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Inequality and Riots
By
Klaus Abbink ‡, David Masclet* and Daniel Mirza#
This version : March 2008
Abstract
One of the perhaps rare subjects that have inspired research across a variety of social science disciplines is that of the relationship between inequality and inter-groups conflicts. In this paper, we focus on social inequality. The latter arises whenever some groups experiment discrimination and thus have limited access to some social and labour resources like education or employment. The aim of our paper is two fold. First, we experimentally investigate under which conditions social inequality explains inter-group conflicts. Second we investigate the factors that make preferences for riot translate into actions. Indeed like all collective actions, civil conflicts and riot require coordination. Our experiment consists of a two stages game. In a first stage, subjects play a proportional rent seeking game to share a price. The share of the prize depends both on their effort and that of the other players. Social inequality is modelled exogenously by attributing to some subjects (the advantaged group) a larger share of the price than other subjects (the disadvantaged group) for the same amount of effort. In a second stage, after being informed about the first stage payoff of each group member, players can coordinate with the other members of their group to reduce (“burn”) the other group members’ payoff. Several treatments are considered : the treatments differ in the degree of social inequality set between the two groups. We find that despite the cost of riot, a non negligible number of players chooses to destroy other group's money. Our results also indicate that disadvantaged groups significantly riot more than advantaged groups for intermediate levels of inequality. In contrast no conflicts are found for very low and/or very high levels of inequality. Key words : Design of experiments, Experimental economics, Social Inequality, Conflicts JEL classification: D72; C91 ‡ Universiteit van Amsterdam, Faculteit Economie en Bedrijfskunde (FEB) CREED; Roetersstraat 11 , 1018 WB AmsterdamThe Netherlands; [email protected].
* Corrresponding author : CREM (CNRS – University Rennes 1), 7, place Hoche 35065 Rennes, France. Tel : +33 223 23 33 18. Email : [email protected]
# CREM (CNRS – University Rennes 1), 7, place Hoche 35065 Rennes, France. Tel : +33 223 23 33 19. Email : [email protected]
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Introduction
When a wave of violence swept through the suburbs of French cities in 2004, the nation was
desperate for answers. How could it happen that, in a civilised and highly developed society
youths all over the country indulged in raw violence? And why did it happen then? Many
observers pointed at long-standing problems in the suburbs, which are mainly populated by
immigrants from northern Africa. Neglected by society, these youths faced a bleak future with no
perspective of integration into the regular job market. Tensions arising from discrimination and
inequality then erupted into violence and widespread rioting.
The link between inequality and violent rebellion is almost a universal assumption.1 The
intuition behind this positive relationship is that both poverty (“absolute deprivation” theory) and
high levels of inequalities (“relative deprivation”) would lead the disadvantaged people, when
they have nothing to lose, to express their emotion and achieve redistributive demands when it is
possible by resorting to civil violence (Gurr, 1970). While these theories seem immediately
plausible, they do not explain spontaneous outbreaks of revolt alone. In the French example, it is
widely accepted that the immigrant youths in suburban ghettos are socially and economically
disadvantaged. Yet this has been the case for decades and the situation has not noticeably
deteriorated prior to the riots. So if inequalities caused the riots, why has it been quiet for so
long? How could the unrest suddenly emerge out of the blue?
To answer these questions one has to look at the strategic environment. While many
disadvantaged people may have a preference for unrest, turning this urge into action is another
matter. A single rioter will not gain much satisfaction from his endeavour. In all likelihood he
will be arrested and that is the end of the game. Only if the rioters reach a critical mass, they
stand a chance against the authorities. The crucial factor lies in the beliefs that a rioter has about
the actions of like-minded individuals. When a frustrated youth believes that sufficiently many
other frustrated youths will turn to the streets, then it becomes the best response for him to join.
If, however, he believes that most others will stay at home, then he better stays calm himself.
Thus, the riot game has two extreme equilibria: One in which nobody riots and one in which all
1 The lineage of this idea runs from Aristotle and Plato, to de Tocqueville. Aristotle considered inequality to be the "universal and chief cause" of revolutions, contending in The Politics that "Inferiors revolt in order that they may be equal, and equals that they may be superior." source of political faction. According to Plato “if a state is to avoid the greatest plague of all—I mean civil war, though civil disintegration would be a better term—extreme poverty and wealth must not be allowed to arise in any section of the citizen-body, because both lead to both these disasters” (Plato, cited in Cowell 1985:21). Tocqueville's "dread" of "the insistent and immediate demand for equality in our live implies a strong relationship between inequalities and conflicts: "the spread of norms of equality makes invidious comparisons universal and all forms of subordination illegitimate. This will spur the universal, permanent, inevitable, and irresistible revolution of emancipatory movements among the disadvantaged."
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potential rioters do.2 With this strategic situation in mind, it becomes clear that if there is a
relationship between inequality and riots, it must work in an indirect way: Not only must
disadvantaged individuals develop a level of frustration that makes them want to take destructive
action, but also they must form a believe that sufficiently many others will take action at the
same time. Due to the two extreme equilibria of this game it is not surprising anymore that,
although frustration may build up slowly over years, outbreak of violence happens extremely fast
and seemingly out of the blue.3 Preferences may change slowly, but beliefs about others’
behaviour can flip almost instantly.
The two-equilibria structure of the riot “game” makes it extremely difficult to assess causes
of violent unrest empirically. There is a natural element of unpredictability as to when and where
precisely the beliefs of potential rioters will flip over and trigger the riot equilibrium. Further,
with this strategic environment in mind, it is no longer clear that more inequality will necessarily
lead to a higher propensity for riots to break out. As Collier and Hoeffler (1996) argue, a “greater
inequality significantly reduces the risk and duration of war” The reason is that a high degree of
inequality may induce more resources necessary for repression for the advantaged group
possesses. In contrast, increasing levels of inequalities would induce lower level of resources for
the disadvantaged group, which are necessary for collective action.4 Hence, observing a high
degree of inequality potential rebels will anticipate that the government will have a greater
capacity than perhaps otherwise to finance a military repression against them, thus reducing the
chances of success in rebellion.
While the idea of a relationship between inequality and conflict is appealing, conclusive
empirical proof of its existence has been elusive. Indeed there is no clear relationship in the data
between inequality and violent conflicts. Some have found positive relationships between income
inequality and political violence (Park 1986; Muller 1985; Boswell and Dixon 1990, 1993 ;
Muller and Seligson 1987, Midlarsky 1988, Londregan and Poole 1990, Brockett 1992,
Binswanger, Deininger and Feder 1993 and Schock 1996) Others have found no such relationship
(Hardy 1979; Weede 1981, 1987). This is partly because it is hard to clearly disentangle
economic inequality as a reason for conflict from other factors such as cultural, ethnic or
2 Abbink and Pezzini (2004) have argued in a similar way for spontaneous rebellions against wrongdoing
dictators. 3 The trigger for the French riots was the accidental electrocution of two immigrant youths. It was claimed that
these teenagers died while they were chased by the police, a charge the authorities denied. Tragic as this case was, it would usually not be sufficient as a cause of a rebellion of that scale. However, it certainly served as a coordination device.
4 Another justification for this position lies in the social comparison processes of human beings. As Samuel Johnson said, "it is better that some should be unhappy, than that none should be happy, which would be the case in a general state of equality." In other words, under moderate economic inequality, some are unhappy; but under pure economic equality, everyone is unhappy. This position was common to the nineteenth-century conservative political thought of Burke, Bonald, and others.
4
religious differences or political contexts. Moreover, efforts to test this assumption has frequently
been characterized by “working backward”, starting with cases where civil violence occurred and
investigating factors that seem to have contributed to the outcome, with no attempt to seek out
other cases where similar factors were present but violence did not occur.
In this paper we analyse the relationship between inequality and riots in a novel way. We first
set up a game theoretic model of a situation with two groups of individuals. One of the groups is
disadvantaged and has less ability to gain a share of the total income. In a second stage
individuals can revolt against the income distribution. We find that the structure of the game with
two extreme equilibria at the second stage makes the game theoretic prediction indeterminate,
leaving it to empirical analysis to identify links between inequality and rioting. We provide such
empirical data by conducting a controlled laboratory experiment using our game theoretic model.
Evidence based on experimental analysis has the advantage of a controlled environment
(political, social and religious context), defining a priori the reference group, rather than having
to infer it from survey data, and of avoiding any possible role for contextual effects. Finally, our
analysis relies on actual and costly decisions instead of subjective reported behaviour. Three sets
of questions are addressed in this paper: First, under what conditions, if any, will inequality lead
the disadvantaged group to “burn” resources of the advantaged group through violent conflict?5
In this paper we investigate the relationship between inequality and conflicts in a situation that
prevent agents from using conflicts as a means to obtain a better relative situation. In other word,
inequality is exogenously determined and riot cannot affect the current inequality level between
the have and the have not. Such context makes the situation relatively unfavourable to the
apparition of a relationship between conflicts. Indeed subjects have no strategic gains
(expectation of higher income in the future) from using conflicts. Moreover observing some high
degree of inequality potential rebels will anticipate that the advantaged group will have more
resources to finance a repression against them, thus increasing the cost of the rebellion.
Second, we will investigate to what extent the relationship between inequality and conflicts is
linear. In particular, we investigate to what extent an increase in inequality may have a negative
effect on the probability of rioting by giving the advantaged group more resources to use
repression and in contrast providing lower level of resources for the disadvantaged group, which
is necessary for collective action. The idea behind this is that an increase in inequality may result
5 Three main motives could explain why people would rebel against inequality. First, conflicts may illustrate the
desire to obtain a better absolute and/or relative situation and thus ensure a higher income in the future (strategic motive). Second, individuals with distributional concerns who suffer from disadvantageous inequality may be willing to coordinate in order to reduce earnings inequality, if the cost they bear is smaller than the impact of sanctions on the target's payoff (Fehr and Schmidt 1999; Falk, Fehr and Fischbacher 2006; Bolton and Ockenfels, 1999). Third, It might also be the case that both poverty (i.e absolute low incomes) and high levels of inequalities (relative low incomes) would lead the disadvantaged people to express their emotion and achieve redistributive demands when it is possible since they have nothing to lose and thus resort to force. Hence, as economic inequality increases, the probability of conflict should increase.
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in a higher willingness to riot but in contrast lower level of resources for collective action but
more resources for repressing conflict. Moreover, following Nagel (1976), it might also be the
case that while the "tendency to compare" decreases with the level of economic inequality.
Finally the third aim of this paper is to investigate to what extent preferences for riot translate
into actions. Indeed preferences may not immediately translate into actions. In fact like all
collective actions, civil conflicts and riot require coordination. Many conflict theorists have
considered the atomisation/organisation of dissidents to be a crucial factor affecting the
inequality-conflict relationship. According to these theories, several variables affecting the
strength of conflict organisations, such as leadership, coalitions with powerful actors (e.g., the
Church), organisational resources (including intangibles like solidarity), moral perceptions, and
other factors play an important role in conflict.
To anticipate our results, we first find that, despite the cost of riot, a non negligible number of
players chooses to destroy other group's money. Our results also indicate that disadvantaged
groups significantly riot more than advantaged groups. This effect is even stronger under a
stranger matching protocol that prevents from repression. In addition we also found that riot
decreases with the extent of inequalities.
3. The game
We model the riot game as a game in two stages. Players are divided into two groups called
group A and group B. The first stage consists of a proportionate rent-seeking game in which both
players A and players B compete (by purchasing tickets) to share a prize P. This stage models the
competition to gain resources, e.g. access to education and good jobs. The share of the prize
received by each participant equals the proportion of her tickets relative to those of the entire
group (including all players A and players B). This stage also endogenously induces the
inequality of chances we want to model. Group B, the disadvantaged group, has a much harder
time to gain its share of the cake, as their lottery tickets have a much lower winning power than
those bought by individuals of group A. This is modelled by varying the costs ci per ticket, which
is higher for individuals of group B. Denoting by xi the number of tickets individual i buys, the
individual’s share si of the prize is then
1
i
ii n
j
j j
x
cs
x
c=
=∑
.
With the rent-seeking game in the first stage we wanted to capture two important features of
the real-life competition for jobs and income. First, we wished to induce inequality of chances
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rather than inducing income inequality directly. All members of society are involved in a
competition in which they can gain resources. Members of the disadvantaged groups also can
gain, though their chances are worse than those of the advantaged group.
At the second stage of the game the two groups can engage in rioting. This is modelled as a
coordination game in which the members of the group can simultaneously choose to take action
in order to reduce the payoffs of the members of the other group. If the number of group
members who choose to riot reaches or exceeds a critical threshold m, then each member of the
other groups receives a payoff reduction. The own incentives to riot follow the structure of a
mass coordination game. If fewer than m group members riot, then rioters receive less than non-
rioters, a feature that captures sanctions from the authorities. If m or more group members riot,
then it actually pays off to join the riot, which reflects the ostracism that inactive group members
receive from their fellow group members. The exact payoffs are given in section 4.
4. The experimental design
4.1. The parameterisation of the game
At the beginning of the experiment, each participant is assigned a role of player A or player
B. They keep this role during the entire experiment. Besides, the computer assigns randomly half
of the players the role of player A (advantaged) and the other half the role of player B
(disadvantaged). Hence, each 6-players group consists of 3 A-type and 3 B-type players. Each
player keeps her role during the entire experiment. There are six treatments in the experiment, all
of which have a first and a second stage of interaction in common.
Our main research question involves the relationship between inequality and riot. Thus, we
vary the level of inequality across the four treatments of our first experiment. As a control
treatment we conduct sessions with a symmetrical setup, in which both groups are identical. We
then run three experimental conditions in which we vary the cost parameter ci, making it
increasingly harder for the disadvantaged group to compete. We have sessions with ci = 4 and ci
= 8 in the asymmetric treatments. The cost parameter for the advantaged group is always ci = 1,
in the symmetric treatment ci = 1 holds for both groups. In all experiment the prize to be won was
set to P = 576.
At the first stage of the game players can invest any amount between 0 and 80 tokens. By
restricting the strategy space we made sure that the equilibrium predictions are the same for the
asymmetric treatments. The interior equilibrium would lie outside the feasible range, such that a
corner solution applies. Advantaged players choose the maximum feasible investment,
disadvantaged players choose zero (see next section).
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Table 1. Characteristics of the First Experiment
Session Number Number of individuals
Matching protocol
Treatment
1-3 48 Partner Sym 4-6 54 Partner Asym4 7-10 60 Partner Asym8
In the first experiment all sessions were run using a partner protocol; i.e. the composition of
the groups remains the same throughout the experiment. In a second experiment, which we had
set up to separate two competing explanations for the results we obtained, we use a strangers
protocol in which the groups are randomly rematched in every round. This treatment will be
described in section 6.
In the second stage of the experiment subjects decide whether or not to riot. A riot is
successful if at least two of the three group members participate. The payoff are chosen in a way
that it is always preferable for an individual player to swim with the tide, i.e. to riot if the other
group members riot and to abstain if the others do. The cost of being the only rioter is chosen to
be greater than the cost of being the only absentee. Thus, we assume that the consequences of
being caught (e.g. fines or arrest) are more severe than those of abstaining from a successful riot,
which are mainly loss of face before an individual’s peers. The following table shows the payoffs
for the combinations of choices in the second stage subgame. These payoffs are simply added to
the earnings obtained in the first stage of the game.
Table 99. Second stage payoffs
Choice of player I
Choice of subject 2
Choice of subject 3
Cost Z for the opposite group
Payoff for player i
R R R -40 -5 R R NR -40 -5 R NR NR 0 -20 NR R R -40 -10 NR NR R 0 0 NR NR NR 0 0
4.2. The conduct of the experiment
The experiment consisted of 25 sessions of 20 periods each. Experimental sessions were
conducted at the University of Rennes, France. 432 subjects were recruited from undergraduate
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classes in business, art, medicine, literature and economics. None of the subjects had previously
participated in a similar experiment and none of them participated in more than one session. The
experiment was computerised using the Ztree software.
In each session we aimed at running three experimental games in parallel. In one session not
enough participants showed up, such that we could have only twelve subjects. Subjects were not
told who of the other participants were in the same group, but they knew that the composition of
the groups did not change. The subjects were visually separated from one another in order to
ensure that they could not influence each other’s behaviour other than via their decisions in the
game.
Each session began with an introductory talk. A research assistant read aloud the written
instructions (reproduced in the appendix). The language used in the instructions was neutral, i.e.
we avoided references to the riot context. By this we wanted to focus participants on the
incentives given in the game, and avoid that possibly strong opinions on the French experience
could guide their choices.6
The total earnings of a subject from participating in this experiment were equal to the sum of
all the profits he made during the experiment. On average, a session lasted about an hour and 20
minutes including initial instructions and payment of subjects. At the end of the experiment,
subjects were paid their total earnings anonymously in cash, at a conversion rate of one euro for
1500 talers. Subjects earned between €99.99 and €99.99 with an average of €99.99, which is
considerably more than students’ regular wage in Rennes. At the time of the experiment, the
exchange rate to other major currencies was approximately US-$1.20, £0.70, ¥9.99 and RMB
9.99 for one euro.
5. Game theoretic predictions
The two-stage game can be solved by backward induction. It is easy to see that the second
stage game, as mentioned earlier, has four pure strategy equilibria, two for each group. In one
equilibrium nobody riots, in the other one everybody. This is independent from the decisions
made in the other group, as all players decide simultaneously. Thus, every combination of one
equilibrium in one group with an equilibrium in the other group is an equilibrium of the second
stage game.
6 Evidence for the effects of instruction framing has been very mixed so far. In a tax evasion experiment Baldry
(1986) finds far more evasion if the task is presented neutrally as a gambling opportunity. Alm, McClelland, and Schulze (1992), however, do not find any differences. A study by Burnham, McCabe, and Smith (2000) reports significant less trustful choices in a reciprocity game when the other player is called “opponent” rather than “partner”. On the other hand, Abbink and Hennig-Schmidt (2002) do not find significantly different behaviour between a neutrally and a naturally worded version of a bribery experiment.
9
For the first stage equilibrium we first look at the rent-seeking game in isolation. Identifying
the equilibrium of the first stage, and subsequently the subgame perfect equilibrium of the whole
game, is technically more involved. The symmetric case is straightforward: The equilibrium is
the solution of the standard rent-seeking game (the fact that players receive shares rather than
winning probabilities does not change equilibrium predictions). The equilibrium investment can
is given by
Pn
nxxi 2
**
)(
)1( −== .
This yields an equilibrium investment of 80, which is the maximum amount allowed.7
In the asymmetric cases the heterogeneity of the players from the different groups needs to be
taken into account. We derive the first order conditions for the optimal investment, given the
investment of the other players, as
* ( 1) . ( 1)1
( 1) ( 1) 1 with
i ii
j jj j
ji i
c p P c nx
c c
cc cn n
P cn n nc c
− − = −
− − = − =
∑ ∑
∑
In the asymmetric treatments this would imply equilibrium investments of 128 and 86.9 for
the advantaged players, and –64 and –51.4 for the disadvantaged players, for ci = 4 and ci = 8
respectively. Since these investments lie outside the feasible range of 0 to 80 we have an identical
corner equilibrium for all three asymmetric treatments. The advantaged players invest the
maximum allowed, the disadvantaged invest nothing. So only the advantaged players receive a
share of the prize (an amount of 192) in equilibrium. Note that although the equilibrium
prediction is identical, the treatments may behaviourally very well differ.
The game as a whole has multiple equilibria. If, for example, the disadvantaged group selects
the riot equilibrium in response to the first stage equilibrium, but the no-riot equilibrium for some
neighbouring first stage outcome, then the advantaged players would choose different
investments at the first stage. However, the one in which all players choose the first-stage best
responses is very persistent. In particular, the disadvantaged group cannot use equilibrium
selection as a threat to secure a positive share of the pie by forcing the advantaged players to
7 Previous rent-seeking experiments have shown investments that are systematically above equilibrium levels.
This possibility is excluded through our imposed restriction of the strategy space. In this study we are not interested in the behavioural properties of the rent-seeking game, but we rather use the game as a device to induce inequality of opportunities to study their effect on behaviour at the second stage. For that, it is actually desirable if subjects predictably reach the upper bound of the range, as it improves the comparability of observations.
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invest less. This is because the equilibrium in which the three advantaged players choose
(80,80,80) for all second stage response patterns except those that are characterised by: “Riot
against (80,80,80) but do not riot against (80,80,y)”, where y < 80. If such an equilibrium
response pattern is selected, then it can be a best response for an individual to deviate from a
choice of 80 and invest y instead. The individual’s unilateral deviation then avoids the riot and
this can lead to a higher profit for the individual. However, the smallest number y that can be
used as a threat is 38, even lower values make it preferable for the individual to stick to an
investment of 80 despite the riot. Against an investment of the advantaged group of (80,80,38),
however, a disadvantaged player’s best response is still to invest zero. Note that the threat must
be chosen in a way that only one player is forced to reduce his investment, otherwise an
advantaged group investment of (80,80,80) remains a subgame perfect equilibrium pattern. In
such a case an individual reduction of the investment would not avoid the riot but only reduce the
deviator’s payoff.8
5. Experimental results
We follow our research agenda and first present the data from the original setup with partners
matching. Sessions with a strangers protocol were added later to test two competing hypotheses
against one another. We will introduce them in section 5.99.
5.1. Average level of effort and first stage profit in the rent seeking game
The first stage of the game was designed to implement inequality between the groups. The
rent-seeking game is designed such that, in equilibrium, advantaged players would invest the
maximum allowed and disadvantaged players the minimum of zero. In the symmetric treatment
all players are predicted to invest the maximum. Note that we chose a set-up in which we
expected that this would be the outcome likely to occur in the experiment, and therefore cut off
the strategy space. Figure 1 shows that, at least over time, this expectation was correct. The figure
illustrates the the average individual effort in the rent seeking game by period, and shows that
investments quickly converge to the predicted outcome.
Figure 1. Number of tickets bought in each treatment over time
8 These deliberations turned out to be empirically irrelevant, as in the experiment the focal equilibrium
investment was reached very quickly (see next section).
11
0
10
20
30
40
50
60
70
80
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Periods
Ave
rag
e n
um
ber
of
tick
ets
SYM partner ASYM4 partn D ASYM4 partn A ASYM8 D
ASYM8 A Theoretical prediction Sym Theoretical predictions D ASYM4 strang D
ASYM4 strang A SYM stranger
Turning next to first-stage profits, Figure 2 shows the average first-stage payoff by group for
each treatment. The first stage payoffs for advantaged groups under a partner matching protocol
are 211.28 and 215 for the asym4 and asym8 treatments, respectively. Payoffs are significantly
lower for disadvantaged groups, 96.73 and 91.71 for the asym4 and asym8 respectively. Thus, we
indeed observe strong inequality between advantaged and disadvantaged players, but very similar
results across the asymmetric treatments.
Figure 2. Average first stage profit per treatment
12
0
50
100
150
200
250
SYM ASYM4 ASYM8
Treatments
Fir
st s
tag
e p
rofi
ts
1 STAGE PROFIT GP D 1 STAGE PROFIT GP A
4.2. Determinants of conflicts
4.2.1. Inequality and conflicts
After having satisfied ourselves that our first stage procedure has indeed induced the
predicted levels of inequality to a large extent, we now turn to our main research question: What
is the link between inequality and the emergence of riots? As mentioned earlier, we would expect
that (1) disadvantaged players riot more than advantaged players, and that (2) we observe the
more riots the greater the inequality becomes. Figure 99 shows that the first hypothesis is
strongly supported. In both treatments with asymmetry the advantaged players riot much less
than disadvantaged players. The difference is significant at p=0.99 according to the Wilcoxon test
applied to the difference in average frequency of riot between groups in the single independent
observations.
Result 1: Disadvantaged groups significantly riot more than the advantaged groups in both
asym 4 and asym8.
With respect to our second hypothesis figure 99 shows a surprising result. The frequency of
riots decreases with the relative disadvantage of the own position. In fact, most clashes are
observed in the SYM treatment, in which there is no disadvantage at all. When there is inequality
13
the overall riot rates drops sharply. The disadvantaged groups riot less when the inequality is
extreme than when it is moderate.
Figures 3-6 illustrate the time path of the average share of conflicts (including both riots and
counter riots) by period respectively for advantaged and disadvantaged groups in each treatment.
These figures show the same pattern for all treatments : there is initially a positive rate of
conflicts for both groups and it declines when the game is repeated across periods (except for the
symmetric treatment in which the average rate of conflicts does not change appreciably as the
game is repeated). We also observe that the disadvantaged group riot more than the advantaged
for intermediate levels of inequality (i.e asym4 partner and stranger treatments). In contrast, for
lower and/or higher levels of inequalities (asym2 and asym8 treatments, respectively), the
disadvantaged groups do not riot more than the advantaged groups.
Figure 3. Average rate of conflict in the Sym treatment over time (partner and stranger)
Conflict frequency
0,43
0,14
0,35
0,230,29
0,00
0,20
0,40
0,60
0,80
1,00
SYM ASYM4 A ASYM4 D ASYM8 A ASYM8 D
14
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Period
Ave
rag
e sh
are
of
con
flic
ts
SYMD partner SYMA partner SYM A stranger SYM D stranger
Figure 4. Average rate of conflict in the Asym2 treatment over time
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Period
Ave
rag
e sh
are
of
con
flic
ts
ASYM2D ASYM2A
15
Figure 5a. Average rate of conflict in the asym4 treatments over time (partner protocol)
0
0,1
0,2
0,3
0,4
0,5
0,6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Periods
Ave
rag
e sh
are
of
con
flic
ts
asym4D partner asym4A partner
Figure 5b. Average rate of conflict in the asym4 treatments over time (stranger protocol)
16
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
0,5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Periods
Ave
rag
e sh
are
of
con
flic
ts
asym4D stranger asym4A stranger
Figure 6. Average rate of conflict in the asym8 treatment over time
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
0,5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Periods
Ave
rag
e sh
are
of
con
flic
ts
ASYM8D ASYM8A
17
Result 1 summarizes our findings about the differences between advantaged and disadvantaged
groups.
Result 1 : disadvantaged groups significantly riot more than the advantaged groups only for
intermediate levels of inequality (asym4 treatments).
Support for result 1 : Table 3a and 3b show the average rate of conflicts for each treatment.
Table 3a indicates the average rate of conflict in each treatment under a partner matching
protocol for each group. Table 3b provides similar results under a stranger matching protocol.
Both Tables 3a and 3b indicate a strong heterogeneity among groups, which reflects the extence
of two equilibria : a peaceful equilibrium with very levels of conflicts and a war equilibria with
very high levels of conflicts. Table 3a also shows that in all asymmetric treatments the average
level of riot is higher for the disadvantaged groups compared to the advantaged groups. In
particular, the average rate of conflicts are 0.35 and 0.14, respectively for the disadvantaged and
advantaged groups of the asym4 treatment. A nonparametric Wilcoxon sign-ranked test9 between
the advantaged and disadvantaged groups under the asym4 partner treatment shows that the
difference in average rate of conflict between the disadvantaged and the advantaged groups is
significant at the p < .05 level, (z=-2.371, two-tailed). A similar test for the asym4 under a
stranger matching protocol also indicates that groups D significantly riot more than groups A (z
=-2.201, p<0.05, two-tailed test). In contrast, no significant difference is found for low (asym2)
and high levels of social inequalities (asym8). Indeed no significant difference is found between
the disadvantaged and the advantaged groups in the asym2 treatment (z =-1.187, two-tailed).
9 In all statistical tests reported in this paper, the unit of observation is the group for the partner treatments and
sessions in the stranger treatments.
18
This result indicates that low inequality levels do not lead to differences in rates of conflicts
across groups. Similarly, no significant difference between the advantaged and disadvantaged
groups is found in the asym8 treatment (z = -0.408;two-tailed).
Before going into more details about this result, one immediate reason that come into mind is that
a conflict initiated by the disadvantaged at a given period might be systematically followed by a
repression behaviour (revenge) by the advantaged at the following period. One simple way to
test this idea is to look at between group differences in conflicts in the first period of each game.
Considering the first period only of the asym8 treatment, we find disadvantaged group riot
significantly more (z =-1.710). A similar result is found for the first period of the asym2
treatment. However, a Wilcoxon Mann Withney test does not show any significant differences
between partner and stranger treatments in first periods of asym4 treatments. A similar test
provide the same results for the sym treatment. Hence, there are other factors at stake that are
affecting differences (or similarities) in riots between the two groups than only repression
behaviours.
19
Table 3a. Average rate of conflict per treatment (partner matching protocol)
Sym Asym2 Asym4 Asym8 All gps Adv.
Gps Disad. Gp
Adv. gps
Disad. gp
Adv. gps
Disad. gp
Group 1 0.566 (0.497)
0,2 (0.40)
0,783 (0.41)
0.38 (0.49)
0.65 (0.48)
0,033 (0.18)
0,85 (0.36)
Group2 0.616 (0.488)
0 (0)
0,066 (0.25)
0.03 (0.18)
0.816 (0.39)
0 (0)
0,016 (0.129)
Group 3 0.058 (0.235)
0,683 (0.46)
0,93 (0.25)
0 (0)
0.083 (0.27)
0 (0)
0.033 (0.181)
Group4 0.666 (0.473)
0.766 (0.426)
0.566 (0.499)
0.1 (0.302)
0.183 (0.390)
0.016 (0.129)
0.35 (0.480)
Group5 0.625 (0.486)
0.2 (0.403)
0.033 (0.181)
0.016 (0.129)
0.016 (0.129)
0.25 (0.436)
0.516 (0.503)
Group6 0.641 (0.481)
0.066 (0.251)
0.666 (0.475)
0.033 (0.181)
0.033 (0.181)
0.05 (0.219)
0.016 (0.251)
Group 7 0.216 (0.213)
0.7 (0.462)
0.583 (0.497)
0.583 (0.497)
0.933 (0.251)
0.566 (0.499)
0.35 (0.480)
Group 8 0.058 (0.235)
0.383 (0.490)
0.85 (0.360)
0.166 (0.375)
0.45 (0.501)
0.066 (0.251)
0.066 (0.251)
Group 9 0.016 (0.129)
0.016 (0.129)
0.016 (0.129)
0.016 (0.129)
0.85 (0.36)
0.36 (0.48)
Group 10 0.55 (0.50)
0.35 (0.48)
Average 0.431 (0.495)
0.32 (0.48)
0.49 (0.49)
0.14 (0.35)
0.35 (0.47)
0.23 (0.42)
0.29 (0.45)
20
Table 3b. Average rate of conflict (stranger matching )
Sym
Asym4
All gps A D Session 1 0.61
(0.48) 0.133 (0.340)
0.294 (0.457)
Session 2 0.46 (0.49)
0.083 (0.277)
0.233 (0.424)
Session 3 0.51 (0.50)
0.211 (0.409)
0.344 (0.476)
Session 4 0.43 (0.49)
0.022 (0.147)
0.288 (0.454)
Session 5 0.31 (0.48)
0.2 (0.401)
0.288 (0.454)
Session 6 0.24 (0.43)
0.194 (0.396)
0.411 (0.493)
Average 0.426 (0.47)
0.140 (0.347)
0.310 (0.462)
Table 4 provides more formal evidence about the influence of being in a disadvantaged group on
riot decisions. We estimate random effects Probit models with individual decisions to burn
money (ie. go into conflict) in the tth period as the dependent variable. Regressions are
undertaken first for the symmetric treatment and then for asymmetric treatments. All individual
observations are pooled across groups, time (periods) and type of protocol (partner and stranger).
A dummy is introduced however to differentiate between being in a stranger or a partner
protocol. Our main independent variable of interest here is a dummy which indicates one’s
belonging to the disadvantaged group. We also include other variables that are expected to be
relevant. The first is a dummy variable indicating the desire to take revenge in time t given that
the “other group rioted in t-1”.We also include information about co-ordination to riot with the
variables of oneself being the “Only one not to riot in t-1” and “Only one to riot in t-1” Finally
some demographic variables are included in the estimates.
21
Table 4. Determinants of conflicts (Random Effects Probit)
Note: standard errors reported between brackets; ***,** and * designate significance at 1, 5 and 10% respectively
The estimates summarized in Table 4 confirm our previous findings. The first model reveals that
there are no differences between groups in the benchmark treatments. In contrast, the variable
“being in the disadvantaged group” is highly significant in the asymmetric treatment (see column
2), suggesting an important effect of social inequality. However a more detailed analysis shows
that this effect is more important for intermediate levels of inequality than for lower or higher
levels of inequality. Indeed, consistent with our previous results, this variable has a positive and
(1) (2) (3) (4) (5) (6)
Sym treat. Asym Asym Asym2 Asym 4 Asym8 0.125 0.598*** 0.669*** 0.177 0.735*** 0.661** Disad. group (0.151) (0.146) (0.135) (0.196) (0.190) (0.276) 0.291*** 0.548*** 0.684*** 0.694*** 0.781*** 0.144 The
othergroup rioted in t-1
(0.063) (0.078) (0.074) (0.144) (0.096) (0.131)
0.791*** 1.159*** 1.206*** 1.051*** 1.137*** 0.917*** Only one not to riot in t-1 (0.076) (0.071) (0.070) (0.157) (0.089) (0.101) Partner -0.023 -0.011 0.221 -0.02 (0.164) (0.141) (0.126) (0.180)
-0.06 -0.070 -0.40 0.162 -0.215 -0.175 Period 20 (0.133) (0.127) (0.133) (0.252) (0.183) (0.288)
Age 0.042 (0.026) Men -0.104 (0.119)
0.195 Father blue collar (0.193)
0.574*** Live in poor suburbs (0.148)
0.263* Housing public subsidies
(0.140)
0.125* Work in group (0.634)
-0.925*** -2.01*** -4.167*** -1.277*** -2.11*** -2. 03*** Constant (0.124) (0.146) (0.648) (0.187) (0.182) (0.288)
Observations 2964 5244 5244 1026 3078 1140
22
significant coefficient for the asym4 treatments (see column 5). In contrast columns (4) and (6)
also show that the variable “disadvantaged group” is not significant for low levels of inequality
(asym2) and is less significant for high levels of inequality (asym8) Table 4 also shows that the
variable "the other group rioted in t-1" is positive and highly significant in all treatments (except
in column 6, asym8 treatment), indicating that a part of willingness to reduce other’s payoff can
be explained by the willingness to take revenge. It explains both the repression decisions from
the advantaged groups but also the fact that disadvantaged groups also react to repressions or
other money burning decisions set by the advantaged group at an earlier period.. This result is
consistent with previous other studies which have shown that the use of force may, sometime be
counterproductive. In particular, the use of coercive force may result in an increase of the risk of
further riots (Gurr [1970], Hirschman [1981], Gupta [1990], Bourguignon [1999], Boix [2004]).
Political opportunity theorists suggest that coercive responses by political authorities to collective
action may lead to an escalation of protest from nonviolence to violence (e.g., Tilly 1969, 1978).
In cross-country studies, a positive relation has been found between government sanctions and
political violence (e.g., Hibbs 1973; Muller and Seligson 1987). Note that the variable "the other
group rioted in t-1" is also positive and highly significant under the stranger matching protocol,
which indicates a non negligible part of blind revenge.
Table 4 also provides information about co-ordination and non material resources that are
necessary for rioting. It indicates that peer pressure (‘I was the only one not to riot in the previous
period’) affects the current decision of rioting. Indeed, the variable “Only one not to riot in t-1” is
positive and statistically significant (except for asym8 treatment), indicating that individual feels
pressure of the group. We also include an end of game dummy variable ‘Period 20’ to see
whether players burn money at the end of the game when they know that other group cannot
respond. No end of game effect is detected, however. Finally, column (3) shows that adding
23
individual characteristics variables does not change the effect of the main variable. However,
although most individual type variables are not significant, some features of particular interest to
our study turn to have an effect on riots : the “living in poor suburbs” variable is positive and
highly significant, indicating that those who live in poor suburbs are more likely to riot.
4.2.2. Does revolt decline with the increase of inequality?
In this section we investigate to what extent the relationship between inequality and conflict is
linear. Figures 7a and 7b illustrate the time path of the average share of conflicts for each
treatment in the partner and stranger matching protocols, respectively.
Figure 7a. Average number of conflicts per treatment over time (partner treatments)
0
0,1
0,2
0,3
0,4
0,5
0,6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Period
Ave
rag
e n
um
ber
of
con
flic
ts
SYM partner ASYM2 ASYM4 ASYM8
Figure 7a. Average number of conflicts per treatment over time (stranger treatments)
24
0
0,1
0,2
0,3
0,4
0,5
0,6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Period
Ave
rag
e n
um
ber
of
con
flic
ts
asym4 stranger Sym stranger
Figure 7 and 7b show that the level of conflict steadily decline with the extent of inequality. They
show that in both stranger and partner matching protocol, the level of conflicts is significantly
higher when inequalities are lower. We also find that conflict level is higher in the absence of
inequality than in context with two different groups. Result 2 summarizes our findings.
Result 2 : While disadvantaged significantly riot more than advantaged people, they tend to riot
less and less when inequality increases.
Support for result 2. A Wilcoxom Man Whitney test shows that the level of conflict in the sym
treatment under a partner matching protocol is significantly higher than under the asym 4
treatment (z =-1.6) and than the asym2 treatment (z =-1.78). Significant results are found for the
stranger matching protocol between the asym4 and sym treatments (z = -2.491).
25
In order to investigate further the role of between observations variability in determining riots, we
plot the rate of inequality against that of riots by the disadvantaged and the advantaged people by
considering across observations variability only in figures 8a and 8b. Figure 8a and figure 8b
show that both the level of riot from the part of disadvantaged people but also counter riot with
the extent of inequality. While riot declines concavely, counter riot declines convexly, which
explain why the level of riot is significantly higher than counter riot for intermediate levels of
inequality. Figures 8a and 8b also provide interesting results concerning the importance of
coordination in the decision to riot. Indeed, it shows two different levels of riot depending on
whether people coordinate or not on the riot equilibrium. Then, there seems to be two equilibrium
regimes perfectly consistent with our second stage theory game: a conflict regime and a peace
regime. Both regimes arise when players coordinate either to go into conflict or when they
coordinate to maintain peace respectively. This is why in the first case, riot rates are around 50 to
90% (systematically, a majority coordinate to go into a riot) while in the second case, riot rates
hardly ever reach 20% (only a minority chooses to do so).
Figure 8a: Riot rates of disadvantaged and inequality of profits (profits A/profits D)
26
0.5
1
1 1.5 2 2.5 3prof1_ineq
(mean) Rriot Fitted values95% CI Fitted values
Figure8b.: Riot rates of advantaged and inequality of profits (profits A/profits D)
0.5
1
1 1.5 2 2.5 3prof1_ineq
(mean) Rriot 95% CIFitted values
27
Table 5 provides additional support for these results. It presents the results of estimates on the
rate of conflicts for disadvantaged and advantaged groups including dummies variables for each
treatment. It shows the estimation of random effects probit models that explains the rate of
conflicts both for the disadvantaged and the advantaged players. In order to investigate the
relationship between inequality and conflicts for these players, we pool all individual
observations over all of the asymmetrical treatments and include in the regression three treatment
fixed effects. Hence, Asym2, Asym4 and Asym8 in the first column of table 5, measure the
impact of low, intermediary and high levels of social inequality on revolts undertaken by the
disadvantaged (respectively counter riot from the advantaged people).
Table 5. Determinants of conflicts and extent of inequality (Random Effects Probit models)
All treatments Disadvantaged group
Advantaged group
0.533*** 0.568*** 0.387*** The other group rioted in t-1 (0.154) (0.1002) (0.092) Disadv. Group 0.525*** (0.094) Asym2 Ref. 0.416*** 2.008*** (0.152) (0.377) Asym4 -0.613*** Ref. Ref. (0.154) Asym8 -0.945*** -0.372*** 0.691*** (0.164) (0.122) (0.178) Period 20 -0.234* -0.203 -0.035*** (0.121) (0.161) (0.007) Constant -0.636*** 0.691*** -1.905***
(0.163) (0.082) (0.226) Observations 5244 2622 2622
28
Table 5 indicates that Disadvantaged people tend to riot more compared to advantaged people as
seen by the positive coefficient associated with the variable “Disadvantaged group” but that the
level of conflicts significantly decreases across treatment. The second model confirms the fact
that the disadvantaged tend to riot less and less when inequalities increase. In contrast, we
observe that the level of counter riot increases for very high inequality level compared to the
intermediate level of inequality.
How can we explain such results? A potential reason for this result is that increasing levels of
inequalities would induce lower level of resources for the disadvantaged group necessary for
collective action. In the opposite, increasing levels of economic inequality would be associated
with higher levels of resources for the “advantaged groups” to repress, and hence hold down,
political dissent. While conflicts result from inequalities, too high inequalities would therefore
induce insufficient resources to riot while it would provide an increase of resources for the
repressive state. To examine this possibility we ran additional estimations on the level of
repression (i.e the probability of counter riot for a given riot). If our assumption is correct one
should observe that the level of repression should increase with the extent of inequality because it
induces higher level of resources for rioters. Table 6 shows the sensitiveness of repression to
inequality. The dependent variable “repression“ takes the value 1 when the advantaged group
attacks in case of a riot in a previous period. It takes 0 otherwise.
29
Table 6. Determinants of repression for advantaged players (Random Effect Probit)
Asym4 Ref.
Asym8 0.638*
(0.357) Period 20 0.024
(0.353) Constant -1.255***
(0.170) Observations 657
Standard errors in parentheses * significant at 10%; ** significant at 5%; *** significant at 1%
Table 6 shows that the level of repression significantly increases with the extent of
inequality, indicating that advantaged groups are more and more inclined to counter riot when
inequalities increase. This result is consistent with the idea that an increase in inequality may
decrease conflicts because increasing levels of economic inequality would be associated with
higher levels of resources for the “advantaged groups” to repress, and hence hold down, political
dissent.
An alternative potential explanation to explain why disadvantaged people riot less for very high
levels of inequality relies on the idea of polarization. According to polarization assumption,
conflicts would be more likely when it opposes very similar groups. Hence the "tendency to
compare" would decrease with the level of economic inequality. In other words, people would
tend to resign when inequality is too important. This hypothesis has been advanced by Nagel
(1976). If it is correct we should observe that the willingness to burn money would decrease with
the extent of inequality. To elicit these patterns we confronted subjects with two different
"burning money" scenarios after the experiment. The idea of these two additional questions was
to elicit the willingness to burn money irrespective of the necessity to coordinate with other
30
players as well as the possibility of revenge. These two additional questions were paid. In a first
scenario, players were randomly paired with another participant in the room. Each player is
informed that he will receive 50 points while player j receives 100 points. Then, he has the
opportunity to reduce player j’s payoff by 50 points. Burning money costs 10 points. In a second
scenario, player i receives 50 points while player j gets 200 points. As it was the case in the first
scenario, player i can reduce player j’s payoff by 50 points. Both players are informed that at the
same time the other player takes the same decision. If our conjecture about resignation is correct,
one should therefore observe a lower level of burning decisions in the second scenario than in the
first one. In contrast, no significant difference between both scenarios should lead us to reject this
assumption. In order to control for order, the order of the two questions was reversed in half of
the sessions. The two scenarios are summarized in Table 7.
Table 7. Willingness to burn money and resignation
Questions Scenarios : Results Question 1. You receive 50 points while
player j receive 100 points. You have the opportunity to reduce player j’s payoff by 50 points. It will cost you 10 points. Do you want to reduce player j’s payoff ?
Mean : 0.291 Std. Dev.: 0.455
Question 2. You receive 50 points while player j receive 200 points. You have the opportunity to reduce player j’s payoff by 50 points. It will cost you 10 points. Do you want to reduce player j’s payoff ?
Mean : 0.184 Std. Dev. :0.389
31
Figure 9. Average number of burning decision in each scenario
0
0,05
0,1
0,15
0,2
0,25
0,3
Scenario 1 Scenario 2
Per
cen
tag
e o
f b
urn
ing
dec
isio
n
no to the other question yes to the other question
Both Table 7 and Figure 9 show that the average number of burning decisions
significantly decreases in the second scenario compared to the first one. One average, in one third
of the decision, subjects reduce the other player ‘s payoff in the first scenario while it represents
only 20% in the second scenariao. A wilcoxon sign rank test shows that this difference is
significant ( z = 2.598; p<0.01). Moreover our results indicate that 67% of subjects who burn
money in the first scenario do not burn in the second one. Finally, only 9% of players choose to
reduce player ‘j ‘s payoff in both scenario. These results strongly support the idea that individuals
tend to resign when inequality are too much high.
32
5. Conclusion
In this paper we seek to contribute to the literature on the relationship between conflicts and
inequalities by investigating experimentally to what extent inequality explain inter-group
conflicts. Our experiment consists of a two stages game. In a first stage, subjects play a
proportional rent seeking game to share a price. The share of the prize depends both on their
effort and on the effort of the other players. In our experiment, inequality arises exogenously by
attributing to some subjects (the advantaged group) more part of the price than other subject (the
disadvantaged group). In a second stage, after being informed on the first stage payoff of each
group member, they can coordinate with the other members of their group to reduce (“burn”)
other group members’ payoff. The treatments differ in the degree of inequality between the two
groups.
Two main results are found in this study. First, we find that despite the cost of riot, a non
negligible number of players chooses to destroy other group's money. However our result also
indicate that the level of conflicts significantly declines with the extent of inequality. Two main
explanations supported by our results are given to explain why riot declined with the extent of
inequality. First, an increase in inequalities induces insufficient resources to riot while it provides
an increase of resources for the repressive state. Second, the "tendency to compare" decreases
with the level of economic inequality.
A potential extension of this work would be to investigate to what extent the availability for the
advantaged group to redistribute money to the less privileged group would be a mean to reduce
the cost of rebellion. Indeed violent conflicts are bad for economic growth and social welfare by
destroying resources (Stewart, Fitzgerald and Associates [2001], Fearon and Laitin [2003]). An
alternative option to prevent civil conflicts would be to resort to social policies that allow the
33
transfer resources to less privileged groups. Increases in redistributive policies may have an
important role to play in the establishment and/or maintenance of stable socio-political
environments in countries.
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