then A strictly decreases (when starting from
A > 0). Note that, to obtain our results, we do not need to further specify the properties of A, i.e., our results
hold for any speci…cation of A having the aforementioned property. E.g., we do not need to specify what happens
to A if one individual increases her dissent while another individual decreases hers.
7

distinguish much between small and large dissent.
Each individual has a privately preferred political policy or opinion t 2 T R, also referred to
as the individual’s blisspoint or type, with g (t) denoting the probability-density function of types,
which is assumed to be continuous. When expressing a stance s, the individual bears a cost for
deviating from her blisspoint:
D (s; t) = jt sj ; > 0: (2.2)
D can be interpreted as discomfort from expressing a political opinion not in line with a person’s
conviction. I.e., individuals can be viewed as driven by a will for self expression.10 Thus, jt Rj
captures how deviant the individual’s ideology is from the regime’s, on how many issues she disagrees
with the regime or how vocal against it she would like to be, while jt sj captures how much
she restrains herself in such dissent. For short, we refer to individuals with private views far
from the regime (large jt Rj) as extremists and to those with private views close to the regime
(small jt Rj) as moderates. I.e., a type’s extremeness is always relative to the regime –a liberal
democrat under the Taliban regime is an extremist in our de…nition. The parameter , which will
be important for our analysis, captures how the individual perceives small versus large deviations
from her blisspoint. It is illustrated in Figure 2.2. With a large (> 1) an individual is insensitive
to small deviations from the blisspoint while large deviations are very costly (left schedule). This
further implies extremists will …nd it very costly to fully follow the regime while for moderates this
will be nearly costless. With a small (< 1) an individual perceives even small deviations as very
costly but hardly distinguishes between small and large deviations (right schedule). This further
implies it will be almost equally costly for extremists to follow the regime as it is for moderates.
We assume all individuals in society have the same (it can be interpreted as a cultural trait) but
discuss the e¤ect of having a population with heterogenous in Appendix A.4.
The choice problem of an individual with t 6= R is how to trade o¤ the sanctioning when
dissenting against the regime and the disutility of deviating from her own privately held opinion.
I.e., the individual minimizes
L (s; t; R; K (S)) = D (s; t) + P (s; R; K (S)) . (2.3)
It is immediate from this choice problem that each individual will take a stance somewhere weakly
in between her t and R. The extent to which the individual feels forced to go towards the regime
depends on the regime’s strength K (S) and hence indirectly on the stances taken by all individuals
in society.
We have now outlined the properties of the static model and can thus de…ne what a Nash
equilibrium entails in our setting: it is a mapping t ! s such that each individual is best responding
(minimizing (2.3)) given the actions of the other agents. The stance that minimizes L for an
individual with opinion t is denoted by s (t), and the distribution of all such chosen stances by the
10
Alternatively, if t re‡ects one’s optimal economic behavior, D can be interpreted as a material cost of deviating
from the individual’s economic interests.
8

Figure 2.2: D for di¤erent values of .
population is denoted by S . Just like in any game with complementarities between the actions
of agents, there may exist multiple equilibria in our static game –the more some agents dissent,
the more other agents are prone to dissent too. E.g., there may exist an equilibrium where js Rj
is small for most types and the regime is strong (A, K are large). Alongside, there may exist
an equilibrium where js Rj is large for most types and the regime is weak (A, K are small).
In particular, we set A to equal 0 whenever s (t) = t 8t, so that this will always constitute an
equilibrium, as it implies that P (s; R; K) = P (s; R; 0) = 0 and so s (t) = t 8t. This can be
interpreted as a state with no regime or as a state with a regime that has no control over the
population.
Being interested in the dynamics of revolutions, we wish to analyze the movement from a Nash
Equilibrium where the regime is strong to one where it is weaker (see more details below). For
that purpose we now add a simple dynamic structure to the model. Our dynamics are standard
in games with large populations (e.g., Young 1993; Bala and Goyal 2001; Young 2015) and in the
analysis of revolutions (e.g., Granovetter 1978; Kuran 1989). In these dynamics agents are best
responding in period i + 1 to the actions taken in period i:
si+1 (t; R; K (Si )) = arg min
si+1
fL(si+1; t; R; K (Si ))g; (2.4)
which we for short denote by si+1 (t). The formulation in (2.4) means that the regime strength
(K) that a¤ects stances in period i + 1 is determined by the stances taken in period i. This could
capture, e.g., the assertion of the regime’s troops at day i + 1 of a revolution after observing the
9

dissent of the population on the previous day. This dynamic structure implies that the distribution
of stances Si+1 is a function of Si and that
Ai+1 = f (Ai)
where f describes the dynamics of approval between periods. We wish to emphasize that we choose
these adaptive dynamics for tractability and for brevity in presenting the results but the speci…c
dynamic modeling does not drive our results.11 A steady state is reached when si+1 (t) = si (t)
8t, i.e., when each person’s best response in period i + 1 equals her action in period i. Hence, a
steady state also constitutes a Nash Equilibrium. In such a situation f (Ai) = Ai. We consider
a steady state to be stable, with its approval denoted by Ass, if there is convergence back to it
following a small perturbation to Ass. Otherwise the steady state is unstable, with its approval
denoted by Auss. Our measure for the stability of the regime following a shock to its approval is
the distance between the regime’s approval at a steady state Ass and the approval at the closest
unstable steady state below it, i.e., Ass Auss, because the zone of convergence to Ass from below
is A 2 (Auss; Ass).
A revolution is de…ned as a dynamic process where the approval is converging to a new, lower,
steady state (i.e., a revolution is not a situation where a small change to a parameter leads to a
small change in the steady-state approval). A successful revolution is one where A = 0 in the new
steady state and a failed revolution is one where A > 0 in the new steady state. Catalytic events
are events that may trigger a revolution. These are exogenous changes or shocks that either imply
that a previously stable steady state seizes to exist or decrease the approval to a point where it
will, endogenously, decrease further.
The main focus of our analysis is on the evolution of participation (i.e., which types dissent)
and of statements (i.e., which stances they express) over time during the revolution. The model
predicts three classes of revolutions depending on the combination of the parameters and , as
depicted in Figure 2.3 and expressed in the following proposition.12
Proposition 1 There are three distinct and exhaustive classes of revolutions:
1. (Extremists starting with extreme dissent) If < min f1; g, then initially the dis-
senters are extremists, and later in the revolution types who are more moderate join, but
dissent less than the initial extremists.
2. (Moderates starting with moderate dissent) If < min f1; g, then initially the dis-
senters are moderates, and later in the revolution types who are more extreme join and dissent
more than the initial moderates.
11
We have also solved a version of the model with forward-looking agents and strategic interaction between them.
The main results about the three classes of revolutions –in particular the existence of revolutions initiated by
moderates –are the same. But it is substantially harder to show our further results about two-sidedness of revo-
lutions, policies that may trigger a revolution and the distinction between successful and failed revolutions.
12
For brevity we ignore here the special case of = 1 with its unique technicalities.
10

Figure 2.3: Parameter space of the di¤erent classes of revolutions.
3. (Extremists starting with moderate dissent) If 1 and 1 (and at least one
inequality is strict), then throughout the revolution the most dissenting types are extremists,
who start by dissenting moderately and increase their dissent over time.
These three classes of revolutions fundamentally di¤er in how participation and statements
evolve during the revolution. We defer explaining the intuition of Proposition 1 to the upcoming
three sections, where we analyze each class of revolutions separately and describe further results.13
A more formal description can be found in Appendix A.
Figure 2.3 is instructive for highlighting the main drivers and the overarching pattern of the
model results –who the initiators of the revolution will be and what statements they will make
initially. The higher we are on the vertical axis (for any value on the horizontal axis) the more
likely we are to be in a case where the initial statements in the revolution are moderate. I.e., the
structure of sanctioning ( ) determines how extreme the initial statements will be. In particular,
if the regime punishes severely even moderate dissent but does not distinguish much between
moderate and extreme dissent (small ), then the initial statements are more likely to be extreme.
On the other hand, if the regime is punishing dissent only when it is extreme (large ), the initial
statements in the revolution are more likely to be moderate.
Moving instead along the horizontal axis (for any value on the vertical axis), the further to the
right we are (large ) the more likely the revolution is to be started by extremists. I.e., whether
individuals distinguish between small and large deviations from their blisspoints determines who
the initiators of the revolution will be –moderates or extremists. In particular, if individuals are
largely insensitive to small deviations from their blisspoints but perceive large deviations as very
costly (large , illustrated on the left part of Figure 2.2) then extremists are more likely to start a
13
These further results were attained using a uniform distribution of types in [ 1; 1] and the approval function
given in equation (B.1) in the appendix.
11

revolution since they perceive it as very costly to keep silent. On the other hand, if individuals are
very sensitive to small deviations from their blisspoints, but do not distinguish much between small
and large deviations (small , illustrated on the right part of Figure 2.2) then instead moderates are
more likely to start a revolution. The intuition behind these results is explained in the upcoming
sections.
3 Extremists starting with extreme dissent
We start by considering the case where < min f ; 1g which, as Proposition 1 outlines, implies that
any potential revolution entails extremists starting it by dissenting extremely. Since the predictions
of this section largely align with the binary model, we keep it short. A detailed and more formal
analysis, which includes a mapping of the Nash equilibria and an analysis of the stability of the
various steady states, can be found in Appendix A.1. Here we only focus on the intuition behind
the results.
The key property of this case is that is small, which implies that the regime applies a (very)
concave punishment whereby even small dissent is heavily punished while more extreme dissent
is punished only slightly more. This will naturally induce an individual to either fully follow the
regime or, if she does not fully follow it, she might as well dissent quite a lot. Then, since extremists
perceive the highest discomfort (D) when following the regime, they will be the ones who may
dissent –and, given their extreme views, dissent quite a lot if they do –while moderates will be
silent. Put di¤erently, a large misalignment between an individual’s ideology and the regime’s policy
is what triggers dissent. This further implies that increased misalignment between the regime and
the population as a whole may trigger a revolution. Such misalignment may be the result of either
the regime implementing unpopular policies or a shift in the preferences of the population (the
t-distribution) away from the regime. Figure 3.1 illustrates what a revolution would entail in the
latter case. On the top schedule we are in a steady state where the regime is non-biased (R = 0)
and is su¢ ciently strong to induce no dissent. In the …gure this can be seen by the distribution of
statements being completely centered on R. On the next schedule, the preferences of the population
have shifted to the right to the extent that the increased misalignment between the population and
the regime triggers some dissent on the far right. This reduced approval weakens the regime and
this in turn, on the third schedule, enables more moderate types on the right to speak their minds
too. The increased dissent weakens the regime’s sanctioning further, enabling even more moderate
individuals to dissent, eventually implying that people on the left start dissenting too (bottom
schedule). Hence, overall, we get that the revolution is initiated by extremists dissenting extremely,
while more moderate individuals join the revolution later and dissent less.14
An interesting aspect of this revolution is that it is one-sided initially (dissent comes only from
one side of the political spectrum). Since new recruits come only from one side, the momentum of
14
Other potential catalytic events, which in fact apply to all the three classes of revolutions, are shocks to ei-
ther the regime’s force or to its approval. Such shocks, if large enough, imply convergence to a new, lower level of
approval (potentially even A = 0, implying a collapse of the regime).
12

Figure 3.1: Distribution of stances over time in a stylized case of a revolution starting with ex-
tremists dissenting extremely ( < 1). R = 0 and …xed while the distribution of types
changes.
the revolution will be weak initially, implying further that during this phase the revolution may fail
(see Figure A.2 in Appendix A.1 and the discussion there). However, once the revolution becomes
two-sided then, by the fact that new dissidents appear on both sides of the political spectrum, the
momentum picks up and the regime is bound to collapse –the approval goes to zero.15
3.1 A historic example
We now provide an example, from Iran in 1979, of an actual revolution that …ts the dynamics
described in this section – of extremists starting with extreme dissent. Another example – the
Mexican Revolution of 1911-1913 against Francisco Madero –is provided in Appendix C.1. Note
15
If the revolution fails, the regime becomes “semi-democratic”where some (but not all) individuals speak their
minds –there is in practice some freedom of speech. This regime will be weaker and is more likely to collapse in
case a subsequent revolution breaks, which is in line with the robust empirical observation that semi-democracies
are the least stable regimes while pure democracies and pure autocracies are the most stable (see, e.g., Gurr 1974,
Gates et al. 2006 and Knutsen and Nygård 2015). Appendix A.4 provides more details on how this is represented
in our model.
13

that this is not an empirical test of the model. Rather the purpose is to illustrate that the pat-
terns obtained theoretically have been observed in reality. A proper empirical test would link the
parameter conditions (in particular for and ) of a large set of revolutions to the predictions of
the model. This is in principle possible but requires gathering a large set of detailed data which is
beyond the scope of this paper. In Appendix A.4 we provide a set of testable predictions (based
on the results found here and in the upcoming sections) that could be used for proper empirical
testing of the model, brie‡y discuss what kind of data is needed and how to get around problems
of unobservable parameters.
The overall pattern of the class of revolutions just described aligns with the dynamics of the
Iranian Islamic Revolution against the Shah in 1978-79. The Shah’s regime was intolerant to any
dissent, large and small alike (Milani 1988, p.122).16 Against this backdrop the revolution be-
gan, following a gradual increase in the misalignment between the Shah’s secular policies and the
increasingly religious sentiments in society (Moaddel, 1992). In line with Figure 3.1, this misalign-
ment pushed the hardest opponents of the regime –Khomeini and his closest group, who held an
extreme religious ideology –to initiate the revolution.17 Given the Shah’s continued policy of not
distinguishing between moderate and extreme dissent (Milani 1988, p.197), the radical Muslims did
not bother to mask their extreme views and dissented extremely. Meanwhile, the moderates were
not taking an active part in the revolution: “moderates among the various opposition groups...were
prepared to work within the system, and even welcomed the Shah’s proposal for free elections
scheduled for July 1979”(ibid, p.196). But later on, the dissent of the extremists paved the way
also for the moderates, who gradually started joining the revolution too (Razi 1987, Moaddel 1992,
Ghamari-Tabrizi 2008, Shadmehr 2015b). These moderate individuals advocated less extreme poli-
cies and used less extreme slogans than Khomeini, and even among Khomeini’s closest supporters
many were advocating a less religious policy than Khomeini himself (Ghamari-Tabrizi, 2008). Even-
tually also individuals from the other edge of the political spectrum (Marxists and others) joined
the protests (Milani,1988, p.197). These moves of the opposition weakened the Shah’s sanctioning
power and he felt forced to relieve the punishment on dissent. This led to the removal of censorship
and to increased usage of televised debates, i.e., acceptance of dissent in general (Milani 1994,
p.117). In line with our theoretical results, Milani (1994, p.116) claims that, in order to remain in
power, the Shah “either had to crush the growing movement or to relinquish some of his power and
strike a deal with the moderate faction of the popular movement. He opted to do neither.” I.e.,
what could possibly have saved the Shah was either an increase of force (K in our model) or the
implementation of popular policies (moving R in the religious direction).
16
This suggests a small : Milani (1988, p.122) writes: “the Shah, from 1958 to 1975, pursued a strategy that
was founded on a combination of controlled elite circulation and outright suppression of all manifestations of politi-
cal dissent”(our emphasis).
17
It is hard to pin down the exact starting point of the revolution. Some trace it back to 1977 and even earlier.
Our own account starts with the …rst violent clashes at Qom in January 1978 and the subsequent riots in several
cities in February that year.
14

4 Moderates starting with moderate dissent
4.1 Analysis
We move now to our main case of interest. Here < min f ; 1g. As Proposition 1 states, this
case entails that each revolution will be started by moderates dissenting moderately while extremer
individuals join later and dissent more than the initial moderate dissidents. A detailed formal
analysis can be found in Appendix A.2.
To understand the intuition behind this result note that the key property of this case is that
is relatively small, as depicted on the right side of Figure 2.2 (and in particular smaller than
). It is best illustrated by considering close to zero implying D is a step function. Then an
individual will perceive a high cost from even a small deviation from the blisspoint, but will not
distinguish between small and large deviations. This implies she will either speak her mind or, if
this is too di¢ cult given the sanctioning, be willing to go a long way to avoid punishment by the
regime –there is no point in compromising on a stance in between the blisspoint and the regime
when D is as large when doing so as when staying silent. Then, since an extremist who speaks her
mind is sanctioned heavily (large jt Rj hence large P), the extremist will submit to the pressure
and follow the regime. In a sense, the extremists are giving up on expressing their ideology if
they cannot express it exactly as they wish, thus they stay silent. Meanwhile, for a moderate it
will be equally costly to follow the regime as it is for the extremist (since D is a step function).
But, compared to the extremist, the moderate will face lower sanctioning when speaking her mind,
hence will prefer to speak her mind over taking the large personal discomfort of deviating even
slightly from her blisspoint. Put together, this implies that, if a revolution is started, moderates
will be the …rst out dissenting. Speaking their minds, these moderates pose only mild critique of
the regime. When the moderate individuals start dissenting, the approval (and thus strength) of
the regime falls, which enables less moderate types to speak their minds too. This further weakens
the regime’s punishment, enabling extremer individuals to express their extremer views as well and
so on. Thus, in contrast to the previous case and to the binary model, the revolution here is started
by moderates while extremists join only later.
The above description implies that great misalignment between an individual’s ideology and the
regime’s policy will induce the individual to stay silent. This has important implications for the
stability of regimes and for what may trigger a revolution. A biased regime (R 6= 0) can employ less
force yet remain stable: since the regime induces silence by those with private opinions su¢ ciently
far from it, a biased regime, whose policy is far from many in society, will have more approval
than a central regime with the same force. In Figure 4.1 this is illustrated on the left side (Case
1). Here, an increase in the misalignment between the regime’s policy and the people’s preferences
(when going from the …rst to the second schedule), due to a shift in the population’s preferences
away from the regime, induces less dissent.
The e¤ect of implementing popular policies is the opposite. The regime policy then aligns with
the views of more people and, since those who largely agree with the regime are the ones dissenting,
15

there will be more dissidents speaking their minds. Hence, a popular policy decreases the regime’s
approval and may ultimately be the catalytic event that starts a revolution. That is, unlike with
revolutions started by extremists, here popular policies can trigger the revolution.
An equivalent logic applies when the people’s preferences move to align more with the regime,
as illustrated on the right part (Case 2) of Figure 4.1. On the top schedule we start in a steady state
where the regime is very biased to the left. On the second schedule, the population’s preferences
have shifted to the left, i.e., they have become more aligned with the regime. This induces the
“new moderate left”to dissent, which reduces the regime’s approval thus its strength and enables
extremer individuals both on the left and on the right to join (third schedule). This reduces the
approval further, which enables also the most extreme rightists to …nally speak their minds. This
way, what started as a leftist revolution, following a leftward movement of public sentiments, ends
up being a rightist revolution, where the center of expressed opinions is eventually to the right of
the regime that collapsed, revealing that society was all along more rightist than the regime.
The fact that the revolution will be two-sided from the beginning implies that its momentum
will be strong initially – new dissenters will join from both the left and the right. Eventually,
however, like is depicted in the …gure, the potential new recruits are exhausted on the left, and
the momentum will be reduced. At these later stages the revolution may fail (see explanation and
Figure A.4 in Appendix A.2). Thus, unlike the revolution started by extremists, here the revolution
is strong initially and weak later.
4.2 Historic examples
The revolutionary pattern just described provides a theoretically-consistent explanation for an
important class of revolutions and mass protests that were previously unexplained by formal theory.
E.g., it aligns with many of the protest movements that led to the communist-regime collapses
in Eastern Europe in 1989-91 (…rst and foremost the soviet regime in the USSR, on which we
will elaborate) and to the recent Arab-Spring revolution in Egypt. We will brie‡y describe these
revolutions and protests through the lens of our theory. In Appendix D we discuss some alternative
mechanisms and their ability to explain these events.
4.2.1 The collapse of the USSR in 1989-1991
The fall of communism in the USSR …ts our description both in being triggered by Gorbachev’s
implementation of a popular policy (Perestroika, to be discussed shortly) and by the evolution of
participation from moderates to extremists. The …rst to protest was indeed a party insider –Boris
Yeltsin – who at various meetings in 1986-1988 openly criticized Gorbachev and his government
for the reforms not being su¢ ciently far reaching (Breslauer, 2002 p.130-132).18 His dissent spread
18
Also in other Eastern-European countries the initial protesters were moderates or even party insiders. E.g., in
Poland and Hungary, moderate dissidents instigated liberal reforms and made demands for free elections (Pfa¤,
2006, p.1). Hungarian communist-party leader Karoly Grosz was quoted saying that “the party was shattered not
by its opponent but –paradoxically –from within”(Przeworski 1991, p. 56).
16

Figure 4.1: Distribution of stances over time when < 1. In both cases R = 0:8 and
…xed while the distribution of types changes. Case 1: the shift of private preferences to the left
does not trigger a revolution. Case 2: the shift of private preferences to the right does trigger a
revolution starting with moderates dissenting moderately.
17

within the party to other, more liberal (i.e. extremer) members eventually joining forces with
Yeltsin in forming the inter-regional deputies group in 1989 (Lane and Ross, 1994). The news
about Yeltsin’s insubordination spread and enabled the formation of dissident groupings also out-
side the communist party in 1990. E.g., the Democratic Russia Election Bloc and the Democratic
Russia Movement were formed by grassroots, pro-democracy and anti-communist organizations
and generally politically-una¢ liated persons. These groups had a liberal and democratic political
agenda that was extremer than that of Yeltsin, with the main goals of removing the Communist
Party from power, transforming the economy to be market based and ridding society of the commu-
nist legacy (Brudny, 1993).19 The protests spread, not least with the help of these groups (Urban
et al., 1997; Brudny 1993), to broader parts of society. They evolved to mass protests and rallies
in 1990-91 demanding democratic reforms and economic liberalization far beyond Perestroika.
Beyond the progress of participation and statements from moderate to extreme, another im-
portant feature of this class of revolutions in our model is that the undermining of the regime is
initiated by individuals from both sides of the political spectrum. This implies that regimes may
be undermined by truly “strange bedfellows”, in the sense that they are pulling the public opinion
in two di¤erent directions. Indeed, the dissent against Gorbachev was two-sided early on (Sander-
son, 2015, p.126). Apart from “liberal” Yeltsin, hardline communists within the party criticized
Gorbachev’s liberalization reforms (but for being too far-reaching) and later even tried to overturn
them by staging a coup. Part of the communist opposition to Gorbachev came from the Soyuz
(Union) group which, formed in 1990 by two army generals, wanted to preserve the Soviet insti-
tutions and way of doing things –a form of conservative opposition to Gorbachev and his reforms
(Lane and Ross, 1994). In sum, the dissent against Gorbachev increased from all directions and
his total support fell dramatically as documented by voting records within the party.20 Since the
population in the USSR had a more liberal and more democratic inclination than the communist
party (Gibson, 1997) this was the main direction the protests took.
The further puzzle is, of course, that the trigger of the revolution in the USSR (which then spread
to Eastern Europe) was the movement of the regime’s policy in the direction of the liberal sentiments
in society. Perestroika (i.e., economic reforms) is the equivalent of a decrease of policy bias (jRj)
in our model. Gorbachev implemented Perestroika as a form of popular policy – in the hope to
revitalize and modernize the Soviet Union –and thus to increase the regime’s approval (Gorbachev,
1987). However, these reforms instead were the trigger of a revolution as they unleashed social
forces that brought about the dissolution of the USSR (Lane and Ross, 1994; Brown, 1997). These
19
At various stages of the revolution some of these groups supported Yeltsin. However, the relationship between
Yeltsin and these groups was never frictionless and collapsed when Yeltsin disagreed with the radical agenda these
groups wanted (Brudny, 1993). E.g., the Moscow Association of Voters (the predecessor of Democratic Russia) had
an agenda of radicalizing Perestroika and of economic and institutional reform. Democratic Russia itself wanted to
overthrow the Nomenclatura and urged Yeltsin to call upon Russians to vote against the union in a referendum.
He refused and instead signed the new union treaty in July 1991. Democratic Russia then decided to openly crit-
icize Yeltsin. In earlier occasions Yeltsin had distanced himself from Democratic Russia and its platform of over-
coming the communist legacy in ideology and politics, transforming to a market economy etc. See Brudny (1993)
for further details.
20
See Figures 5 and 6 in Lane and Ross (1994) and the descriptions on their pp. 450-451.
18

consequences were unintended by the leadership (see Gorbachev, 1987 p.17), came to the surprise of
most experts (as documented by Kuran 1991 and Lipset and Bence 1994) and are indeed counter to
the predictions of the standard models of revolutions. How can popular reforms, such as Perestroika,
trigger a revolution? Our model provides a possible answer to this largely unresolved question. In
the case described in this section, the implementation of popular policies leads to increased dissent
by moderates as it becomes easier for them to speak their minds when their views are closer to
the new policy. In the USSR example, Yeltsin found it easier following Perestroika to express his
critique since this critique was not considered as extreme by the regime after it had changed its
own policy. In earlier days, before Perestroika, Yeltsin’s critique would have been considered very
far from the regime’s policy and hence would have been sanctioned heavier. The initial moderate
critique then paves the way for more extreme dissidents and for extremer critique. Our answer
to Przeworski’s (1991, p.1) challenge to “identify the theoretical assumptions that prevented us
from anticipating these developments”is thus that previous models assume that individual dissent
is triggered only by a great misalignment of preferences with the regime. Popular policies reduce
such misalignment and hence cannot trigger a revolution in these models. If instead one looks at
a theoretically microfounded model of dissent, like ours, it follows that also moderates may start
a revolution (as observed) and hence that popular policies can be the trigger. In fact, possibly
realizing that his reforms had triggered the dissent, Gorbachev tried at the end of his rule to undo
them and instead strengthen the post of the executive presidency (Lane and Ross, 1994 p. 448).
But this was evidently too late. Note that, in parallel to Perestroika, Gorbachev also implemented
Glasnost (increased openness and freedom of speech). In our model this is equivalent to a decrease
in K, which fosters more dissent. Thus, both these reforms had the e¤ect of undermining his
regime.
4.2.2 The Arab Spring in Egypt in 2011
Also in Egypt dissent was initiated by moderates. Prior to 2011, extreme opposition to Mubarak
was harshly sanctioned (Muslim-Brotherhood members were banned from running to parliament
and many of them were arrested during the 2005 parliamentary elections campaign) hence to a
large extent excluded from the public sphere. Meanwhile, moderate opposition was present and
practically ignored by the regime. E.g., moderate opposition movements like Kefaya, which was
founded by Egyptian intellectuals in 2004 to protest against Mubarak’s intention to transfer power
directly to his son Gamal, were allowed to run for parliament and protest on the streets.21 Likewise,
when the Arab Spring revolution broke in 2011, the initial protesters on the Tahrir Square were
moderate liberals and moderate conservatives (Al Jazeera 2011, Lesch 2011). The most extreme
factions (i.e., the Muslim Brotherhood, Gama’a al-Islamiyya and the Sala… movement) were not
present in the protests initially. They only joined later, after Mubarak had been weakened by the
21
One of Kefaya’s founding members, Hany Anan, even declared: “We are showing Egyptians that we can chal-
lenge the ruler, we can tell him we don’t want you, that’s enough, you go, and we can do this in public and still go
back to our homes, maybe with some wounds or some bruises, but we still go home”(Saleh 2005).
19

initial protests and it was safer for them to express their views.22 Once they joined, they were
advocating the implementation of Sharia law thus challenging the claims of the initial protesters.
Just like with the hardline communists and liberals in the USSR, the Arab-Spring revolution in
Egypt was two-sided essentially from the beginning. The protesters on the Tahrir Square consisted
of some who suggested that Mubarak’s regime was not su¢ ciently liberal and of others who said
he was not su¢ ciently conservative and religious. Furthermore, while a shift in private opinions
towards more liberalism (a leftward movement of the opinion axis when moving from the …rst to the
second schedule of Case 2 in Figure 4.1) may have been conducive to the burst of the revolution,
the later protests and elections revealed a di¤erent picture of the true preferences of Egyptian
society (POMEPS, 2011).23 It showed that, in fact, Egyptian society as a whole was even more
conservative than Mubarak’s regime (in line with the description in Case 2 in Figure 4.1, where
the average opinion after the shift is to the right of R = 0:8, which represents Mubarak’s regime
in that …gure). This way, as predicted by the model, what started as mainly a leftist (liberal)
revolution ended up being a rightist (conservative) revolution instead.
In Appendix D we discuss some alternative and complementary explanations that are orthogonal
to ours, such as those attributing the cause of the revolution to economic incentives. However, we
brie‡y mention here a few mechanisms that are captured by our model and may have contributed
to the starting of the revolution. There seems to be a consensus that the spark of the revolution in
Egypt was the adjacent Tunisian Revolution, which initiated the whole Arab Spring. One possible
reason for this contagion in protests is that beliefs about the regime’s strength or legitimacy changed
after the largely successful protests in Tunisia were observed. This has been modeled formally as
a domino-theory of protests between countries by Chen and Suen (2016). In our theory this would
be captured, in a reduced form, by a shock to K that leads to lower approval or by a direct
shock to the approval itself. Another possible explanation is that the Tunisian Revolution, and
the pictures observed from there, increased the emotions of the Egyptian population, essentially a
non-rational-choice argument as has been emphasized by, e.g., van Stekelenburg and Klandermans
(2007, ch. 5) and Aminzade (2001). Increased emotions would in our model imply a shift in the
relative weight towards the private preferences of the individuals and away from the sanctioning,
which is equivalent to a reduction in K. Furthermore, social media helped coordinate protesters
and thus enabled overcoming the collective-action problem (see ElTantawi and Wiest, 2011; Lim,
2012; and Chwe 1999 and Edmond 2013 for formal modeling). In our framework, the case where
coordination reaches a crucial point where it is suddenly revealed that objection to the regime is
widespread, is captured by a shock to the approval.
22
E.g., a BBC news pro…le on the Muslim Brotherhood reports that initially “(t)he group’s traditional slogans
were not seen in Cairo’s Tahrir Square. But as the protests grew and the government began to o¤er concessions,
including a promise by Mr Mubarak not to seek re-election in September 2011, Egypt’s largest opposition force
took a more assertive role”(BBC, 2013).
23
The shift in the population’s preferences towards more liberalism/secularism may have been the result of the
economy-wide growth (Davies 1962; Gurr 1970; Inglehart and Welzel 2006) or the increase in the level of educa-
tion (see Goldstone 2011 and Campante and Chor 2012). The further potential e¤ects of the education reforms are
discussed in Appendix D.
20

5 Extremists starting with moderate dissent
5.1 Analysis
The …nal case is when > 1 and 1. This case shares the moderate-to-extreme progress of
public statements during the revolution with the case of the previous section, while sharing the
leading role of extremists in the revolution with the class of revolutions described in Section 3. A
detailed and more mathematical analysis can be found in Appendix A.3, here we only focus on the
intuition behind the results.
An important feature of this case is that > 1 (P is convex), which represents a regime that
is tolerant towards small dissent while punishing harshly larger dissent (see Figure 2.1). This
intuitively implies that each type will compromise between fully obeying the regime and speaking
her mind: since the regime is tolerant toward small dissent, the citizens do not have an incentive
to keep completely silent. At the same time, when D is convex, the citizens are lax about small
deviations from their blisspoints and hence do not mind compromising a little. But the convexity of
D also implies they are sensitive to large deviations from their blisspoints, implying that extremists,
whose blisspoints are far from the regime, dissent more than moderates. Hence, those starting
a revolution will inevitably be the extremists. However, as dissenting extremely is sanctioned
harshly, they will start o¤ by posing mild critique. When they do so, the approval and thus
strength of the regime fall and these extremists then …nd it possible to express harsher critique.
Meanwhile more moderate individuals increase their dissent too. This implies further weakening of
the regime, enabling extremer dissent and so on. This way, the most extreme types lead the way
during the revolution and continuously push the freedom of speech further, backed up from behind
by moderates. This is an important di¤erence between this class of revolutions and the revolutions
described in Section 4. While both are characterized by statements becoming extremer over time,
they di¤er in who the initiators are –moderates in Section 4 versus extremists here.
The fact that extremists dissent more than moderates also implies that it is great misalignment
between an individual’s ideology and the regime’s policy that triggers dissent. Hence, implemen-
tation of unpopular policies, whereby the regime becomes more misaligned with the population,
can trigger a revolution. This is depicted in Figure 5.1 where, on the top schedule, we are in a
steady state with a somewhat left-biased regime. The regime then implements more left-biased
thus unpopular policies (second schedule) . This triggers more dissent, thus weakening the regime,
inducing more dissent and so on until the regime collapses on the bottom schedule.
Unlike the two previous classes of revolutions, here the revolution never loses its momentum
since it is the gradual shift of statements that drives it instead of recruitment of new protesters.
Hence, once a revolution has started it will always succeed, unless the regime reacts on time by
either increasing its force (e.g., by recruiting more troops) or implementing popular policies to
appease the population.
21

Figure 5.1: Distribution of stances over time in a stylized revolution starting with extremists dis-
senting moderately ( > 1, 1). The regime starts at R = 0:3 and in the second period
moves to R = 0:5 (which triggers the revolution) and stays there. The distribution of types is
constant. For expositional purposes, the diagram depicts a case of = :
22

5.2 A historic example
The main feature characterizing this class of revolutions is that here during the whole revolution it
is the extremist dissenters who are the ones expressing the strongest criticism. Furthermore, these
extremists constantly increase their dissent against the regime and pull other factions of society
along with them.
An example of a successful revolution of this class –the April Revolution in South Korea in 1960
–is provided in Appendix C.2. Here we analyze instead the student-led protests on Tiananmen
Square in Beijing in 1989 (for a detailed account see Zhao 2001), with the important di¤erence
being that in the case of Beijing the protests did not develop into a successful revolution – the
regime survived.
The former politician, Hu Yaobang, who was popular among students, passed away on April 15
1989 and this led a large number of students to mourn his death (Pan, 2008). Two days later, a
commemoration (which was considered more dissenting than individual mourning) was organized.
This organization quickly evolved into a declaration of demands for political reform and thereafter,
on April 18, to a sit-in where students demanded to meet with the leadership of the political party.
On April 21, students began organizing themselves formally into unions and some workers into a
federation, writing texts challenging the regime (Walder and Xiaoxia, 1993) and the next day serious
rioting broke out in several places. Five days later, the Autonomous Student Union staged a march
to the Tiananmen square breaking through police lines after which the leaders of the union, Wang
Dan and Wu’erkaixi, called for more radical measures to regain momentum. This led to hunger
strikes and also to the expressed support for the strikes by others who did not themselves strike. On
May 17–18, around a million Beijing residents, including low-ranked representatives of the regime
such as party o¢ cials and police o¢ cers, demonstrated in solidarity of the hunger strikers. I.e.,
also moderates started protesting, though less …ercely than the initiators. This was a sign of the
decreased approval of the regime, as predicted by our model, with the sign of the regime’s consequent
weakening being the increasingly open and positive reports about the protests in the media. All this
time, the soft approach of the regime –of showing sympathy toward the demonstrators and looking
for a dialogue with them –as advocated by Zhao Ziyang, the General Secretary of the Communist
Party, was giving the tone. This approach of containment of the moderately deviant expressions is
predicted, if not interrupted, to have led to the eventual collapse of the regime. However, on May
17, a leadership meeting was called, where Zhao Ziyang’s concessions-based strategy was thoroughly
criticized and it was decided to declare martial law (martial laws are more generally analyzed in
Appendix A.4). In terms of our model, this was a decision to substantially increases K. The
implementation of the martial law that led to the heavy-handed crackdown on the protests on June
4 eventually stopped the mass protests.
In the case of the protesters on Tiananmen Square it is hard to say what the catalytic event
starting the protests was. The regime had been implementing popular policies throughout the
1980s. These reforms were initiated by Chairman Deng Xiaoping, the successor of Mao Zedong,
and were indeed generally well received by the public. According to our model, such policies would
23

make a revolution less likely and hence cannot be the cause of the revolution. We emphasize the
words “less likely”since this policy change does not mean a revolution cannot happen at all. What
could have led to the start of protests despite the policy change is an even greater shift of the
private views of the population towards liberalism. This is indeed in line with the accounts of
Davies (1962), Gurr (1970) and Inglehart and Welzel (2006), who show that economic reforms tend
to shift preferences towards more liberalism. Another possibility is that the regime had reduced
its force during the liberalization process. Finally, there may have been a temporary shock to the
approval of the regime as part of the general revolutionary wind that blew all over the communist
world, and in particular following the initial gathering to mourn the death of Hu Yaobang, which
had helped the participants overcome the collective-action problem during their meeting.
6 Conclusions
This paper has presented a uni…ed framework to explain three classes of popular revolutions and
mass protests that have been observed historically: 1) revolutions starting with extremists dissent-
ing extremely; 2) revolutions starting with moderates dissenting moderately; and 3) revolutions
starting with extremists dissenting moderately. Earlier models of ideologically-driven revolutions
invariably predict that the revolution will be initiated by ideological extremists and are silent about
the extent to which each individual will dissent and how this will change over time. Thus they
cannot distinguish between the …rst class (Iran 1978-79) and the third class (Tiananmen Square
in 1989) of revolutions and are outright inconsistent with the second class of revolutions (Egypt in
2011 and the fall of Communism in 1989-91).
The classi…cation into three classes of revolutions is shown to be exhaustive in our model. It
spans the parameter space of and , the parameters that capture the curvature of the two costs
a¤ecting the individual choice of dissent during a revolution: the cost of deviating from the private
blisspoint (or economic interest) and the sanctioning cost for dissenting against the regime. Each
class of revolutions has its own unique set of attributes, characterizing which faction in society
– moderates or extremists – initiates the revolution, how it progresses to other parts of society,
which views are expressed by participants at various stages, how the regime may unknowingly
trigger the revolution and what it can do to stop the revolution at di¤erent stages. The overarching
pattern is that the extremeness of the initial statements is determined by the curvature of the
regime’s punishment. Concave sanctioning e¤ectively silences moderate dissent hence, under such
sanctioning, a revolution will start with extreme dissent. On the other hand, a convex sanctioning
discourages extreme dissent hence a revolution will start with moderate dissent. In comparison,
which faction (extremists or moderates) will start the revolution is determined by the curvature
of the cost of deviating from the individual blisspoint. A convex ideological cost makes it costless
to deviate a little from one’s blisspoint hence moderates will stay silent while extremists are more
prone to start a revolution since for them it is too costly to stay silent. On the other hand, a
concave ideological cost induces people to either perfectly speak their minds or stay completely
24

silent. Hence moderates, who are not heavily punished when speaking their minds, may initiate a
revolution while extremists will be the last out to protest.
Naturally, not all actual revolutions follow one of the three patterns. Furthermore, our analysis
abstracts from important factors, e.g., intervention by outside forces; con‡icts between di¤erent
revolutionary groups about the targets of the revolution; di¤erences between individuals other than
ideological; optimal reactions by a forward-looking regime; and changes in the regime’s leadership
during the revolution (as was shown to be crucial in the case of the protests on Tiananmen Square).
However, as the historic examples provided in the paper demonstrate, our model is able to capture
many important aspects of real revolutions that cannot be captured with the existing models.
Naturally, our framework can be used to study other aspects of revolutions and mass protests,
where further questions could be answered and more parameters could be endogenized.
25

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30

APPENDICES FOR ONLINE PUBLICATION
0

A Detailed description of the three revolution classes and empir-
ical predictions
This section describes in more detail the analysis based on the model outlined in Section 2. Most
of the results in the paper, and in particular those stated in Proposition 1, hold for any continuous
distribution of types g (t) and without setting any restrictions on the functional form of the approval
function A, and in fact can be derived also with more general functional forms for P and D.
However, showing some speci…c further results requires a more explicit functional form of the
distribution of types and of A. For analytical tractability we will thus assume from now onwards
that t U ( 1; 1) and that the approval of the regime is linear in the deviations from it. I.e.,
A = max 0; 1
Z 1
1
js (t) Rj dt . (A.1)
This is a speci…c functional form of the approval function A for which A = 1 if nobody dissents
(s (t) = R 8t). We normalize = 1 so that a non-biased regime (R = E [t] = 0) has zero approval
precisely when all types speak their minds (s (t) = t 8t).24 This ensures that for any R 2 [ 1; 1]
we get A = 0 whenever all types speak their minds. It further implies that, when a regime is biased
(R 6= 0), A may equal 0 also without all types speaking their minds (which re‡ects that, when all
speak their minds under a biased regime, dissent is larger than when all speak their minds under
a non-biased regime). This normalization is largely without consequence apart from implying that
even a central regime loses all of its strength when all speak their minds (which would not be true
for < 1). Like we did in the body of the paper, we refer to a regime with R 6= 0 as biased and
use jRj as a measure of the regime’s bias.
A.1 Detailed analysis of extremists starting with extreme dissent
We start by considering the case where < min f ; 1g. This case can be further divided into two
subcases: < 1 and < 1 < . While these two cases di¤er in some details, they are largely
the same from the point of view of what we are interested in. Hence, for ease of exposition, we will
focus here on the subcase < 1.25 We begin by analyzing the individual’s choice of dissent
for a given K and then analyze how the individual stances a¤ect K.
By di¤erentiating L (in (2.3)) twice with respect to s it is immediate that when < 1 the
second-order condition is not ful…lled, implying that an individual will choose either s (t) = R or
s (t) = t. It is simple to further show that each individual has a unique best response: there exists
a cuto¤ distance = K
1
such that all types closer to the regime than will fully follow the
regime (i.e., s (t) = R when jt Rj ) while types further from the regime than will speak
their minds (i.e., s (t) = t when jt Rj > ), as illustrated for a biased regime in Figure A.1.
Hence, the regime induces silence by those who largely agree with it.
The intuition is easy to understand. The important property of this case is that is relatively
small, which implies that the regime applies a (very) concave punishment whereby even small
dissent is heavily punished while more extreme dissent is punished only slightly more. This will
induce an individual to either fully follow the regime or, if she does not fully follow it, she might
as well dissent quite a lot. Then, since types far from the regime perceive the highest cost (D)
when following the regime, these types will be the ones who may dissent –and dissent quite a lot
24
I.e., = 1= 2
R 1
0
tdt = 1.
25
See Appendix sections B.2.2 and B.3.1 for a treatment of the other subcase ( < 1 < ).
1

Figure A.1: An illustration of an equilibrium distribution of stances under a biased regime for
< 1.
if they do given their extreme views –while types close to the regime will be silent. The cuto¤
between those following the regime and those who do not is naturally increasing in the strength of
the regime K, so that a stronger regime sees less dissent. The result that extremists speak their
minds and moderates stay silent has important implications for the stability of regimes and for the
revolutionary dynamics as expressed in the following proposition.
Proposition 1 When < 1 :
1. Existence of a stable steady state: A stable regime exists i¤ it employs su¢ cient force,
and the more biased its policy is the more force it needs to employ.
2. Catalytic events: A revolution may start following a shock to the regime’s approval or force
or following implementation of unpopular policies.
3. Dynamics of participation:
(a) Initially only the most extreme types participate in the revolution, but over time types
who are more moderate join it too.
(b) For any regime with jRj 6= 0, the revolution will start only on one side of the political
spectrum.26
4. Dynamics of statements: Initially dissents are extreme and over time, as moderates join
the revolution, the new statements are more moderate.
Proof. See Appendix B.4.
We start by explaining the dynamics of the revolution (parts 3 and 4) since this largely deter-
mines what makes a regime stable (part 1) and which events may initiate a revolution (part 2). The
revolutionary process follows from the dynamics of the cuto¤ between those who dissent and those
who do not ( i). As explained earlier, when the regime uses (very) concave sanctioning, it induces
26
Unless there is a very large shock to the force or approval of the regime or a very large change to its policy.
2

Figure A.2: < 1 and a moderately biased regime (jRj 2 ]0; 0:5[). The full line depicts the
intertemporal-dynamics function Ai+1 = f (Ai) and the dashed line depitcs the 45-degree line
where Ai+1 = Ai. The vertical lines depict the stable (Ass) and the unstable (Auss) steady states.
Note that when the regime is very biased (jRj 2 ]0:5; 1[), the phase diagram will not contain the
left convex part.
dissent by extremists but not by moderates. This means that, if a revolution starts, the …rst ones
to dissent are the most extreme types. When these extremists start dissenting, the strength of the
regime falls, which makes it possible also for less extreme types to dissent. This way, increasingly
moderate types join the revolution and they dissent less than those who started it (as summarized
in parts 3a and 4 of the proposition). If the regime is, say, left of center (R < 0), the …rst dis-
senters will be on the far right –the revolution starts only on one side (part 3b of the proposition,
illustrated in Figure A.1). During this phase, the revolutionary momentum is rather low, since new
recruits are only coming from the right, while later, if the regime has gotten su¢ ciently weak, new
recruits might appear also on the left side of the regime. This has important implications for the
fragility and success of a revolution as will be explained later.
As a tool to understand the additional results, consider the phase diagram in Figure A.2 which
depicts a stylized example of the intertemporal-dynamics function Ai+1 = f (Ai). The higher is
current approval (Ai), the higher is the regime’s strength (Ki), which implies less dissent thus higher
approval in the next period (Ai+1). Hence, Ai+1 is a (weakly) increasing function of Ai as can be
seen in the …gure. Quite naturally, for any approval level Ai, an increase of the regime’s force K
raises Ai+1 (through an increase of Ki+1 = KAi). This implies that the function Ai+1 = f (Ai) in
Figure A.2 shifts up as K is increased. For su¢ ciently small K, Ai+1 is always below the 45-degree
line, implying no Nash equilibrium with a stable regime exists.27 This naturally implies that there
is a minimum amount of force a regime has to employ to stay stable. For su¢ ciently large K there
may exist one, two, or three (inner) intersections with the 45-degree line. The …rst intersection
27
Note that f (A) is a summary statistic of the best responses of the population for each A. In particular, each
value of A > 0 corresponds to a unique value of (A). Hence, an intersection of f (A) with the 45-degree line at a
given value of Ai(> 0) corresponds to a Nash equilibrium.
3

from the left is an unstable steady state, since below it f (Ai) < Ai and above it f (Ai) > Ai. The
second is stable and the third is unstable. Additionally, as is the case in the …gure, there is one
stable steady state at Ai = 0 and there may be one at Ai = 1.
As those with views far from the regime are the ones dissenting, a biased regime, with policies
far from most of the population’s views, will induce more dissent for any given level of regime
strength Ki (biasness shifts down the dynamic approval function in Figure A.2).28 Hence, biasness
has to be compensated for by the employment of more force (K) for a stable steady state to exist
(part 1 of the proposition). Furthermore, since increasing the bias decreases the approval function,
the unstable steady states move right while the stable steady states move left in the phase diagram.
This means that biased regimes are inherently less stable and that an implementation of unpopular
policies (increase in the bias) may ultimately be the catalytic event that triggers a revolution by
making a previously stable steady state seize to exist (as stated in part 2). Other catalytic events
are a shock to the regime’s force (a shift downward of the approval function) or a shock to the
approval (lowering Ai), if they put Ai+1 = f (Ai) in a zone where the political system converges
downwards. Thus, in order to prevent the success of the revolution, the regime has to either increase
its force (K) or implement policies that are more popular (thereby lifting the dynamic approval
function).
The phase diagram in Figure A.2 captures further properties of the dynamics. It is easier to
understand them when reading the diagram from right to left, which is the direction in which
approval changes (falls) during a revolution. For illustration, suppose the regime is left-biased
(R < 0). The rightmost part of the …gure is where, as approval (Ai) falls, dissent in the next period
increases only on the right side of the regime (the extremists dissent). At some point approval is
su¢ ciently low so that also individuals on the far left start dissenting. This is where f (Ai) kinks
and becomes steeper (to the left of the kink) since from here onwards new recruits come from both
sides of the regime, implying approval falls faster.29 The …nal ‡at part of the approval-dynamics
function is where current approval is so low that the regime will not be able to gain any approval
at the next period (f (Ai) = 0).
As explained earlier, when the kink exists in the phase diagram there may be up to two stable
steady states with Ass > 0 (one internal and one where Ass = 1 as in Figure A.2). If there is
only one stable steady state with Ass > 0, a shock that eliminates it will lead to a successful
revolution (one that ends with Ass = 0). However, when two stable steady states with Ass > 0
exist, a revolution that starts from Ass = 1 may fail to topple the regime. Suppose the regime is
left biased. The revolution will start with the extremists on the right side recruiting less extreme
followers on their side of the political scale. But, since new recruits come only from the right side
of the regime, the momentum of the revolution will be low and the revolution fragile. In particular,
the revolution is bound to fail if the shock that sparks it eliminates only the stable steady state with
Ass = 1, while the internal steady state is not eliminated. However, if the revolution eventually
reaches the stage (to the left of the kink) where approval is so low that also the most extreme leftists
start dissenting, then the revolution becomes two-sided, gains momentum and is bound to succeed.
This has the implication that a revolution that starts with extreme dissent is fragile initially but
strong at later stages.30
28
More precisely, an increase in bias shifts the convex part to the right of the kink downwards and at the same
time widens this part outwards in both directions. This has to do with the fact that biasness a¤ects dissent not
through a¤ecting –which is independent of jRj –but through a¤ecting the actual mass of types at distance
larger than from the regime, which increases in jRj when the regime is su¢ ciently biased to induce dissent only
at the opposite extreme side, as can be seen in Figure A.1.
29
The kink is the point where Ai induces i+1 = 1 jRj (in Figure A.1, 1 jRj is the distance from the regime
to the left edge corner).
30
Note that when the regime is very biased (jRj 2 [0:5; 1]), the phase diagram will not contain the left convex
4

It is worth noting that a shift of private opinions, say to the right, is equivalent to the regime
changing its policies to the left. This is since it is the relative position of the type space vis-à-vis R
that matters. This means that our results about a change in the regime’s policy have an equivalent
in an opposite change of private preferences. E.g., what may start a revolution is that, over time,
the private preferences of the population shift away from the regime’s policies as depicted in Figure
3.1.
A.2 Detailed analysis of moderates starting with moderate dissent
We move now to the case where < min f ; 1g. This case can be further divided into two subcases:
< 1 and < 1 < . While these two cases di¤er in some details, they are largely the same
from the point of view of what we are interested in. Hence, for ease of exposition, we will focus
here on the subcase < 1.31
As in the previous section, we start by describing the individual choice of dissent for a given K.
By di¤erentiating L twice with respect to s it is immediate that when < 1 the second-order
condition is not ful…lled, implying that an individual will choose one of the corner solutions: either
s (t) = R or s (t) = t. It is simple to further show that there exists a cuto¤ distance = K
1
such that all types further from the regime than will fully follow the regime while types closer to
the regime than will speak their minds, as illustrated for a biased regime in Figure A.3. Hence,
as opposed to the …rst class of revolutions, here the regime induces silence by those who dislike it
the most while those who largely agree with the regime pose mild critique of it. To understand
the intuition behind this result note that the important property of this case is that is relatively
small and in particular smaller than . Consider, e.g., the special case of = 1. First note that,
since < 1, individuals will perceive a relatively high cost from even a small deviation from their
blisspoints, but will not distinguish much between small and large deviations. Hence, they will
either speak their minds or, if this is too di¢ cult given the punishment, be willing to go a long way
to avoid punishment by the regime. Then, as = 1 implies that speaking one’s mind is considerably
harder for extremists, they will be the ones submitting to the pressure and following the regime,
while moderates will …nd it bearable to speak their minds. The cuto¤ value – between those
speaking their minds and those staying silent –is decreasing in K, re‡ecting that the stronger the
regime is, the smaller is the share of the population speaking their minds.
The result that extremists keep silent while the moderates are speaking their minds has impor-
tant implications for the stability of regimes and for the revolutionary dynamics as expressed in
the following proposition.
Proposition 2 When < 1 :
1. Existence of a stable steady state: A stable regime exists i¤ it employs su¢ cient force,
and the more biased its policy is the less force it needs to employ.
2. Catalytic events: A revolution may start following a shock to the regime’s approval or force
or following implementation of popular policies.
3. Dynamics of participation:
part. This implies that the regime can collapse even if dissent is only on one side of it, re‡ecting an inherent weak-
ness of very biased regimes. For example, a very left-biased regime can be toppled by a purely right-wing revolu-
tion.
31
See Appendix sections B.2.3 and B.3.2 for a treatment of the other subcase ( < 1 < ).
5

The dynamics of revolutions

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