Do voting rights encourage group cooperation in
rent-seeking experiments?∗
Klarizze Anne Martin Puzon† and Marc Willinger‡
April 15, 2015
Abstract
We investigate the role of voting rights in a contest setting. We propose
a rent-seeking experiment where group members may endogenously decide
to share the prize. In the first stage, selected members of the group
determine how much of the prize to costlessly protect and equally share.
In the second stage, the unprotected fraction is competed for in a rentseeking game. In contrast to exogenously imposed protection, we consider
two institutions: majority voting (i.e. all group members participate) and
dictatorial rule (i.e. only one member decides). Under majority voting,
rent-seeking is reduced even if groups implement no prize protection in the
first stage. This result becomes stronger when the prize at stake suddenly
increases. When only one member selects the protection level, groups are
sometimes worse off than when protection is exogenously imposed. We
argue that extending voting rights encourages group cooperation to avoid
rent-seeking.
Keywords: Aggregate rent-seeking, stake size, democracy, contests, laboratory experiment.
JEL Codes: C90, D72, D02.
∗ We wish to thank participants at the 2013 Economic Science Association World Meetings in Zurich, 2014 APESA Conference in Auckland, and 2015 Eighth Annual NYU-CESS
Experimental Political Science Conference for their valuable feedback. The usual disclaimer
applies.
† Universite Montpellier. Address: Faculte d’economie, Universite Montpellier, Ave. Raymond Dugrand, 34960 Montpellier, France. [email protected]
‡ Universite Montpellier. [email protected]
1
1
Introduction
We study experimentally the interplay between democratic participation and
group rent-seeking behaviour. We conjectured that when people are involved
in setting the extent of property rights (e.g. protection of a given prize), rentseeking would be substantially reduced compared to a situation where protection
is imposed. In our experimental setting, group members can select the environment governing their interactions. To do this, we slightly modify the standard
rent-seeking game by introducing a preliminary stage in which selected group
members can choose the level of protection of the prize. The protected portion
of the prize is equally shared by all group members at no cost. The amount of
unprotected prize is competed for in the subsequent stage, a proportional-prize
contest. We observe that when the level of protection is chosen by members
of the group, it is sometimes more efficient than when exogenously determined
(e.g. imposed by an external party, the experimenter).
Different from existing literature, we also find that the degree of democratic participation within groups matters. We considered two institutional
treatments: majority voting (full participation) and dictatorial rule (limited
participation). Since voting is neither costly nor advantageous, the only difference between these two treatments is the degree of inequality in voting rights
among group members in the protection stage. In the majority voting treatment, all members of the group participate in the protection stage. Under the
dictator treatment, only one member chooses the amount of unprotected prize
to be competed by everybody in the rent-seeking stage. The majority voting
institution is more democratic, but involves a coordination issue on the level of
protection. The dictator institution involves no coordination issues with respect
to the choice of rent protection, but is less democratic. We assess the efficiency
of the two institutions in providing protection with respect to two dimensions.
First, we compare their performance with respect to a baseline treatment where
voting rights are absent, i.e. none of the members of the group can participate
in the process of setting the level of protection, which is instead exogenously
imposed. Second, we compare the relative performance of the two institutions
after a sudden exogenous jump on the size of the prize. These two dimensions
refer to two different strands of the literature on contests. We briefly highlight
our contribution to each of them.
First, our findings contribute to an emerging experimental literature dealing
with the impact of democracy on cooperative behavior. Early political scientists
2
like Tocqueville (1838) implied that political participation is beneficial. As we
quote: ”It is not always feasible to consult the whole people, either directly
or indirectly, in the formation of the law; but it cannot be denied that, when
such a measure is possible, the authority of the law is much augmented”. This
idea is also related to the concept of ”procedural justice” in social psychology
according to which there is greater satisfaction when people experience direct
democracy (van de Bos, 1999). In non-experimental economics-related literature, meanwhile, Frey (1998) observed that greater political participation leads
to less tax evasion in Swiss districts. In addition, Bardhan (2000) reported that
farmers are more likely to follow irrigation rules that they have themselves selected. In contrast, a limited number of experimental papers on democracy and
cooperative behaviour in social dilemmas have mainly focused on how subjects
democratically select institutions. For instance, Putterman et al. (2011) showed
that if group members can vote on sanctions in public good experiments, groups
tend to impose on themselves sanctions that lead to optimal contribution levels.
Another example is Walker et al. (2000) who conducted a commons experiment
that compares two voting rules: majority voting and unanimity. In their set-up,
each player proposes how much each member of his group should extract from
the common-pool. If one proposal wins, then the second stage automatically
implements the proposal. They have found that both voting rules substantially
decrease extraction from the common-pool.While these studies found that democratic participation by all group members can lead to efficient outcomes, they
did not question the behavioral impact of the ”mere existence” of participative
voting. Are the behavioral impacts of exogenously chosen policies (i.e. set by
an external party) more or less effective than endogenously chosen policies (i.e.
set by group members)? Only a small number of recent papers provide a partial
answer to this question. Sutter et al. (2010) have observed that rewards and
punishments in public good games have greater impact on contributions when
they are allowed democratically. Dal Bo et al.’s (2010) modified prisonner’s
dilemma game exhibited that the level of cooperation is greater when the policy is selected democratically by the subjects than when exogenously chosen.
However, these papers only explored the differences between exogenously and
endogenously determined institutions. We contribute to this literature by varying the degree of democratic participation (i.e. voting rights) in selecting the
level of protection of an otherwise contested prize. Unlike existing studies, we
thus analyze the role of democratic participation in an inherently and explicitly
competitive setting, i.e. a rent-seeking game. To our knowledge, our experi3
ment is the first attempt in contest literature to investigate experimentally how
voting institutions may avoid wasteful rent-seeking expenditures (Dechenaux et
al., 2014).
Second, by varying the prize at stake, we are also able to comprehensively
compare the efficiency of different institutions when an unexpected increase
in the initial size of the prize occurs. Doing this is consistent with Sachs
and Warner’s (1995) historical and macro-econometric observation that sudden abundance in rents from natural resources leads to socially inefficient outcomes. In this so-called “resource curse” literature, higher oil rents intensify
rent-seeking (Hodler, 2006; Puzon, 2013; Wick and Bulte, 2006). Nonetheless,
this result is conditional on the strength of institutions, e.g. property rights
protection and democratic governance (Hodler, 2006). Behind this literature,
we find examples such as oil-rich Nigeria, Sudan, and Sierra Leone where rentseeking and conflict are dominant. In contrast, there are countries characterized
by a well-functioning rule of law and strong property rights like Norway and
Botswana which are able to avoid the negative effects of resource abundance
(Mehlum et al., 2011). From a behavioral perspective, however, most (if not
all) experimental literature found that stake size does not matter in determining group cooperation. Several papers that have investigated stake effects have
found that an increase in stakes does not significantly affect the average behavior
in distribution games (Carpenter et al., 2005). In a recent study, Kocher et al.
(2008) found that stake size does not affect cooperation in public good games
with punishment. To date, nonetheless, no rent-seeking experiment has carefully explored the impact of stake size on group cooperation. More importantly,
none has analyzed the role of varying degrees of within-group voting rights
in rent-seeking experiments. By incoporating institutions in a proportionalprize rent-seeking experiment and testing their effectiveness in reaction to stake
jumps, our paper contributes to this literature by filling the aforementionned
gap. We observe that groups under externally imposed protection as well as
under dictatorial rule behave as predicted, i.e. increasing the prize at stake
leads to greater rent-seeking. Interestingly however, groups under majority voting are able to avoid this negative externality. When the initial prize at stake
suddenly goes up, there are no significant changes in aggregate rent-seeking
expenditures of groups who undergo majority voting. In contrast, under the
dictator treatment, aggregate rent-seeking becomes higher than expected. Because there are no stastically significant differences in frequency distribution of
protection levels between treatments, the degree of voting rights is the main
4
explanation for differences in group rent-seeking behaviour. When there is sudden abundance in the prize at stake, full democratic participation encourages
group cooperation. For instance, we have obtained a strong result where even
if groups implemented no prize protection in the first stage, they are still able
to cooperate in the second stage and minimize rent-seeking behaviour.
The remainder of this paper is structured as follows. In Section 2, we present
our modified rent-seeking game. Section 3 describes our experimental design in
detail. Section 4 presents the results, while section 6 concludes.
2
The game
In this section we introduce our theoretical framework, which extends the
previous works of Hodler (2006) and Wick and Bulte (2006). The two-stage
rent-seeking game is solved by backward induction. In the first stage, groups
determine the amount of prize that will be protected and equally shared amongst
the members of the group. In the second stage, players choose rent-seeking
expenditures to obtain a share of the remaining prize.
2.1
Stage 2: Non-cooperative rent-seeking expenditure
Each player i = 1, ..., n has an endowment Ei = Wi + Fi which he allocates
between a productive activity (Wi ), and a rent-seeking activity (Fi ). The productive activity has constant marginal returns captured by the parameter α.
Player i’s payoff from the productive activity is denoted ΠiW and defined as:
ΠiW = αWi + λ R
n , i = 1, ..., n, 0 < α < ∞. Given others’ expenditures, the
expected payoff from rent-seeking is given by: ΠiF = pi (1 − λ)R where R is the
total value of the prize at stake, pi is a contest function determining the share
of prize player i grabs, and λ corresponds to the fraction of the prize protected
from rent-seeking (i.e. property rights). If λ is close to 1, there is a low incentive
to invest in rent-seeking because expected returns are close to zero. If the level
of protection is close to 0, players have more incentive to engage in rent-seeking.
n
X
Let F =
Fi . The contest function is specified as follows:
i=1
pi =

 Fi ,
if F > 0,
1,
if F = 0
F
n
5
(1)
The player who spends relatively more in rent-seeking gets a larger share
of the remaining prize. If no player invests in rent-seeking, i.e. all players
cooperate, each one receives an equal share of the unprotected prize. Each
player i chooses Fi to maximize his total expected income Πi = ΠiW + ΠiF ,
given (1) and F−i the allocation decisions of others:
maxFi Πi = αWi + λ
R
+ pi (1 − λ)R
n
(2)
Player i’s allocation decision satisfies the first-order condition that the marginal
returns to both activities are equal:
∂ΠiW
∂Wi
=
∂ΠiF
∂Fi
. Assuming the n-players
decide simultaneously and that the individual payoff functions are common
knowledge, the symmetric Nash equilibrium level of allocation to rent-seeking
is: F N = ( n−1
αn2 )(1 − λ)R. At the group level, aggregate rent-seeking is therefore
equal to nF N = ( n−1
αn )(1 − λ)R. This leads us to prediction 1.
Prediction 1: Rent-seeking is more aggressive when the initial size of the
prize at stake R is high, or when the level of protection λ is low.
Although an increase in the unprotected prize (1 − λ)R leads to more rentseeking, it can be crowded-out by stronger protection (i.e. second order derivative is negative). Under non-cooperative play, each player gets ΠN = αE +
R
n [1
N
− ( n−1
n2 )(1 − λ)]. Group income or welfare is thus denoted as ΠT otal =
nαE + R[1 − ( n−1
n2 )(1 − λ)].
2.2
Stage 1: Choice of protection level
Before choosing rent-seeking expenditures, m out of n players determine how
much of the prize to protect and share equally. Solving by backward induction,
each players chooses λ to maximize his profit:
maxλ ΠN = αE + [1 − (
n−1
R
)(1 − λ)]
n2
n
(3)
The result is straightforward, yet rather surprising. When there is a prior
stage of rent protection, players choose the highest value of λ. Under the symmetric Nash equilibrium and assuming a feasible set for λ[0, 1], they will choose
full protection that is λ = 1. More generally, if the feasible set is λ{λ, ..., λ},they
6
will always choose the highest λ = λ.
1
In the second stage, players have no
incentive to rent-seek as the level of unprotected prize is negligible. If full protection is chosen, aggregate rent-seeking diminishes to zero. With the ability to
set protection in the prior stage, groups provide less incentives to rent-seek as
the remaining prize to compete for is lower. Because implementing any protection level is costless, it does not matter how many players within the group (m
out of n ) decide in Stage 1. Prediction 2 summarizes these findings.
Prediction 2: If selected members of the group can choose λ, they always
set the highest possible protection level, λ.
3
Experimental design
The game presented in Section 2 was played in groups of size n = 3. The
experiment consisted of two sequences of 10 rounds of the rent-seeking game2 .
Each round was broken into two stages in the following order: a protection stage
and a rent-seeking stage. Subjects’ task in stage 2 of the experiment was to allocate their endowment between a private activity (Activity M) and a collective
activity (Activity R). They were told that each token invested in Activity M
was worth 5 points, while the number of points received from their investment
in Activity R depended on their own investment and the other members’ investments. It was made clear that the fraction of the unprotected prize that
a subject would receive was determined according to the following rule: “you
investment in activity R over the total investment of your group in activity R”.
In each decision round, subjects disposed of an endowment of 20 tokens that
they had to allocate between activity R and activity M.
The experiment was designed to assess the performance of alternative institutions in mitigating rent-seeking activities. This constitutes stage 1 of the
experiment. There are two types of institutional treatments: exogenous and
endogenously determined protection. These institutions vary in the degree by
which subjects can participate in the protection stage. Under exogenously imposed protection, no subject is able to participate in the protection stage (i.e. external treatment). Subjects were told that the experimenter (i.e. the program)
would randomly choose the level of protection. Under endogenously determined
1 Each player has a dominant strategy of choosing the highest protection level. Any coalition
of players including singletons agrees to select the strongest protection level.
2 Sample instructions in French and English are available upon request.
7
protection, it is decided either through majority voting or dictatorial rule. Before the token allocation stage, each group determined how much of the points
in the common account should be protected and shared equally by the three
members. Three different levels of protection were feasible: λ∈ {0, 0.3, 0.7}
with λ = 70%. We chose the highest protection at less than 100% to reflect
the fact that property rights are usually imperfect in real word settings (e.g.
Chichilnisky, 1994). Nonetheless, 70% protection is high enough to exhibit its
disparities with weak protection (30%) and non-protection (0%). This setting
also allows us to investigate the effectiveness of institutional protection in driving group cooperation. In the majority voting treatment, all group members
participate in the protection stage. If an option gains 2/3 of the votes, it is
implemented. If members disagree and no option has acquired the majority,
then the prize remains unprotected. In the dictatorial treatment, participation
is restricted to one arbitrarily chosen member of the group who unilaterally
decides about the level of protection. This was done by selecting randomly an
anonymous dictator at the beginning of each round in each group. Because
voting is costless and subjects do not gain rent-seeking advantage in choosing
protection levels, the only differences between the two institutional treatments
are the degree of voting rights among subjects within the same group and the
possibility of disagreement among voters.3
Each session involved up to 18 subjects randomly assigned to a triad for
the duration of the experiment. In each triad, subjects interacted during 20
rounds. The 20 rounds were divided into two sequences of 10 rounds each. In
one of the sequences the size of the prize at stake was “low”, while in the other
sequence it was “high”. We set the low level at 100 units and the high level at
200 units. Motivated by resource curse literature (Wick and Bulte, 2006) which
states that sudden resource abundance encourages rent-seeking behaviour, we
explore the impact of a change in the prize at stake. Indeed, exploring the
change in prize size allows us to better compare the efficiency of institutions.
4
After each round subjects were given the following information: the chosen level
of protection (e.g. frequency of votes for each protection option), their share of
the unprotected collective account in Activity R, their gains from Activities R
and M, their profit for the current round, and their cumulative profit from the
3 From
a theoretical point of view, miscoordination should not arise because all players
have the dominant strategy of choosing the strongest protection level.
4 Wecntrol for the ordering of the sequences by comparing sessions which involve sudden
abundance (i.e. from 100 to 200 points) to sessions involving sudden scarcity i (i.e. from 200
to 100 points).
8
beginning of the sequence.
Upon their arrival at the experimental room, subjects received written instructions and check-up questionnaires for the first sequence only. However, the
instructions mentioned that they would play a second sequence shortly after the
first one, and that at the end of the experiment one of the two sequences would
be randomly selected to be paid. Including the show-up fee, the average payment for each subject was approximately 23 euros. Overall, the experimental
design allows for both within-group analysis (initial size of the prize at stake)
and between-group analysis (voting institutions). A total of six sessions were
conducted at the LEEM-University of Montpellier (France). Table 1 summarizes
the number of groups and subjects for each treatment.
As implied above, the parameters chosen for the experiment are as follows:
n = 3, R ∈ {100, 200} , α = 5 , E = 20 and λ ∈ {0, 0.3, 0.7}. The predictions are
summarized in Table 2. In the first stage, groups are expected to choose λ = 0.7
and invest 4 (8) tokens on the aggregate to rent-seeking when R = 100(200).
Based on the model of section 2, groups under all treatments are predicted to
choose the same level of rent-seeking expenditure in Stage 2.
INSERT TABLES 1 AND 2 HERE.
4
Results
We breakdown the presentation of our results into three subsections. In
the first two subsections, we concentrate on the data of the sudden abundance
regime. In subsection 4.1, we analyze the endogenously chosen levels of protection of the prize depending on the nature of the institution.. Meanwhile,
we analyze how protection affects group rent-seeking in subsection 4.2. Finally,
subsection 4.3 contrasts the findings for the sudden abundance regime to those
of the sudden scarcity regime.
4.1
Implemented protection levels
Because our key question is whether and how institutions affect decisions on
prize protection and group rent-seeking, we present the data at the group level .
We first compare the distributions of selected protection levels by groups for the
vote and dictator treatments. Table 3 contains information on the frequency of
9
each protection level, i.e. λ = 0, 0.3, 0.7, for all rounds.
RESULT 1: Stake size does not affect the choice of the protection level in
the vote treatment. In the dictator treatment, the strongest protection level is
more likely chosen when the size of the prize is higher. Support: Chi-squared
tests in Table 3.
As can be checked from table 3, the distributions of protection levels in the
vote treatment are very similar under low and high stakes. The relative frequencies of the strongest protection level (λ = 0.7) under low and high stakes are
71% and 76% respectively (Permutation test, p-value= 0.467). In total, almost
three-fourths of the groups implement 70% protection in the two sequences. In
contrast to the vote treatment, groups in the dictator treatment choose more
frequently high protection (from 56% to 68%, Permutation test, p-value= 0.061)
when stakes are increased.
According to the Nash prediction groups should always choose the highest
protection level, i.e. λ = 0.7. The institution is therefore irrelevant from the
perspective of profit maximization: choosing weaker protection levels cannot
provide larger private benefits to group members. However, because subjects’
decision might be “noisy” under the vote treatment, it could be that the empirical distribution differs from the prediction. If subjects’ decisions are “noisy”,
disagreements become likely and could result in the lack of protection. Result 2
below, however, does not provide sufficient evidence for this hypothesis. When
the size of the prize is low (sequence 1), 70% of groups in the vote treatment
selected the strongest protection as compared to only 55.8% of the cases in
the dictator treatment (Permutation test, p-value= 0.022). This difference is
mainly due to the observation that dictators are more likely to choose the weak
protection level of 30%. This contradicts the hypothesis that “noisy votes”
may lead to failures of protection under majority voting. When the size of the
prize is high (sequence 2), 76% of the groups in the vote treatment implement
70% protection compared to 68% in the dictator treatment. However, there
are no significant differences in the frequencies of implemented protection levels
between the two institutions (p-value= 0.249) when the prize is high.
RESULT 2: Comparing between institutions, strongest protection is more
frequently implemented in the vote treatment when the stakes are low. When
10
stakes become high, there are no significant differences in implemented protection levels. Support: Chi-squared tests in Table 3.
4.2
Group rent-seeking behaviour
We now explore whether there is a difference in group rent-seeking across
stake sizes and institutions. Do groups rent seek more when the prize is high?
Does it depend on the institutional environment and the level of protection
that is chosen for the group? In what follows we define an institution to be
more efficient if it leads to less group rent-seeking . In addition to the two
endogenous treatments (i.e. vote and dictator), we will also compare the result
for the baseline case where protection is exogenously chosen, i.e. the value of λ
is randomly selected with uniform probability.
RESULT 3: For the vote treatment, stake size does not affect group rentseeking behaviour. For the dictator and external treatments, increasing the size
of the prize intensifies group rent-seeking. Support: Table 4.
The impact of stake size on group rent-seeking is explored by sign-rank tests
in Table 4. Table 4 reports the overall mean rent-seeking expenditures of all
groups for all rounds during a sudden prize abundance. Looking at the results for
exogenously imposed protection, the increase in prize size leads to an additional
11-point allocation to rent-seeking (p-value = 0.027). When the prize becomes
high in the second sequence, one-third of the tokens are deviated towards rentseeking. Under the dictator treatment, group rent-seeking expenditures increase
1.6 times from 10 to 16 (p-value = 0.004). Under voting, doubling the stakes
does not intensify rent-seeking (p-value = 0.388). The change in group rentseeking expenditures is negligible at one unit.
Moving to between-group analysis, we now look at the effect of the type
of institutions on group rent-seeking. Findings in the previous section indicate
that, when the stakes are low, the vote treatment is more effective than the
dictator treatment in implementing the strongest protection level. Nonetheless,
this significant difference fades away after a sudden prize abundance. Given
these behavioural observations, we could expect that aggregate rent-seeking in
the vote treatment should be lower than in the dictator treatment only when
the prize at stake is low. However, Result 4 contradicts this conjecture.
11
RESULT 4: Following a sudden stake abundance, the voting institution is
more efficient than dictatorship. Moreover, in the dictator treatment groups
rent-seek more than in the external treatment when the prize at stake is high.
Support: Tables 4 and 5
The mean change in rent-seeking expenditures after a sudden prize increase
significantly differs between institutional treatments (rank-sum tests, see table
4). The mean difference in total group rent-seeking expenditures under the
external treatment is double than those under dictators (p-value = 0.049) and
eleven times those under voting (p-value of 0.007). Meanwhile, majority voting
and dictatorial rule are (weakly) significantly different in terms of efficiency
(p-value = 0.073).
Because prize protection is costless, the only difference between the majority
voting and dictator treatments is the degree by which subjects can participate
in the protection stage. Theoretical predictions indicate that there should be
no difference between these institutions in terms of protection: the number
of participants in the protection stage does not matter because subjects are
predicted to always prefer the efficient protection level. Our findings do not
support this prediction: the vote treatment is most efficient in curbing rentseeking after a sudden prize jump. Looking at the panel data regressions in
Table 5, and controlling for time effects, we find no institutional treatment
effects when the prize at stake is low. When the prize is high however, groups
in the vote treatment rent-seek less than in the dictator treatment (Wald test
p-value=0.082). Under voting the reduction in rent-seeking with respect to the
external treatment is almost twice as large than the equivalent reduction under
dictatorship. These results are also supported when data is disaggregated by
protection level as stated by Result 5.
RESULT 5: Group rent-seeking does not differ across institutions when 70%
prize protection is implemented. For lower protection levels groups rent-seek the
least in the vote treatment. Support: Table 6.
Table 6 shows that, when 70% prize protection is chosen , the vote and
the dictator treatments do not lead to a different level of rent-seeking than the
external treatment, both for low and high stakes. However, when a lower protection level is implemented, groups in the vote treatment rent-seek significantly
less than groups in the dictator treatment when stakes are high. More specif12
ically, groups in the vote (dictator) treatment rent-seek less (equally) than in
the baseline, both when λ = 0.3 and when λ = 0. Therefore, group rent-seeking
is affected in the dictatorial institution only when protection is high. Otherwise, the institution has no impact on rent-seeking compared to the baseline.
In contrast, under the vote treatment , when stakes are high group rent-seeking
is always negatively affected by the institution compared to the baseline. When
stakes are low, except when 0% protection is chosen, the two institutions do
not behave differently with respect to rent-seeking than the external treatment.
Under low stakes and in the absence of protection, surprisingly groups rentseek significantly more in the voting treatment than in the external treatment.
Aggregate rent-seeking increases by ten and four points relative to groups in
the external and dictator treatments, respectively (significant at the 1% level).
Different from the case of high stakes, when the initial prize size is low and the
highest protection is not implemented, exogenously determined protection levels are no longer significantly less efficient in reducing rent-seeking. As implied
earlier, when 0% is chosen under low stakes, groups in the external treatment
significantly rent-seek less than those subject to endogenously determined protection. Finally, it is also worth noting that group rent-seeking in the dictator
treatment does not significantly differ from the external treatment when 0%
protection is chosen and the initial prize at stake is high. When 30% protection
is chosen in the high-stake case, groups in the dictator treatment (26 points)
rent-seek more than those in external treatment (22 points).
4.3
Extension: Group behaviour under sudden scarcity
The results of subsection 4.2 are consistent with historical anecdotes on the
resource curse. Group rent-seeking intensifies when sudden prize abundance
occurs. However, this is highly conditional on the effectiveness of institutions
(Mehlum et al., 2006). As we have seen, in response to sudden abundance,
groups wherein everybody has the right to vote is most effective in curbing
out rent-seeking behaviour. Meanwhile, groups characterized by limited or no
democratic participation suffer from intensified rent-seeking. In this subsection,
we compare our findings to those of the case of sudden scarcity (i.e. high stakes
in the first sequence and low stakes in the second sequence). That is, does the
degree of voting rights matter too during a sudden fall in the prize competed
for? Results 6 to 8 below, indicate that, in the case of sudden scarcity, the two
institutions studied are not more efficient than the case where the protection is
13
randomly chosen.
Table 8 shows that groups’ implementation of λ = 0.7 protection is unaffected by the size of the prize, except for the vote treatment where sudden
scarcity induces more groups to choose λ = 0.7 (from 74.5% to 95.5%, Permutation test, p-value = 0.000 for vote and 0.114 for dictator). Furthermore, for the
two stakes levels, groups under the vote treatment are more likely to implement
λ = 0.7 protection than those in the dictator treatment (Permutation test, pvalue = 0.000 for low and 0.035 for high). Finally, groups under the dictator
treatment tend to choose 0% (30%) more frequently (low and high). This lead
us to Result 6.
RESULT 6: Regardless of the stake size, groups in the vote treatment choose
the strongest protection more frequently than those in the dictator treatment.
Support: Table 8.
Result 6 implies that groups who participate in a majority vote are more
likely to choose the highest protection for the prize. But, on the aggregate, are
these groups also able to cooperate more effectively in the rent-seeking stage?
In contrast to what we observed in the sudden abundance regime, despite the
differences in the frequencies of protection levels chosen, group rent-seeking
behaviour under sudden scarcity is not sensitive to the nature of the institution.
RESULT 7: Under sudden scarcity, mean differences in group rent-seeking
expenditures indicate that the effectiveness of institutional treatments do not
differ. Support: Tables 9 and 10.
The interpretation of group behaviour under sudden scarcity is different from
those under sudden abundance. Under sudden abundance, we defined an institution as efficient if it was able to prevent a rise in group rent-seeking. In other
words, we expect the mean difference in rent-seeking (“high minus low” stakes)
to be negligible or nil. But under sudden scarcity, an institution is efficient
if it leads to a decrease in rent-seeking expenditures, which would correspond
to a large mean difference in rent-seeking. Sign-rank tests in Table 9 show
that all institutional treatments lead to a fall in aggregate rent-seeking expenditures when groups experience sudden scarcity (respective p-values = 0.002,
0.004, and 0.027 for the vote, dictator, and external treatments). Meanwhile,
rank-sum tests indicate that the vote treatment (7 tokens) weakly leads to less
14
rent-seeking than the external treatment (10 tokens) when the prize is low (pvalue = 0.026). For both stake sizes, the external and dictator treatments lead
to the same results: 10 (19) tokens for low (high) stakes. However, the two
institutions are equally efficient under sudden scarcity. Looking at mean difference data, there are no significant differences between institutions. Controlling
for time effects, these results are confirmed by regressions in Table 10. Once
disaggregated, Table 11 implies that voting does not necessarily lead to the least
rent-seeking expenditures. Fo each protection level and regardless of the stake
size, groups in the external treatment sometimes rent-seek the least. Moreover,
looking at the regressions for 70% protection when the stakes are low, those
in the vote treatment rent-seek significantly more than those in the external
treatment. This, however, is crowded-out by the lack of observations for 30%
protection and the insignificant difference in group rent-seeking behaviour for
0% protection. Overall, these could explain the lack of treatment differences on
the aggregate (Result 7).
5
Discussion
Using a modified rent-seeking game, we provided experimental evidence
about the potential link between the degree of voting rights and group cooperation in an explicitly competitive environment. Compared to previous laboratory experiments on democratic participation, our paper is the first experimental exploration of the role of inequality in within-group voting rights in a
proportional-prize contest. We proposed a modified rent-seeking game where
selected members from the same group can vote to protect and share equally
the prize. We considered institutions differing in the degree by which members
from the same group are involved in setting the level of protection of the prize.
It is only when democratic participation is full that aggregate rent-seeking is
reduced. Contrary to recent experimental literature (Kocher et al., 2008), we
have also found that stake size affects cooperation. The importance of voting
rights is more pronounced when the stakes are suddenly increased. A higher
prize leads to relatively more rent-seeking when there is limited or no democratic participation in the protection stage. In contrast, higher stakes lead to
more cooperation only when there is full participation of group members.
Because the implementation of prize protection is neither costly nor advanta-
15
geous5 , theory suggests that group members should always choose the strongest
protection level. If the prize is strongly protected, all group members can share
costlessly a large fraction of the prize and save on rent-seeking costs. Theoretical predictions imply that the degree of voting rights should not affect rentseeking behaviour. Aggregate findings for the case of sudden scarcity somehow
is consistent with theory. Even if there are differences in the frequency distribution of protection levels, there are almost no significant differences in group
rent-seeking behaviour between institutional treatments. In contrast, groups
experiencing sudden abundance behave differently from the predictions of the
theoretical model. These results are more consistent with anecdotes on the socalled resource curse, i.e. the impact of sudden rent abundance is conditional on
institutional effectiveness (Mehlum et al., 2006 and Hodler, 2006). Thus, from
a behavioural perspective, in the proceeding discussion we focus on what drives
the aforementioned deviation.
Strong deviations of behavioural observations from theory can either be attributed to (a) to differences in the frequencies of protection levels between
treatments, or (b) to differences in democratic participation between treatments.
To restate, is group cooperation in the rent-seeking stage driven by the degree
of voting rights or the frequency differences of protection levels? In order to
discard option (a) we rely on Figure 1, which illustrates aggregate rent-seeking
expenditures decomposed by stake size and protection levels. As already stated
in the previous section, when the level of prize is high, there is lower group rentseeking under majority voting than in the dictator treatment. On the other
hand, when the size of the prize is low, rent-seeking expenditures do not differ
much between the voting and the dictator treatments. But clearly, the strong
fact is that the change in rent-seeking expenditures after sudden abudance is
negligible in the vote treatment. Even if the protection level chosen is 0%,
groups do not rent-seek more when the stakes are increased. When 0% protection is implemented, the mean difference in rent-seeking is the same as to when
there is 70% protection. Competition does not increase even if the stakes are
high, i.e. there is only a one-unit deviation as a consequence of sudden prize
abundance. This is also the case when 30% protection is implemented. The
deviation is negative: rent-seeking is lower when the initial size of the prize goes
up.
In contrast, groups in the dictator treatment had extreme results. Despite
5 This design allows us to provide a direct link (if any) to first and second stage decisions.
It also simplifies the tasks which experimental subjects are set out to undertake.
16
the absence of coordination issues under dictatorial rule and costless protection,
the dictator’s decision is only effective when he chose the strongest protection
level (70%). This may be because the failure to achieve highest protection under
voting might be easier to accept than under dictatorship. When he chose 30%,
group rent-seeking did not decrease as predicted. When the prize suddenly
became abundant, rent-seeking increased to almost twice the predicted level.
Although part of the prize was protected, subjects competed like under 0%
protection. When the dictator chose the low level of protection (30%) instead of
the strongest level, positive protection was unsuccessful in lowering rent-seeking
expenditures. Instead of encouraging less rent-seeking by group members, it
actually reinforced competition.
From the discussion above, we conclude that the degree of voting rights is the
main explanation for the differences of institutional treatments. More specifically, after a sudden prize abundance, groups involved in a majority vote institution tend to cooperate more in the rent-seeking stage. Even if they failed to
implement protection, changes in group rent-seeking expenditures remain negligible. Zero protection does not automatically lead to intensified rent-seeking.
Indeed, when groups in the vote treatment fail to cooperate in the first stage,
it was observed that they eventually reach more cooperative outcomes in the
second stage. This is not the case for the dictator treatment where there is
over-investment in rent-seeking for protection levels lower than the optimum
(70%). Because Section 4.1 indicates that there are no treatment differences in
the frequency distribution of protection levels, we can thus attribute differences
in group rent-seeking behaviour on the degree of voting rights. Overall, when a
sudden stake jump occurs, data from this experiment has shown that full democratic participation encourages group cooperation in an explicitly competitive
setting.
There are several potential extensions of our experimental design. First, one
may assume asymmetry among subjects. In one of the treatments, dictators can
have the option to choose a protection level that may give him unfair advantage
in the rent-seeking stage. Second, to provide value-added to the analysis, one
may add voting costs in the first stage. Third, the impact of group size on
institutional effectiveness is also of interest. These extensions are parts of the
authors’ future research agenda.
17
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Tables
Table 1: Number of independent groups and subjects per treatment
Treatment
VOTE, V
DICTATOR, D
EXTERNAL (control), E
Total
Groups
12
12
6
30
Subjects
36
36
18
90
Table 2: Rounded-off theoretical predictions on group rent-seeking efforts
λ, protection
None: λ = 0
Weak: λ = 0.3
Strong: λ = 0.7
R, stake size
Low: R = 100
14
9
4
High: R = 200
27
19
8
Mean difference in rent-seeking:
13
10
4
19
Table 3: Frequency of implemented protection by stake size and institutions
Institutions
VOTE
DICTATOR
EXTERNAL
STAKE SIZE
Low
High
Low
High
Low
High
70%
85 (70.8%)
91 (75.8%)
67 (55.8%)
82 (68.3%)
21
17
30%
12 (10%)
9 (7.5%)
25 (20.8%)
12 (10%)
17
20
0%
23 (19.2%)
20 (16.7%)
28 (23.4%)
26 (21.7%)
19
23
Total
120
120
120
120
60
60
Protection
Table 4: Mean group rent-seeking by stake size and voting institutions
Institutions
VOTE (V)
DICTATOR (D)
EXTERNAL (E)
Stake size
Rank-sum (p-value)
M v. D
E v. M
D v. E
Aggregate rent-seeking (std dev)
Low
11.71 (5.23)
10.73 (4.75)
10.70 (3.78)
0.488
0.742
0.925
High
12.04 (5.27)
16.02 (6.71)
21.93 (2.02)
0.112
0.005
0.075
Mean difference
0.33
5.29
11.23
0.073
0.007
0.049
# of group tokens
60
60
60
# of groups
12
12
6
Sign-rank (p-value)
0.388
0.004
0.027
Table 5: Impact of voting institutions on group rent-seeking efforts
RE-GLS Regression with clustered s.e. by group.
Dep var: Group rent-seeking
High stake
Coef.
SE
Low stake
Coef.
SE
vote
-9.891***
1.676
vote
1.016
2.066
dictator
-5.916***
1.904
dictator
.025
1.969
external (base)
28.199***
2.536
external (base)
13.283***
1.789
round
-.404***
.150
round
-.469**
.183
Overall R-sq
0.154
R-sq
0.030
obs
300
obs
300
Wald test: vote=dictator (p-value)
Significance level: * 10%, **5%, ***1%.
0.082
20
0.619
Table 6: Effectiveness of institutions, disaggregated by protection level
OLS Regression with robust s.e.
Dep var: Group rent-seeking
Protection (%)
70
30
0
High stake
Coef.
SE
Coef.
SE
Coef.
SE
vote
-2.455
1.729
-6.372***
2.262
-8.932***
2.519
dictator
-1.411
1.732
4.683*
2.701
-1.936
2.858
external (base)
12.411***
1.634
22.15***
1.634
28.782***
1.749
R-sq
0.018
0.259
0.1325
obs
190
41
69
Wald test: vote=dictator (p-value)
0.196
0.0002
0.018
Low stake
70
30
0
Coef.
SE
Coef.
SE
Coef.
SE
vote
1.058
1.46
1.745
3.029
8.556***
2.843
dictator
-0.507
1.44
-0.508
2.083
4.518**
2.228
external (base)
8***
1.27
15.588***
0.830
10.052***
1.561
R-sq
0.014
0.011
0.119
obs
173
54
70
0.520
0.162
Wald test: vote=dictator (p-value)
0.122
Significance level: * 10%, **5%, ***1%.
21
Table 7: Number of independent groups and subjects per treatment
Treatment
VOTE, V
DICTATOR, D
EXTERNAL (control), E
Total
Groups
11
Subjects
33
12
6
29
36
18
87
Table 8: Frequency of implemented protection by stake size and institutions
Institutions
VOTE
DICTATOR
EXTERNAL
STAKE SIZE
Low
High
Low
High
Low
High
70%
105 (95.5%)
82 (74.5%)
85 (70.8%)
73 (60.8%)
19
20
30%
0 (0%)
13 (11.8%)
18 (15%)
30 (25%)
23
23
0%
5 (4.5%)
15 (13.7%)
17 (14.2%)
17 (14.2%)
18
17
Total
110
110
120
120
60
60
Protection
Table 9: Mean group rent-seeking by stake size and voting institutions
Institutions
Vote (M)
Dictator (D)
External (E)
Stake size
Rank-sum (p-value)
M v. D
E v. M
E v. D
Aggregate rent-seeking (std dev)
Low
7.53(3.07)
10.25 (4.01)
10.5 (2.61)
0.102
0.026
0.606
High
18.63 (4.98)
19.68 (6.48)
19.5 (5.31)
0.665
0.615
0.925
Mean Difference
11.1
9.43
9
0.295
0.546
0.778
# of groups
11
12
6
Sign-rank
0.002
0.004
0.027
22
Table 10: Impact of voting institutions on group rent-seeking efforts
RE-GLS Regression with clustered s.e. by group.
Dep var: Group rent-seeking
High stake
Coef.
SE
Low stake
Coef.
SE
vote
-.863
2.500
vote
-2.963**
1.347
dictator
.183
2.731
dictator
-.25
1.511
external (base)
25.665***
2.520
exo (base)
15.426***
2.212
round
-1.121***
.247
round
-.317***
.119
Overall R-sq
0.089
R-sq
0.063
obs
290
obs
290
Wald test: vote=dictator (p-value)
Significance level: * 10%, **5%, ***1%.
0.655
0.0616
Table 11: Effectiveness of institutions, disaggregated by protection level
OLS Regression with robust s.e.
Dep var: Group rent-seeking
Protection (%)
70
30
0
High stake
Coef.
SE
Coef.
SE
Coef.
SE
vote
5.125***
1.235
7.916***
2.335
7.541**
2.962
dictator
6.293***
1.325
4.008**
1.947
1.176
3.256
external (base)
8.35***
.946
21.391***
1.319
30.058***
2.448
R-sq
0.064
0.143
0.129
obs
175
66
49
wald test: vote=dictator (p-value)
0.339
0.108
0.023
Low stake
Coef.
SE
Coef.
vote
1.908***
.703
no obs
dictator
3.042***
.796
3.077**
external (base)
5.157***
.498
11.478***
R-sq
0.028
0.126
0.009
obs
209
41
40
wald test: vote=dictator (p-value)
0.155
Significance level: * 10%, **5%, ***1%.
SE
Coef.
SE
2.511
3.817
1.404
1.052
3.043
.515
14.888***
1.809
0.727
23
24