Self-Enforcing Clientelism

Jorge A. Gallego

February 15, 2012

Abstract

Political clientelism is a dyadic relation in which a politician (the patron) gives

material goods and services to a citizen (the client), in exchange for political

support. If, at different stages of this relationship, both the patron and the client

have incentives to defect and not honor informal agreements, what makes clien-

telism self-enforcing? The following paper presents a game-theoretical model of

political clientelism in which a candidate disciplines a majority of voters through

the promise of a future flow of benefits. A mixed strategy involving a randomized

allocation of resources among constituencies makes clientelism feasible when the

politicians action is contingent on the result of the election. Higher campaign

budgets and lower voter aversion towards clientelistic parties, as well as higher

patience and higher heterogeneity across groups of voters, make clientelism more

likely. Swing voters tend to be gifted more frequently than core supporters with

this frequency increasing as group heterogeneity increases, presenting a positive

association.

1 Introduction

July of 2007 was the month in which the Colombian government reported that in the

weeks prior, in 16 states of the country, the Sisben (the system used for allocating

welfare state expenses) had been manipulated by politicians for electoral purposes.

This system classifies people according to their income and socio-economic status,

and offers benefits, subsidies, and services according to this classification. It can,

thereby, be inferred from this report that the system is an important instrument

Forthcoming, Journal of Theoretical Politics. I would like to thank Rebecca Morton, Adam

Przeworski, Alastair Smith, Joshua Tucker, Leonard Wantchekon, two anonymous referees and the

editor of the journal for their helpful comments.Department of Politics, New York University. Contact: jorge.gallego@nyu.edu

1

used by politicians for the establishment of clientelistic links: citizens that give po-

litical support and votes to certain candidates that may influence the assignment of

subsidies, may benefit from the system. The problem is that some medium-income

people are classified as belonging to the first tier of the system, which implies the

biggest flow of benefits. In contrast, some low-income citizens are erroneously clas-

sified as those not deserving subsidies. This shows that clientelism may become an

important obstacle for redistributive programs and may perpetuate income inequal-

ity and poverty.

However, clientelism is not an exclusive Colombian phenomenon. Urban politics

during the twentieth century in some of the most important cities in the US reveal

that patronage and clientelism can be found in other latitudes. In his analysis of

Chicagos machine politics, Gosnell (1937) presents the results of a survey involving

over 300 and 600 Chicago precinct captains in 1928 and 1936, respectively.1 One

half of the captains interviewed in 1928, and almost 70% of those interviewed in

1936, acknowledged that they handed out food to those constituents who were in

need. Naturally, they expected political support for their candidates in exchange

for this benevolent behavior. Many of these captains also revealed that they helped

their voters with other goods and services such as coal, Christmas baskets, temporary

shelter, legal aid and juvenile guidance, among others. Not surprisingly, most of them

also acknowledged that they acted in the role of job brokers at different governmental

offices, at the federal, state, county, sanitary district, city, school, and park levels.

As such, this phenomenon seems to present in a global capacity. Important

studies have reported characteristics of clientelism in Southeast Asia [Scott (1972)],

tropical Africa [Lemarchand (1972)], Southern Italy [Golden & Picci (2008)], Japan

[Kobayashi (2006)], Mexico [Greene (2001)] and Argentina [Stokes (2005); Weitz-

Shapiro (2007)], as well as several other countries and regions. How can we define

clientelism? Is clientelism exclusive to twentieth-century democracy or is it found in

other political regimes along human history?

Clientelism is a dyadic (two-person) relation in which a patron gives material

goods, services, benefits, or protection to a client, who reciprocates with some type

of general, political, or military support and assistance. Political clientelism, on

the other hand, is a special case of what we could term general clientelism. Political

1In Gosnells words precinct captains are the backbone of any metropolitan political organiza-

tion, since upon them rests the responsibility for seeing and winning the voters (p.51). They are

extremely important for the party machine as they act as the link between the party organization

and the voters in a determined precinct.

2

clientelism is characterized by a politician who acts as the patron, offering goods, ser-

vices, jobs, resources, protection, or other variables of value to a (group of) voter(s),

in exchange for political support, which in most cases, includes the vote, itself. The

conjunction of several dyads and relations forms a clientelistic network, as those de-

scribed in the examples given above. Nation-level leaders are linked with regional,

rural and urban brokers that establish relations with voters. Although some scholars

typically refer to patronage as the exchange of jobs in the bureaucracy for political

support, in this paper this term is used interchangeably with clientelism.

If clientelistic relations cannot be enforced through contracts, what makes the

agents comply and respect this type of informal agreement? For instance, given

that in many countries (after the introduction of the Australian Ballot) the vote is

intended to be confidential, why should a voter who received a gift from a politician

he dislikes honor the agreement and give him his vote? If during his campaign a

politician promised to his constituency certain goods and services that are costly, why

should he comply after he is elected? The main purpose of this paper is to explain

why clientelism is self-enforcing, meaning that the nature of the relationship between

the patron and client gives them incentives to cooperate with each other and respect

the informal agreement. This paper also tries to solve other questions related to

patronage systems. Some scholars recognize that clientelism is a typical phenomenon

related to poor and unequal societies [Robinson & Verdier (2003); Medina & Stokes

(2007); Stokes (2007)]. If this is the case and a context of scarce resources exists,

then how does a candidate allocate his limited budget among different groups of

the electorate, which are interested in becoming the clienteles? Are core voters

more frequently awarded for being loyal to the candidate? Or, on the contrary,

are swing voters the real target of the politician, given the political value of their

votes? Is group heterogeneity within a society, in terms of ethnic, social, or economic

characteristics, beneficial for clientelistic politicians?

In light of these questions, this paper presents a theoretical model that seeks

to address these issues. Within an infinitely repeated setting, in which elections

take place periodically, a budget-constrained clientelistic candidate has to allocate

his resources among three groups of voters. These groups share a common dislike

towards the candidates party, but differ in their attitude towards the candidate,

him or herself. The repeated nature of the interaction helps both the candidate and

the voters construct reputations and sustain cooperation in the long run. In order

to efficiently allocate campaign resources, the clientelistic candidate plays a mixed

strategy during each period. This involves rewarding more than one group with

3

positive probability, sacrificing the group that is ideologically more distant to the

candidate. Groups play grim trigger strategies in which each periods cooperation is

contingent on observing the politicians provision of gifts in the previous stage. The

politician, in turn, observes the aggregate result of the election and gives a gift in

a certain period, only if he has won the election. Consequently, aggregate electoral

results, as opposed to individual monitoring, discipline voters and motivate them to

comply with clientelistic politicians. The model shows that conditions for clientelism

are more favorable as dislike towards the party diminishes, diversity among the

groups rises, and as voters increasingly value the gifts offered by the candidate. In

this context, increased heterogeneity among the voters is beneficial for the candidate.

The model also predicts that swing voters tend to be gifted more frequently than

core supporters, and that this frequency increases as the groups become more distant

in their political preferences (i.e. as diversity increases).

This paper is divided into five sections, beginning with this Introduction. It then

proceeds to Section 2, which relates the subject of the article to existing literature on

the topic. Section 3 then presents a simple model of political clientelism, demonstrat-

ing how patron-client relations become more or less feasible as a function of several

parameters of interest. The basic feature of this model is that a candidate plays

a mixed strategy when allocating certain goods and benefits among constituencies

and utilizes this as an instrument for disciplining voters. Finally, Section 4 expands

on this analysis, incorporating random shocks into players preferences. A unique

mixed strategy that maximizes the candidates probability of being elected is found.

Comparative statics of this equilibrium show how ideological dislike towards the

clientelistic party, group heterogeneity, and the candidates wealth, affect the allo-

cation of goods among ideologically close or distant groups. Section 5 then presents

the conclusion to this paper.

2 Related Literature

In recent years, clientelism has been actively studied in economics and political

science.2 Stokes (2005), using an infinitely repeated prisoners dilemma, gives a

theoretical explanation of why candidates and voters have incentives to honor their

agreements and establish clientelistic relations. Politicians use what the author refers

to as perverse accountability, by threatening to cease the flow of benefits to a citizen

2Stokes (2007) and Kitschelt & Wilkinson (2007) survey much of the classic and recent literature

related with clientelism and patronage in modern societies.

4

if he fails to comply with a previous agreement. In this model it is assumed that ma-

chines (clientelistic parties) are able to (imperfectly) monitor individuals votes and

reward them, accordingly, in an ongoing interaction. During each period, a weakly

opposed voter either opts to vote for a candidate or not. In turn, the candidate

then simultaneously rewards the citizen or not. Players use grim trigger strategies,

punishing defection whenever the counterpart fails to honor the tacit cooperation.

Nevertheless, even though Stokes (2005) proposes some interesting questions per-

taining to the dynamics of patronage and clientelism, some of them remain unan-

swered. For example, according to the author (p. 315):

Yet in the societies where clientelistic parties or machines are active,

not all poor voters receive benefits. Limited resources force political

machines to choose among poor voters. Machine operatives everywhere

face a version of the dilemma that an Argentine Peronist explains. About

40 voters live in her neighborhood, and her responsibility is to get them

to the polls and get them vote for her party. But the party gives her only

10 bags of food to distribute, ten little bags, she laments, nothing

more. How does she (. . . ) decide who among her neighbors shall and

who shall not receive handouts?

The aforementioned quote reveals one of the main puzzles posed by clientelism.

In a context of scarce and limited resources, how does a clientelistic politician allocate

them among his constituency? Nonetheless, Stokes fails to answer this important

question. In her model, the machine distributes gifts (or at least makes the offer) to

every weakly opposed voter and budget limitations never constrain this distribution.

Some voters are excluded and do not receive a gift, but not because of budget

limitations. Loyal voters are never gifted because they always vote for the party,

regardless of whether or not they are a recipient of a gift. Similarly, opposition

voters never receive gifts, either, because their dominant strategy is to vote against

the party, even if a reward is given. Therefore, only weakly opposed voters are

rewarded. However, the model fails to discuss if the party has to select among this

class of voters due to gift scarcity or other considerations. In particular, if there are

40 weakly opposed voters, but only 10 bags of food, it cannot be inferred from the

model how the machine is going to allocate these resources.

Robinson & Verdier (2003) recognize that for clientelism to be self-enforcing,

neither public goods nor investment are attractive instruments for politicians to

use for the purpose of obtaining votes. For this reason patronage, understood by

5

the authors as employment in the bureaucracy, emerges as a politically efficient

strategy that enforces the relation, although it is economically inefficient. This model

explains why clientelism is significant, as well as frequent in countries that boast high

inequality and poor technology. It is cheaper to buy voters with jobs in a context

of low incomes. It also shows that clientelistic redistribution, with its associated

inefficiencies, tends to be worse in situations where productivity is low, the desire to

hold political power is high (rents are large), where money is relatively un-important

compared to ideology in determining political preferences, and where inequality is

high (p.21).

Wantchekon (2003) is one of the few empirical papers on political clientelism.

Using Benins 2001 presidential election and attempting to understand the effect of

voting platforms on voting behavior, the author randomizes the content of electoral

campaigning across villages. With the active participation of parties in the design of

the experiment, randomized villages were exposed to purely clientelistic platforms,

purely national public-policy platforms, or to a default mix of platforms. From the

results of the experiments, it can be inferred that clientelism is an effective vehicle

for acquiring votes and that, in certain cases, it is, indeed, self-enforcing. Further, it

has been found that clientelism has a greater effect on men, as well as less informed

and segregated voters [Vicente & Wantchekon (2009)]. Clientelism has also been

found to be electorally effective, especially for incumbents and regional candidates.

Incumbents have the advantage of making their clientelistic promises more credible,

perhaps because of their access to public resources. Nonetheless, challengers might be

provided the opportunity to highlight the failure of the incumbent should he neglect

to fulfill previous promises. The experiment also reveals that targets of clientelistic

politicians have traditionally been men, co-ethnics of the candidates and voters with

better access to information.

Myerson (1993) presents a static game-theoretical model that studies candidates

incentives to cultivate minorities and special interest groups, instead of appealing

equally to all voters under different electoral systems. Both in a two-candidate elec-

tion framework and in multicandidate electoral system, politicians choose indepen-

dently and simultaneously an offer distribution made to homogenous voters, in the

beginning of the game. Next, voters go to each candidates campaign headquarters,

receiving a randomly and independently selected offer from each one. Afterwards,

on the day of election, each voter compares the offers and votes for the candidate

that promises a bigger transfer. This framework is especially useful for explaining

why candidates have incentives that favor minorities and special interest groups un-

6

der different electoral systems. However, it fails to explain why this mechanism is

self-enforcing. In particular, it is assumed that voters are homogenous (so that they

do not show an ideological preference for any candidate and they only care about

the amount offered). As such, the model then cannot explain if candidates favor

swing or core voters. Additionally, as in Dixit & Londregan (1996), it is assumed

(and not endogenized) that candidates and voters trust each other and believe in

their promises (of distributions and votes).

Dixit & Londregan (1996) analyze the determinants of success in special-interest

(pork barrel) politics. In the presence of what they term tactical redistribution,

they ask the question: do politicians prefer to favor core voters or to favor swing

voters whose voting decision is not completely determined? Through their theoretical

model, the authors find that when political parties are equally effective in delivering

resources to any group in the society, swing voters are favored by transfers. On the

other hand, when groups have party affinities and parties are better at delivering

economic favors to their own groups, core voters (machine politics) prevail. Given

the static nature of this model, it is assumed that citizens trust politicians and that

they implement their campaign promises of transfers and taxes once they get elected.

In other terms, in this model what this paper seeks to explain is taken as granted,

because it is assumed that politicians honor their campaign promises, while citizens

trust politicians and, therefore, vote accordingly. Thus, even though the model gives

interesting answers to the question of how governments allocate economic benefits

among its constituencies, it does not explain why pork barrel politics is self-enforcing.

It is unclear why politicians redistribute and comply with tax and transfer promises,

as well as why citizens honor their commitment and do not simply vote for the

candidate that they ideologically prefer. Naturally, the static nature of the model

greatly explains this flaw.

One of the main puzzles that scholars aim to solve within this literature is why

clientelism and ethnicity tend to present together. For Fearon (1999), political coali-

tions are motivated to limit their size, so that the portion of the political pork

assigned to each member is not too low. In this sense, ethnicity becomes a natural

and efficient barrier that deters the entrance of people into winning political coali-

tions, limiting its size and thus maintaining a higher amount of material benefits for

each member. But, why is ethnicity the salient trait that identifies clientelism in

some societies, rather than religion, social class, education, party affiliation or any

other characteristic? Fearons basic argument is that a barrier is efficient as long

as potential members cannot choose the criterion that determines if somebody is

7

included or excluded from the group. The politics of pork favors coalitions based

on features not easily chosen or changed by individuals (p. 5). Ethnicity, to some

degree, satisfies this requirement.

Chandra (2007) also studies the relationship between patronage and ethnic pol-

itics. In her theory, patronage adopts the form of ethnic favoritism as the result

of a self-enforcing equilibrium, in which information constraints bias voters to favor

politicians of their same ethnic group, while politicians respond to these biases fa-

voring such categories. In her theoretical reasoning, Chandra questions the role of

secret ballots in patronage democracies and its impact on the enforceability of the

relationship between voters and politicians. She concludes that voting procedures

are unlikely to be confidential under patronage and for this reason candidates and

incumbents are motivated to offer material benefits to citizens in exchange for their

political support.

Signals as time spent in the booth, or aggregate results at group levels, provide

valuable information for the politician and motivates citizens to use their votes as

instruments to extract material benefits (p. 90). This paper follows a similar ap-

proach in the model presented herein. A candidate might ignore who did or did not

vote for him, but observes the aggregate result of the election. This serves a signal

of compliance of the different groups involved in the political transaction. Therefore,

secret balloting is not a barrier for the self-enforcing nature of clientelism. From this

analysis, it is also interesting to note that in patronage democracies citizens have

motivation to form groups in the pursuit of material benefits and politicians have

the motivation to target groups rather than free-floating individuals. In this paper,

clientelism is modeled precisely as the interaction between a candidate and different

groups of voters.

Yet another commonality between Chandras approach and the one developed

within the paper presented here is that, in both cases, it is argued that voters

evaluate candidates promises by checking the past record of patronage transactions.

In this paper this is modeled through an infinitely repeated game in which citizens

follow a grim trigger strategy, penalizing those candidates who do not comply with

the commitment. In Chandras words By probing for broad patterns in the history

of previous patronage transactions by incumbents, they [voters] identify the principle

on which patronage benefits were distributed in the past, which is their best guide

to how they will allot benefits in the future. Perhaps, the main variation between

both approaches is that in Chandras analysis, imperfect information governs the

relationship between citizens and politicians, and consequently ethnicity serves as

8

a signaling device that reduces the impact of this imperfection. For this reason,

Chandra provides an endogeneous mechanism that explains why groups are driven

to conform by members of the same ethnicity. In contrast, in the approach presented

within this article, this feature is not explained and can only be exogenously assumed,

at best. Nonetheless, this is not considered a major flaw of the model given that in

some countries (of which Colombia is a good example) patronage does not adopt the

ethnic flavor that it has in other latitudes.

3 A Model of Political Clientelism

In a context of scarcity and given that politicians are budget-constrained, how does a

patron allocate his gifts among those constituencies interested in becoming the clien-

teles? Are core voters awarded for their loyalty? Or, are swing voters the target

of candidates, given that they can be pivotal in an election? To answer these ques-

tions, consider a game in which a candidate to a public position interacts with three

equally-sized groups (1, 2, and 3). Each group casts one vote for the candidate or

his contender, and at least two out of three are needed in order to win. One of the

most interesting puzzles that the study of clientelism should solve is why citizens

who dislike a candidate and a party will vote for them in an election. Therefore, in

the following model, this paper ignores those citizens who prefer the candidate to his

contender. Instead, this article concentrates on groups that share a natural (ideo-

logical) dislike towards the candidates party. This dislike will be measured through

the parameter < 0, which represents the disutility that each group experiences

each time the party is in office.

Even though the three groups share a common dislike towards the party, they

differ in their sympathy, neutrality, or antipathy towards the candidate. This is mea-

sured by > 0, so that the ideological payoffs for each group when the politician

(p) is elected is given by

pi1(p wins) = pi2(p wins) =

pi3(p wins) = +

with > , so that the third group still experiences disutility if the candidateis elected. Hence, group 1 totally dislikes the candidate, group 2 remains neutral,

while group 3 likes him. Also, can be interpreted as a measure of heterogeneity

9

between the three groups, with a higher implying a higher degree of diversity in

their political preferences. For simplicity, assume that if this candidate is not elected

and his contender wins the election, the ideological payoff for each group is zero. This

means that pii(p loses) = 0, for i = 1, 2, 3.

To answer the questions posed at the beginning of this section, it is important to

recognize that the candidate has scarce resources he must use in order to obtain at

least two votes from the three groups. Assume that g > 0 represents an indivisible

benefit that the politician can only give to one of the groups. We can think of g as

a public job, a local public good, or any other indivisible commodity that cannot

be shared simultaneously by two distinct groups. Consequently, the total payoff for

group i, when the clientelistic candidate is elected, is given by

ui(p wins) =

pii + g if i receives a giftpii otherwiseFinally, assume that ps benefit for winning the election is given by v > 0, and that

g < v, so that the office is sufficiently valued regardless of the cost of buying the

clientele. The timing of the interaction, which will be called the clientelism-game,

is as follows:

1. The candidate p offers g to group 1, group 2, or group 3, or does not offer it

to anyone.

2. After observing ps action, the election takes place and each group votes simul-

taneously for or against p.

3. Payoffs are realized and p wins if he gets two or three votes. Otherwise, his

contender is elected.

Solving this extensive-form game yields five subgame perfect equilibria (SPE): in one

of them the candidate is elected with three votes, and in the other four he receives

less than two votes and loses the election. In every case, the politician chooses not to

give the gift to any of the groups. Clientelism does not exist in equilibrium because

the candidate never has incentives to favor any of the groups. Consequently, if the

game is played once, the underlying structure makes it unsuitable for explaining the

emergence of clientelism within electoral systems.

Now assume that the clientelism-game described above repeats during t = 1, 2, . . .

periods, so that the players ignore the time horizon. Every period the candidate

10

decides who receives g and each group votes or not for the candidate. The feasibility

of this interaction naturally results from the fact that elections are held periodically

and politicians run for reelection, with the possibility of interacting with the same

(group of) citizens every period. Given this new structure, the candidate has no

incentives to give the gift to the same group during each period. But it might be

the case that making uncertain this allocation is in his interest, because this could

discipline at least two groups and make them vote for him. Consequently, in what

follows this paper assumes that the politician might follow, in each period, a mixed

strategy of the form (0, 0, , 1 ), where 0 < < 1 is the probability that group 2receives the gift, while 1 is the probability that the benefit goes to the third group.The first two zeroes in the vector indicate that the candidate assigns probability zero

to the event of not giving a gift to any group, and to give it to group 1, respectively.

In this context, the candidate randomizes between the neutral and the sympathetic

group, and excludes the group that is less likely to vote for him.3

Being more precise, it assumed that players follow grim trigger strategies with

the following characteristics: the candidate plays (0, 0, , 1 ) in t = 1; For anyt > 1, he plays (0, 0, , 1 ) if he won the election in t 1; Otherwise, he plays(1, 0, 0, 0) forever. Group 1 votes against the candidate in every t = 1, 2, . . .. Groups

2 and 3 vote yes in t = 1, and in t > 1 if the candidate won and played (0, 0, , 1)in t 1. Otherwise, they vote against this candidate forever. Define (0, 1) asthe common discount factor for the players. Under what conditions these strategies

form part of a SPE in the infinitely repeated version of the game? Proposition 1

establishes sufficient conditions for the above strategies conforming a SPE.

Proposition 1:

Consider the infinitely repeated clientelism-game defined above, in which the candi-

date and groups 2 and 3 follow grim trigger strategies while group 1 always votes

against the candidate. Then, any mixed strategy of the form (0, 0, , 1 ) can bepart of a subgame perfect equilibrium as long as

g 1 + +

g(1)

for sufficiently close to one.

3In the context of repeated games, we might interpret as the proportion of periods in which

group 2 is honored with the gift. Nonetheless, being strict with the definition of mixed strategy,

is just a probability. Assuming that g in fact is divisible, it is also possible to interpret as the

fraction of the gift given to group 2 during each period.

11

Proof:

It is straight forward to show that the politician has no incentives to unilaterally

deviate from his strategy. Suppose that groups 2 and 3 vote for the candidate. If he

follows his strategy, his discounted payoff is

up(coop) =

t=1

t1(v g)

=v g1

If he cheats and deviates from giving a gift in every period, gets up(cheats) = 0.

Then, because v > g, the candidate always honors his strategy. In subgames that

come from a defection of either group 2 or 3 (or both), the present value of the

candidates payoff after following the grim trigger strategy is 0, while a one-stage

deviation (which implies giving g to either group after losing the election) yields a

payoff of g. Then, the candidate has no incentives to deviate from his strategy.Consider a subgame in which in the first period of the stage game, g is given to

group 2. In this case, group 2s payoff for cooperating is

u2(coop) = g + +t=1

t(g + )

= g + +

1 (g + )

After receiving the gift, if group 2 cheats, its discounted payoff is

u2(cheats) = g + (0) + 2(0) +

= g

Then, group 2 has no incentives to deviate from the grim trigger strategy as long as

g + +

1 (g + ) g

which is equivalent to

g (2)

It is easy to show that (2) is also the necessary condition so that group 2 has no

incentives to deviate in subgames in which the gift was given to group 3. In these

12

type of subgames, group 3s payoff for following the grim trigger strategy is

u3(coop) = g + + +t=1

t[(1 )g + + ]

= g + + +

1 [(1 )g + + ]

If this group cheats, receives u3(cheats) = g. Therefore, group 3 has no incentives

to deviate from the grim trigger strategy as long as

g + + +

1 [(1 )g + + ] g

or, equivalently, if

1 + + g

(3)

Again, (3) is also the condition for group 3s compliance in subgames in which the

gift is given to group 2. Finally, if the candidate and groups 2 and 3 follow their

strategies, no matter what group 1 does, it always receives an average payoff of

u1() = 1 . For the result of the election and the materialization of payoffs, it doesnot matter if this group votes against or in favor of the candidate. Hence, summing

up, a grim trigger strategy that supports a candidates mixed strategy of the form

(0, 0, , 1 ) constitute a subgame perfect equilibrium of the clientelism-game aslong as

g 1 + +

g

which completes the proof. Proposition 1 shows that there an infinite number of mixed strategies that can

be implemented by the politician, in a SPE of the clientelism-game. Within this

paper, the set of mixed strategies that satisfy (1) is referred to as the feasible set.

What are the basic properties of this set of equilibria? How does the feasible set

respond to changes in dislike towards the party, heterogeneity among the groups, the

magnitude of the gift, or players patience? Proposition 2 shows that some interesting

comparative statics of the infinitely repeated clientelism-game can be described.

Proposition 2:

Consider the clientelism-game in which any mixed strategy played by the candi-date in a SPE satisfies condition (1). Then, there exist:

1. A minimum gift (gmin) necessary for equilibrium which is

(a) Increasing in the magnitude of dislike towards the party ().

13

(b) Decreasing in the overall level of group heterogeneity ().

(c) Decreasing in players patience ().

2. A maximum level of dislike (max) towards the party, which is

(a) Increasing in the gift given by the candidate (g).

(b) Increasing in the level of heterogeneity among groups ().

(c) Increasing in players patience ().

3. A minimum level of heterogeneity (min) necessary for equilibrium, provided

that 2 > g. This level is

(a) Increasing in dislike towards the party ().(b) Decreasing in the gifts value (g).

(c) Decreasing in players patience ().

Proof:

1. From condition (1), the minimum necessary gift that the candidate must pay,

in equilibrium, is given by

gmin =2

which implies: a)gmin() =

2

> 0 for any (0, 1); b) gmin

= 1

< 0

for any (0, 1); and c) gmin

=2+

2< 0 for any (0, 1) because we

assumed > .

2. The magnitude of the maximum level of dislike towards the candidate, in equi-

librium, is given by

max = g + 2

which implies: a)(max)

g=

2> 0 for any (0, 1); b)(max)

= 1/2;

and c)(max)

=g

2> 0 for any g > 0.

14

Figure 1: Set of feasible mixed strategies as a function of g

g

(2+)

1

3. From (1), the minimum level of heterogeneity admissible for equilibrium is

min = 2 g

Therefore: a)min() = 2; b)

ming

= < 0 for any (0, 1); and c)min

= g < 0 for any g R++.

Proposition 2 describes the basic comparative statics of the feasible set of equi-

libria, in which the candidate disciplines groups 2 and 3 through clientelism. Even

though an infinite number of mixed strategies might be possible in the SPE of this

repeated game, particular conditions on heterogeneity, dislike towards the party, pa-

tience, and the size of the gift, constrain the politicians ability to establish patron-

client relations with the constituent. From this analysis, it should be clear that a

lower level of dislike towards the party, a higher level of heterogeneity, a higher mag-

nitude of the gift, and a higher level of patience, favor the candidates intention of

establishing a clientelistic relation with groups 2 and 3.

In figure 1 the set of feasible mixed strategies is plotted as a function of the

gift. The lower bound (i.e. the necessary condition for making group 2 comply) is

decreasing in g, while the upper bound (i.e. the necessary condition for disciplining

group 3) is increasing in this parameter. The shaded region represents the set of

mixed strategies that can be implemented by the candidate, for any given value of

15

Figure 2: Set of feasible mixed strategies as a function of

1

g+2

the gift. The intersection of and determines the minimum gift necessary for

equilibrium: gmin =2

. Naturally, this amount is positive because, 2 > .It is interesting to note that if the magnitude of the dislike towards the party ()diminishes, equilibria in which the given gift is lower are still admissible. In other

terms, if citizens feel more identified with the party, lower gifts are needed in order to

buy their votes. In a multidimensional policy-space setting, if citizens and candidates

are less distant in certain issues, like religion or security, it might be easy to explain

why voters support candidates that are apparently more distant in another issue,

even if gifts are not so tempting.

Additionally, this minimum gift is decreasing in the level of diversity among

groups (). Higher heterogeneity means that group 3 feels more sympathy for the

candidate when he is elected, while group 2s ideological utility remains unchanged.

This makes things easier for the candidate, which has to offer a lower gift because

group 3 will be more easily convinced. Finally, players patience (measured through

the common discount factor ) makes groups 2 and 3 value more the cooperative

agreement in which they vote for the patron, making gifts less important.

Figure 2 depicts the set of feasible mixed strategies, but now as a function of

the magnitude of dislike towards the party (.) The lower bound is increasing in while the upper bound is decreasing. This implies that as dislike increases, lessextreme or degenerate mixed strategies are implementable in equilibrium. The

intersection of both bounds yields the maximum level of intolerance to the party:

16

Figure 3: Set of feasible mixed strategies as a function of

1

g 2

max = g + 2

. This level is increasing in g, , and . Richer candidates can buy

voters that dislike more their party. More diversity makes party dislike less costly

to the politician. As stated above, this is because represents the sympathy that

group 3 feels when the candidate is elected. This attenuates and makes clientelism

easier. Higher patience makes intolerance towards the party less important because

the groups value more their future flow of payoffs.

Finally, figure 3 plots the set of feasible as a function of diversity . The lower

bound is constant in this case, because it does not depend on . Group 2s utility

does not depend on this parameter, so that the necessary condition for making

them comply is not a function of heterogeneity. Nonetheless, the upper bound is

increasing in . The intersection of both lines yields the minimum admissible level

of heterogeneity:

min = 2 gAs rises, more heterogeneity is needed to compensate the increased dislike

towards the party. Higher gifts or higher patience, make group 3s sympathy less

necessary for the establishment of clientelism. In this section a simplified model

of political clientelism and the comparative statics just described serve to illustrate

how the feasibility of patronage varies as a function of ideological and economic

conditions.

17

4 Clientelism-Game With Random Shocks

Even though the model presented in the previous section provides some interesting

predictions pertaining to how clientelism becomes more or less feasible as relevant

parameters change, the fact that an infinite number of mixed strategies can be imple-

mented does not solve some of the most interesting questions. As such, the following

section presents an extended version of the clientelism-game, incorporating random

shocks into the groups ideology payments. It was argued that groups exhibit a

natural aversion towards the party ( < 0) and that group 1 dislikes the candidate,

group 3 feels sympathy towards him, and group 2 remains neutral. This paper now

assumes that during each time period t in which the clientelistic candidate is elected,

the three groups are exposed to a random shock i, for i = 1, 2, 3, which increases or

decreases group is ideological payoff at time t. More specifically, groups ideological

payoffs now are given by

pi1(p wins) = + 1pi2(p wins) = + 2

pi3(p wins) = + + 3

where E[i] = 0 for i = 1, 2, 3. For simplicity, assume that i is uniformly distributed

over the interval [k, k], for k R++. Naturally, this implies that E[i] = 0 for eachgroup.

As before, assume that the game repeats during t = 1, 2, . . . periods and that

the candidate and groups 2 and 3 follow the grim-trigger strategies specified in the

previous section. Consequently, during each period the politician plays a mixed

strategy (0, 0, , 1 ) in which he assigns the gift g to group 2 with probability (0, 1). In the last section necessary conditions for equilibrium where establishedon . But how is really determined? What motivates the candidate to give the

gift with a higher probability to the close or to the distant group? Does he prefer to

more frequently solicit the group that ideologically is more distant to him, or is the

group that sympathizes with him awarded for this?

Given these conditions, it is natural to consider cases in which group 1 votes for

the candidate, even though they strongly dislike him and never receive a gift. Define

pi, for i = 1, 2, 3, as the probability that group i votes for the candidate. Therefore,

if [0, 1] represents the probability that the candidate gets elected in a givenperiod, = p1[1 (1 p2)(1 p3)] + (1 p1)p2p3. Assume that in equilibrium the

18

three groups play according to the following rule: If i xi, for certain thresholdvalue xi R, group i votes for the candidate. Hence, xi simply represents a cutpointwhich determines if a group supports or not the clientelistic candidate. Therefore,

the probability of having group i voting for the candidate is

pi = 1 F (xi)

where F (xi) = Pr(i < xi) is the cumulative distribution function (cdf) of i. Con-

sider the case in which the candidate chooses in order to maximize his probability

of being elected in any given period. Then, the clientelistic politicians problem for

each period can be stated as

max = p1[1 (1 p2)(1 p3)] + (1 p1)p2p3s.t. [0, 1]

pi = 1 F (xi)

Naturally, we have to carefully establish the cumulative distribution functions F (x1),

F (x2) and F (x3) in order to solve this game. We know that each period group 1

votes for the clientelistic candidate as long as

+ 1 0

This equation implies that group 1s threshold value is

x1 = + (4)

Similarly, group 2 supports the candidate if

+ 2 + g 0

which implies

x2 = g (5)

Finally, the candidate receives support from group 3 if

+ + 3 + (1 )g 0

Consequently, group 3s threshold value is

x3 = (1 )g (6)

19

Now that we explicitly know the threshold values for each group, it is time to present

the main result of the model: the optimal value that the candidate chooses inorder to maximize the probability of being elected.

Proposition 3:

Consider the infinitely repeated clientelism-game with random shocks in which the

candidate chooses in order to maximize his probability of being elected in each

period. Then, in the optimal mixed strategy supported by a SPE, group 2 receives

the gift in every period with probability

=1

2+

2g

Proof:

We know that i is uniformly distributed in the interval [k, k]. Then, if f(x) is theprobability density function for any x [k, k] it is true that f(x) = 12k . Therefore,for group i

pi = 1 F (xi)

=

kxi

f(x)dx

=

kxi

1

2kdx

=1

2 xi

2k

Substituting (4) into the last equation, we find that

p1 =1

2+

2k(7)

Similarly, using (5) we find that for player 2

p2 =1

2++ g

2k(8)

Finally, from (6) for player 3

p3 =1

2++ + (1 )g

2k(9)

The candidate wants to maximize the probability of being elected, which can be

written as

= p1[1 (1 p2)(1 p3)] + (1 p1)p2p3= p1(p2 + p3) + p2p3(1 2p1)

20

From (7) it is clear the p1 is not a function of , so we can treat it as a constant.

Also, from (8) and (9)

p2 + p3 = 1 +2+ + g

2k

Consequently, p2 +p3 also does not depend on and can be considered as a constant

in this analysis. Therefore, in an interior solution of the candidates maximization

problem, the first order condition is

=(p2p3)

[1 2p1] = 0

From (7), it is clear that p1 < 1/2. Hence, the first order condition implies that

(p2p3)

= 0

Also, from (8) and (9) we know that

p2p3 =

(k + + g

2k

)(k + + + (1 )g

2k

)Consequently, the first order condition reduces to

g

2k

(k + + + (1 )g

2k

) g

2k

(k + + g

2k

)= 0

and solving, we find the optimal mixed strategy for the candidate:

=1

2+

2g(10)

The second order condition isg22k2

< 0

for any . Therefore, is a maximum. It is important to note that since 2g > 0, it is always the case that

> 1/2.This means that group 2, the neutral group (which at the same time is more distant

from the candidate than group 3), receives the gift with a higher probability than

the sympathetic group 3. The politician gives the gift more frequently to the

group that is ideologically less identified with him, probably because a bigger effort

is necessary in order to make this group comply. In other words, 1 < 1/2 is aconsequence of group 3s sympathy to the candidate. This does not mean that the

politician only allocates resources to one group. He still has incentives to randomize

in order to make clientelism self-enforcing. Some interesting features characterize

this randomization, as established by proposition 4.

21

Proposition 4:

In the SPE in which the candidate and groups 2 and 3 use the grim trigger strategies

established in the clientelism-game with random shocks, the optimal mixed strategy

implemented by the politician has the following properties:

1. Higher heterogeneity between groups implies higher odds of giving the gift to

the neutral group.

2. Higher gifts available to the candidate imply lower probability of giving them

to the neutral group.

3. In equilibrium, groups 2 and 3 vote for the clientelistic candidate with the same

probability

Proof:

Partial derivatives (comparative statics) of the optimal mixed strategy reveal that:

1. is increasing in :

=

1

2g> 0

for any pair g > 0.

2. is decreasing in g:

g=2g2

< 0

for any pair (g, ) R++ R++.

3. Substituting (10) into (8) yields

p2 =2k + 2+ g +

4k(11)

While (10) into (9) yields

p3 =2k + 2+ g +

4k

Therefore, in equilibrium, p2 = p3.

Proposition 3 describes the unique mixed strategy that a clientelistic politician fol-

lows in equilibrium. Proposition 4 shows how this mixed strategy varies as a function

of the relevant parameters of the model. First, as diversity between groups rises, the

probability that group 2 receives the gift also increases. This should be intuitive.

22

More diversity, in the context of this model means that group 3 feels more sympathy

towards the candidate, while group 2 remains neutral. Consequently, the candidate

makes a higher effort trying to convince the more distant group (2). Second, as the

gift is higher, is lower. Higher gifts make it unnecessary to bribe the same groupso frequently. A richer candidate will have the capacity to bribe with a relatively

more egalitarian frequency both groups. In other terms, a higher budget makes the

politician more democratic. The third result of this proposition shows that in equi-

librium the candidate chooses in order to make equally likely that groups 2 and 3

vote for him. This explains why > 1/2: It is necessary to reward with a higherprobability (or in a higher proportion) the more distant group in order to compensate

its larger dislike towards the candidate. For this reason, in order to make equally

likely core and swing voters support, in equilibrium the probability of rewarding

swing voters should be higher. Propositions 5 and 6 show how group heterogeneity,

dislike towards the party, and the candidates budget, affect the politicians likelihood

of being elected, and his expected time in office.

Proposition 5:

Define the expected time in office of the candidate, R+, as the expected numberof periods in which the politician serves for the public position he is competing

for. For simplicity, assume that group 1 never votes for the candidate. Then, for

the clientelism-game with random shocks, in equilibrium, the probability that the

politician is elected in every period, and the expected time in office are given by

=(2k + 2+ g + )2

16k2

and

I =16k2

16k2 (2k + 2+ g + )2if the candidate is the incumbent at the beginning of the game, or

C =(2k + 2+ g + )2

16k2 (2k + 2+ g + )2

if he is the challenger.

Proof:

If group 1 never votes for the candidate, p1 = 0 and = p2p3 = p22. Therefore, from

(11) we find out that

=(2k + 2+ g + )2

16k2(12)

23

Also, if the candidate is the incumbent at the beginning of the game, the expected

time in office is given by

I = 1(1 ) + 2(1 ) + 32(1 ) +

= (1 )i=1

ii1

which simplifies to

I =1

1 (13)

Substituting (12) into (13), yields

I =16k2

16k2 (2k + 2+ g + )2

If the candidate is the challenger at the beginning of the game, his expected time in

office is

C = 0(1 ) + 1(1 ) + 22(1 ) +

= (1 )i=1

ii

which is the same as

C =

1 (14)

Using (12) and (14) we find that

C =(2k + 2+ g + )2

16k2 (2k + 2+ g + )2

Which completes the proof.

Finally, proposition 6 presents the comparative statics of both the candidates

likelihood of being elected in each period, and his expected time in office.

Proposition 6:

Suppose that groups dislike towards the party is sufficiently small, so that 2 0

Therefore, it is also the case that j

,j

g , andj

are all positive when 2 0. Then, inthe optimal mixed strategy supported by a SPE, group 2 receives the gift in every

period with probability

=1

2+

2g+k1(k3 k2)2g(+ )

Proof:

Following the same procedure of proposition 3, we know that groups support the

clientelistic candidate with probabilities:

p1 =1

2+ 2k1

; p2 =1

2++ g

2k2; p3 =

1

2++ + (1 )g

2k3

Once more, assuming that in order to win the candidate needs the support of at

least two groups, he is elected with probability

=

(k1 +

2k1

)[1 +

+ g

2k2++ + (1 )g

2k3

]+

(+ k1

)(k2 + + g

2k2

)[k3 + + + (1 )g

2k3

]Given that the candidate chooses to maximize , in an interior solution we have

(k1 + )(k3 k2)g4k1k2k3

+

(+ k1

)(g(k3 k2 + + g 2g)

4k2k3

)= 0

and solving, we find the optimal probability of rewarding group 2:

=1

2+

2g+k1(k3 k2)2g(+ ) (15)

26

The second order condition is(+

k1

)(2g24k2k3

)< 0

Therefore, is a maximum. Given that playing forms part of a Nash Equilibriumof the stage game, the grim trigger strategy supporting in every round of therepeated game is a SPE.

Hence, the probabilities (frequencies) at which groups 2 and 3 are rewarded by

the candidate are now functions of the relative densities of the groups. In other

words, the distribution of clientelistic benefits now also depends on how many swing

or undecided voters comprise each group. Additionally, there are other important

changes in the comparative statics of this equilibrium. Of particular relevance, the

effects of heterogeneity, party identification and the candidates budget on the dis-

tribution of clientelistic benefits, now depend on the relative amount of swing voters

in groups 2 and 3.

Proposition 8:

In the SPE in which the candidate and groups 2 and 3 use the grim trigger strategies

established in the clientelism-game with random shocks and heterogeneous density

functions, the optimal mixed strategy implemented by the politician has the following

properties:

1. Lower density in group 1 implies higher odds of giving the gift to the group

with more swing voters.

2. If k3 k2 increases, the probability of rewarding group 2 increases as well.

3. Higher intergroup heterogeneity increases the probability of rewarding group 2

if k3 k2 is sufficiently small. Otherwise, higher heterogeneity implies thatthis probability is lower.

4. A higher candidates budget increases the probability of rewarding group 2 if

k3 k2 is sufficiently small. Otherwise it decreases such probability.

5. Higher dislike towards the clientelistic party increases the probability of re-

warding group 2 if its density is lower than group 3s. Otherwise, it decreases

such probability.

Proof:

Partial derivatives (comparative statics) of the optimal mixed strategy of the game

with heterogeneous densities reveal that:

27

1. Opposers density:

k1=

k3 k22g(+ )

Therefore

k1> 0 if k3 > k2.

2. Relative density between neutrals and supporters:

(k3 k2) =k1

2g() + > 0

3. Intergroup heterogeneity:

=

1

2g k1(k3 k2)

2g(+ )2

Hence,

> 0 if k3 k2 < (+)2

k1.

4. Candidates budget:

g=k1(k3 k2)2g2(+ )

2g2

Consequently,

g > 0 if k3 k2 < (+)k1 .

5. Party identification

() =k1(k3 k2)2(+ )2

Therefore,

() > 0 if k3 < k2.

The first item of proposition 8 illustrates that having less swing voters in group 1

(higher k1) favors group 2 only if this group is comprised of more swing voters than

group 3. In other words, as group 1 becomes less swing, the candidate allocates

more resources to the group with the higher population of swing voters between

groups 2 and 3. Item 2 depicts that, as the number of swing voters in group 2 in-

creases relative to group 3 (higher k3k2), the probability of group 2 being rewardedalso increases. Thus, with all else being equal, possessing a greater population of

undecided or easy-to-buy voters results in a guarantee of more resources. The

third item of this proposition concludes that when there are sufficiently more swing

voters in group 3 compared to group 2 (k3 k2 sufficiently small), more intergroupheterogeneity increases the amount given to group 2.4 The rationale for this outcome

4It makes sense to talk about amounts if we interpret as a fraction, instead of a probability.

28

is as follows: When group 3 has more swing voters, it is natural to infer that more

resources are given to that group. But if grows, group 3, as a whole, becomes more

loyal so more resources can be given to the neutral group.

The fourth item of proposition 8 suggests that if there are sufficiently more swing

voters in group 3 compared to group 2, more resources are given to group 2 as the

candidates budget increases. The rationale is similar to before. When group 3 has

many more swing voters than its counterpart, it is natural to infer that it receives

more resources. However, if the budget increases, those extra resources can then be

allocated to persuade members of group 2. Finally, item 5 reveals that as dislike

towards the clientelistic party increases (higher ), the probability of rewardingthe neutral group grows if there are more swing voters in group 3 and vice-versa.

Hence, the model predicts that as party identification grows, the group comprised

of more extreme (inflexible) voters will benefit, while the group comprised of more

swing voters will be punished.

5 Discussion: What is Clientelism?

The model presented in this paper describes a particular type of clientelism: the

transfer of material benefits (cash) in exchange for political support. This particular

choice does not mean that any type of transfer between a candidate and the elec-

torate will equate to clientelism. For example, if an incumbent politician running

for reelection favors certain group of voters through a subsidy, it is not necessarily

representative of clientelism. Instead, such strategy could be another form of redis-

tribution as it could simply be the result of the ideological and programmatic agenda

of the candidate. Nonetheless, the way clientelism is modeled in this paper distin-

guishes it from other forms of redistribution for one basic reason: the allocation of

gifts is conditioned in accordance with previous voting behavior.

In the context of the model, if g were to represent a subsidy, for instance, it

would then not be necessary to employ a grim trigger strategy, involving allocation

by the candidate only if the groups formerly supported him. Under programmatic

redistribution, allocation of resources would be modeled based on the maximization

of an ideological utility function and its outcome. Time would only matter if the

structural economic conditions that determine such allocation change. It would not

be because citizens vote in a particular manner. Therefore, in order to appropriately

model clientelism, this paper includes the repeated interaction between the candidate

and the groups of voters even when this is not mathematically required: the one-shot

29

version of the probabilistic voting model presented in section 4 would be sufficient.

But the repeated framework developed in section 3 is kept precisely to distinguish

between clientelism and other forms of redistribution.

Naturally, the transfer of material benefits or cash based on past or present

voting behavior is not the only plausible form of clientelism. In many cases, politi-

cians discipline voters by using mechanisms that determine future flows of income

based on electoral results. Typical examples of this method include employment

in the public sector or public contracts. Robinson and Verdier (2003) discuss this

other form of clientelism, illustrating that, if incumbents and challengers compete

for votes through policies and transfers, then under certain circumstances the incum-

bent has incentives to reduce investment in order to attract supporters. A reduction

in investment makes the private sector less productive, which makes employment

in the public sector appear more attractive for certain groups. Hence, those voters

will support the incumbent, because his victory will promote public sector employ-

ment. Consequently, under a clientelistic regime, a lower level of investment results

in negative consequences to productivity and efficiency, thereby increasing poverty

and inequality.

There is no doubt that employment in the public sector is an important compo-

nent of clientelism. But it is not the only one. In fact, most of the empirical litera-

ture on vote-buying and clientelism shows that cash and other immediate material

goods are widely used all across the globe [see Vicente (2010), Gonzalez-Ocantos

et al. (2012), Finan & Schechter (forthcoming), and Gallego & Wantchekon (2012)].

Robinson and Verdier (2003) do not have a satisfactory theory for this form of pa-

tronage. In fact, in their model the optimal amount of transfers that candidates give

to voters is zero. On the contrary, the model presented in this paper provides a the-

oretical description of why this form of clientelism takes place and is self-enforcing.

6 Conclusion

One of the major puzzles of political clientelism is explaining why agents comply with

these types of agreements, even when they have incentives to cheat and even provided

that in most democracies the vote is confidential. In this paper, a simple mechanism

that explains why clientelism is self-enforcing is presented. The result of the election

provides politicians with a signal of voting behavior. However, more interestingly, the

election results provide a powerful mechanism for disciplining voters. Therefore, in

a repeated context in which votes are unobservable but results are, clientelism might

30

emerge as a result of equilibrium behavior. Citizens have incentives to honor their

agreements in order to maximize their future flow of payoffs, which in many cases

is higher when the clientelistic candidate wins the election and gives future benefits.

In addition, the candidate has incentives to cultivate his clientele and provides them

with goods and benefits (even at a personal expense), in order to promote voter

compliance and secure their vote. It is interesting to note that in this model the

promise of future gifts attenuates the ideological disutility that a citizen experiences

when a disliked party comes into power.

Some contexts are more favorable than others for patron-client relationships. In

the model presented here, the clientelistic politician is favored when dislike towards

his party is not so high, when diversity among neutral and sympathetic groups is

higher, when agents are more patient and place higher value on the future, as well

as when his budget allows him to offer better and more valuable goods or benefits.

Nonetheless, its results are extremely important to understanding what determines a

politicians allocation of scarce resources. Under certain circumstances, swing voters

are more valued and, consequently, they receive higher benefits more frequently. But,

the case also exists that other circumstances make core voters more important in

relative terms, so that allocations are more egalitarian in equilibrium.

Nevertheless, several puzzles remain unanswered. What is the relation between

clientelism and poverty? And with income inequality? In the model presented,

groups differed in their ideological preference towards the candidate. However, it

would be interesting to understand how a clientelistic politician allocates resources

among groups that differ in income. Are poor voters more frequently bribed? Is the

medium class the main target of politicians? Some studies suggest (Stokes, 2005)

that clientelism is more frequent in poor and unequal societies. This seems reasonable

given that for a politician it is cheaper to buy poor voters. In addition, as inequality

increases, the gap between the rich elites that support certain candidates and the

poor voters increases. As such, it would be certainly intriguing to incorporate these

dynamics into the framework described in this paper.

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