This paper analyzes endogenous lobbying over a unidimensional policy issue. Individuals differ in policy preferences and decide either to take part in lobbying activities or not. They are assumed to be group rule-utilitarian such that they follow the rule that, if followed by everyone else in their special interest group, would maximize their group’s aggregate welfare. Once formed, lobbies make contributions to the incumbent government in exchange for a policy favor as in a common-agency model. I show the existence of equilibrium with two organized lobbies. Individuals with more extreme preferences are more likely to join lobbying activities. Therefore, the lobbyists are rather extremists than moderates. However, the competition between those extreme lobbies results in a more moderate policy outcome relative to that initially preferred by the biased government. Lobbies therefore guard against extremism, while acting as moderators of the government’s preferences.

Lobbying is a highly controversial phenomenon, often seen in a negative light by the public at large. There has been, however, an argument put forward in support of lobbying. According to this view, lobbying permits opposing interests to battle preventing extremism (see DeKieffer 2007 ). In other words, the Madisonian view of politics – in which factions compete with each other precluding tyranny – works for lobbies too. The only difference is that disputes are settled by interests groups fighting each other in the post-election stage rather than by elections. The present paper aims to contribute to this line of thinking.

I analyze a model of endogenous lobbying over a unidimensional policy issue. Individuals differ in policy preferences and decide either to join a lobby that represents their special interest group (a pro-policy lobby or an anti-policy lobby) or not to take part in lobbying activities. The incumbent government cares about policy outcomes and lobbies’ contribution payments. Once formed, lobbies make contributions to the government in exchange for a policy favor as in a common-agency model of Bernheim and Whinston (1986) , adapted to lobbying by Grossman and Helpman (1994) .

I follow a group-rule utilitarian approach to the individuals’ coordination problem, inspired by Harsanyi (1980) . According to this approach, individuals are assumed to be group rule-utilitarian such that they follow the rule that, if followed by everyone else in their special interest group, would maximize their group’s aggregate welfare from the policy outcome. I show the existence of equilibrium with two organized lobbies. Individuals with more extreme preferences are more likely to be involved in lobbying activities. In equilibrium, each lobby is characterized by a threshold level of preferences such that all individuals with more pro-policy views (for the pro-policy lobby) or more anti-policy views (for the anti-policy lobby) participate in lobbying activities. This is in line with the results of Glazer and Gradstein (2005) and McCarty, Poole, and Rosenthal (2006) that extremists want to contribute the most.

While the lobby members are rather extremists than moderates, the competition between the lobbies moderates the government’s preferences. In particular, it shifts the final policy outcome in favor of individuals who are initially disadvantaged by the government. Intuitively, consider the case of a government biased in favor of high policy levels. Individuals with preferences similar to the government’s have less stake in the policy, since they are initially favored by the government’s preferred policy. Anti-policy individuals, however, are disadvantaged by the government’s preferences. Owing to the concavity of preferences, anti-policy individuals gain more than pro-policy individuals from the same (in absolute value) policy change.[1] Therefore, they are willing to contribute more to the government for a policy change. As a result, under a government biased in favor of high policy levels, the anti-policy lobby is more numerous and contributes more than the pro-policy lobby. The equilibrium policy level is more moderate than the one preferred by the biased government prior to lobbying, and thus favors anti-policy individuals. A similar argument, in reverse, applies to the case of a government biased in favor of low policy levels under which the equilibrium policy level favors pro-policy individuals. I show therefore that under lobbying, the final policy outcome favors individuals who are initially disadvantaged by the biased government. In other words, lobbies act as moderators of the government’s preferences preventing extremism. These findings contribute to the literature on biased experts and advocates, which also reports the moderating effects of competing lobbies on policy outcomes (see Dewatripont & Tirole, 1999 ; Krishna & Morgan, 2001 ). The difference is that in my setting, the government is assumed to be biased and so the lobbies make efforts to offset the government’s bias by means of contributions.

Under an unbiased government, lobbying does not affect the policy outcome. In this case the lobbies “neutralize” one another, so that the pro-policy lobby’s bids are matched in the equilibrium by the anti-policy lobby’s bids, and political competition results in an unbiased policy outcome. However, each lobby makes a positive contribution to the government to avoid an undesired policy promoted by a competitor. This is in line with the findings of Persson and Tabellini (2002) that diverging lobbies may neutralize each other’s influence.

This paper follows the most prevalent approach in the formal literature, based on the assumption that lobbies influence political decisions through contributions (Baron, 1989 ; Becker, 1983 ; Becker, 1985 ; Snyder, 1990 ). The recent literature follows this approach to address the questions of commercial lobbying (Groll and Ellis 2014 ), lobbying organization structure (Bombardini and Trebbi 2012 ), barriers to entry (Kerr, Lincoln, and Mishra 2014 ), and others. Reviews of this and alternative approaches can be found in Austen-Smith (1997) , Grossman and Helpman (2001) , and Persson and Tabellini (2002) . I use the common-agency model of Bernheim and Whinston (1986) applied to lobbying by Grossman and Helpman (1994) . Lobbying is modeled as a “menu auction”, where lobbies confront government with contribution schedules that map any possible policy into a contribution payment. Several authors have applied the common-agency model of lobbying to study trade policy, commodity taxation, the provision of local public goods, and other policies (Dixit, Grossman & Helpman, 1997 ; Grossman & Helpman, 1996 ; Helpman & Persson, 2001 ; Persson, 1998 ). To address the individuals’ coordination problem, I follow the group-rule utilitarian approach proposed by Harsanyi (1980) . This approach has been applied to political economy questions (in particular, to turnout) by Coate and Conlin (2004) and Feddersen and Sandroni (2006) . My setting is similar to theirs such that each group’s rule is characterized by a critical threshold. An individual with more extreme policy preferences in my case (with lower voting costs in their case) than a corresponding threshold should take part in lobbying (voting) while an individual with more moderate policy preferences (with higher voting costs) should not.

This paper complements the literature on collective action and lobby organization which dates back to the seminal work of Olson (1965) . Recent contributions have addressed the question of lobby formation in several different contexts. Some authors have focused mainly on the formation of lobbies from exogenously given special interest groups with a fixed cost (Drazen, Limão & Stratmann, 2007 ; Felli & Merlo, 2006 ; Felli & Merlo, 2007 ; Laussel 2006 ; Leaver and Makris 2006 ; Mitra 1999 ; Redoano 2010). Others have in some way addressed the problem of individuals’ decisions to lobby. For example, Damania and Fredriksson (2000 , 2003 ) , Magee (2002) analyzed incentives for two firms and for

The rest of the paper is organized as follows. Section 2 lays out a model. Section 3 describes the common-agency model of lobbying. Section 4 develops the concept of lobby formation. Section 5 establishes the existence of equilibrium with two organized lobbies. Discussions are presented in Section 6. Finally, Section 7 concludes the paper.

Suppose that a certain policy option

The society is inhabited by a large number (formally a continuum) of individuals, where the size (mass) of the population is normalized to unity. Individuals differ in their policy preferences. Denote by

The incumbent government decides on a policy outcome

Note that in the absence of political contributions (

Policy-making involves not only government decision-making but also special interest politics, or lobbying. Lobbying is modeled here as a two-stage game. The first stage of the game is a lobby formation stage, where individuals decide whether to participate in lobbying activities or not. The second stage of the game is a contribution game, where lobbies (organized in the first stage) offer the government contributions to affect the policy outcome. The game is described in detail in the following subsections.

Given the policy setting, it is reasonable to focus on the case in which two lobbies can be formed: a lobby of anti-policy individuals, given by a set

while that of pro-policy individuals is equal to

Then an individual faces the following trade-off when deciding on whether to participate in lobbying activities. On the one hand, he realizes that given a continuum of individuals, his participation would not affect the policy outcome but would give him utility from acting according to the rule. On the other hand, shirking would save him a contribution fee in case the rule specifies that he should participate in lobbying. In what follows, the utility from following the rule is assumed to be sufficiently high such that it exceeds the highest possible contribution fee in each lobby.[4] Then individuals have no incentive to shirk and so follow the rule that, if followed by every other individual from the same special interest group, would maximize the group’s aggregate utility from the policy outcome.[5]

Let each special interest group’s rule be a critical policy threshold such that an individual with more extreme policy preferences should take part in lobbying while an individual with more moderate policy preferences should not. Formally, I denote by

I focus on lobbying activities in the context of the common-agency model of Bernheim and Whinston (1986) , adapted to lobbying by Grossman and Helpman (1994) . In this approach, lobbying is modeled as a “menu auction”, where lobbies confront government with contribution schedules that map any possible policy into a contribution payment.

First, each lobby

where

Second, the government sets

(1)
−
γ
−
y
2
+
C
A
y
+
C
P
y
.

Equilibrium of the game is a subgame perfect Nash equilibrium in the contribution schedules, the chosen policy and the lobbies’ compositions. In the following section, the game is analyzed backwards. First, I solve for the policy level

Suppose that two lobbies

The equilibrium policy is Pareto optimal in the bilateral relation between the government and each lobby.

Therefore, the equilibrium policy maximizes the sum of the lobbies’ net objective functions

and the government’s objective (1). This sum equals

(2)
−
γ
−
y
2
+
U
A
y
+
U
P
y
.

Maximizing eq. (2) yields the equilibrium policy level

To find the contribution levels in the equilibrium, define

(3)
y
A
=
arg
max
y
∈
0
,
1
−
γ
−
y
2
+
U
A
y
,

In other words,

Lobby

Now one can solve for the lobbies’ contributions in equilibrium. The following proposition summarizes the results of the lobbies’ common-agency contribution game. Proofs of this and other results are delegated to the Appendix.

There exists an equilibrium in truthful strategies such that the equilibrium policy level is given by

The lobbies’ equilibrium contributions are equal to

If there is just one organized lobby, the government derives exactly the same utility as it would have achieved without any contribution. Thus, a lobby that faces no competition captures the entire surplus from lobbying activities. If two lobbies compete for the final policy, the government captures some surplus from lobbying activities, and each lobby pays according to the political strength of its rival.

The lobby formation stage of the game is analyzed in the following section.

The individuals follow the threshold rules

Once formed, the lobbies care about the aggregate utility of their members. Therefore, their gross objective functions read

In what follows, for ease of exposition and analysis,

The following lemma characterizes the equilibrium policy level

Given threshold rules

The lobbies’ equilibrium contributions in the case of two organized lobbies

In what follows, I show the existence of nonempty organized lobbies

The following proposition establishes the existence of equilibrium with two organized lobbies.

Given the government’s preferred policy

– for

– for

According to Proposition 2, for the government’s preferred policy

The result that some moderates do not lobby in equilibrium arises due to heterogeneity of preferences. The moderates’ interests are represented to some extent by the government that advocates a relatively moderate (though possibly biased) policy. Representing their interests also through lobbying would moderate the corresponding lobby. This would lead to a more moderate outcome, which would definitely benefit those moderates but not their special interest group. Since the individuals are group-rule utilitarian, they follow the rule that maximizes the group’s aggregate utility from the policy outcome and so leave the moderates aside. It is important to point out that this intuition applies to a larger group whose members have more heterogeneous preferences which range from quite extreme to rather moderate. A smaller group is formed by more homogeneous individuals with rather extreme preferences and so is better off including every member in lobbying activities.

It is important to emphasize that the rule each special interest group follows is assumed to take the form of a policy threshold. Consider the anti-policy group, for example. An anti-policy individual joins the corresponding lobbying group if his ideal policy lies in the interval

The following corollary provides comparative statics results.

The more biased the government in favor of high policy levels, the more numerous the anti-policy lobby

The more biased the government in favor of high policy levels, the higher the policy level

When the government is biased in favor of low policy levels,

When the government is biased in favor of high policy levels,

In case of the unbiased government,

Thus, lobbying somewhat moderates the government’s preferences. The implemented policy favors those individuals who are initially disadvantaged by the government’s preferred policy. Consider a biased government (which is in favor of either low or high policy levels). Then individuals whose preferences differ considerably from the government’s have more stake in the policy than individuals with preferences similar to the government’s. In other words, owing to the concavity of preferences, “disadvantaged” individuals are willing to pay more than “favored” individuals for the same (in absolute value) policy change. As a result, the lobby of “disadvantaged” individuals is more numerous and contributes more than the lobby of initially “favored” individuals. And the final policy becomes less extreme and goes in favor of the lobby with higher relative political strength, i. e., the lobby of individuals who are initially disadvantaged by the government’s preferred policy. It is important to emphasize that even though those individuals influence the final policy more than the advantaged group, they have to pay for it. Indeed, in equilibrium, the disadvantaged group’s contributions are higher than those of the advantaged group.

When the government is unbiased, lobbying does not affect the policy outcome. In this case the lobbies “neutralize” one another, so that in equilibrium

I show in Appendix F that the government utility in equilibrium is non-negative, increases in

Note that the equilibrium policy level under a government biased in favor of high policy levels is higher than that under a government biased in favor of low policy levels, with or without lobbying. Therefore, the pro-policy individuals would prefer a government biased in favor of high policy levels to that biased in favor of low policy levels in spite of the fact that under the latter they could influence the final policy in their favor by lobbying. In turn, the anti-policy individuals would prefer a government biased in favor of low policy levels, even though they could lobby more successfully under a government biased in favor of high policy levels.

My model of lobby formation predicts that lobbying over a particular policy issue moderates policy outcomes. This is in line with various facts about lobby impacts on policymaking. For example, in 2000, President Clinton signed the China Trade Bill which extended permanent trade relations with mainland China. Supporters of the bill (such as the US Chamber of Commerce and the Business Roundtable) argued that the bill would provide ample business opportunities and so took a lot of lobbying efforts to get it signed. Opponents of the bill (such as labor unions and environmental groups) opposed the bill because of China’s human rights and labor standards issues. They also believed that it would threaten the U.S. labor market because of job losses. The opponents’ concerns were addressed by a number of provisions, which led to a compromise towards a more moderate policy outcome relative to the initial pro-bill position of the Clinton administration.[7] Another example is the California Clean Energy and Pollution Reduction Act signed into law in 2015. The bill supporters (such as climate change groups and some Silicon Valley companies) advocated establishing new clean energy and greenhouse gas reduction goals. The initial proposal called for a 50 % reduction in gasoline use by 2030. The opponents (petroleum companies and drivers associations) argued that the bill offered no specific policy plans and could lead to gas rationing, driving restricting and fuel prices rising. They launched a massive lobbying campaign which resulted in the bill being amended and the petroleum provisions being dropped. Therefore, their lobbying efforts moderated the policy outcome to some extent.[8]

It is important to emphasize, however, that in the present model the individuals differ only in their policy preferences but not in their financial endowments. In other words, all individuals can pay their corresponding contribution fees. This assumption is crucial for my results. Intuitively, in the case of financial constraints, the individuals would not be able to make the contribution payments and so would not be able to offset the government’s bias. Then the moderating effect of lobbying would not arise. One can think of my setting as an “equal opportunity” environment in which the special interest groups face no or insignificant financial constraints.

The other important assumption of my model is that of no contribution caps (for models of contribution caps, see Cotton, 2012 ; Dahm & Porteiro, 2008 ; Drazen, Limão & Stratmann, 2007 ). Contribution limits would somewhat offset the moderating effect of lobbying in my model. Intuitively, consider a government biased in favor of low policy levels. In case of no contribution caps, the pro-policy lobby contributes more than the anti-policy lobby and so is able to “convince” the government to implement a less biased policy, which gives rise to the moderating effect. Suppose next that contribution limits apply and that the contribution cap falls between the equilibrium contributions of two lobbies. In this case, the pro-policy lobby would contribute the amount equal to the contribution cap while the anti-policy lobby would somewhat adjust its contribution downwards. Still, due to the concave utilities, the pro-policy lobby adjustment would exceed that of the anti-policy lobby. Therefore, the final policy would not be as moderate as in the case of no contribution limits. It implies that in my model, the contribution limits lead to less moderate outcomes and so partially neutralize the guarding effect of lobbying. It is important to stress that this is due to the “equal opportunity” nature of my framework in which individuals have the same financial endowments. In the case of endowment heterogeneity, the introduction of contribution caps might amplify the guarding effect of lobbying.

Note also that the quantitative results of my model depend on the way the anti- and pro-policy special interest groups are defined (with respect to the government’s preferred policy

The present paper studies the impact of lobbying on government decision-making. I develop a model of endogenous lobby formation, which predicts that individuals with more extreme preferences are more likely to participate in lobbying. It follows that the lobbyists are rather extremists than moderates. However, the competition between the lobbies benefits the public at large resulting in a less extreme policy outcome relative to that initially preferred by the government. I show that lobbying somewhat moderates the government’s preferences. The final policy under lobbying favors individuals who are initially disadvantaged by the government’s preferred policy. Indeed, under a government biased in favor of high policy levels, the final policy outcome is somewhat more moderate than that initially preferred by the biased policymakers. Under a government biased in favor of low policy levels, lobbying moderates the final policy in favor of pro-policy individuals. In the case of an unbiased government, lobbying does not affect the final policy, and political competition results in an unbiased outcome. However, each lobby has to contribute the same amount to the government to maintain this policy level.

My paper therefore presents a formal argument in support of lobbying as a guard against extremism. According to my results, the competition between extreme special interests results in a quite moderate policy outcome, which would not be achieved with no lobbies around. Nevertheless, this paper constitutes a partial attempt to study individual lobbying behavior and focuses on a specific form of coordination among citizens. It might be interesting to consider different coordination mechanisms that citizens use to overcome the free-riding problem.[9] It might also be interesting to consider a nonsymmetric distribution of preferences. In this case, I expect that the qualitative results presented above will still hold (except, probably, those for the case of an unbiased government).

The author is grateful to Daron Acemoglu, Antonio Cabrales, Filipe Campante, Luis Corchón, Jacques Crémer, M. A. de Frutos, Raquel Fernández, Rebecca Morton, Ignacio Ortuño Ortn, Albert Solé-Ollé, Allard Van Der Made, Bengt-Arne Wickström, two anonymous referees and Johann Brunner, the editor, for helpful comments, suggestions and encouragement; and to Cung Truong Hoang for research assistance. The grant from Karin-Islinger-Stiftung foundation is gratefully acknowledged. The usual disclaimer applies.

The lobbies’ truthful contribution schedules are

(4)
C
P
y
=
max
U
P
y
−
b
P
,
0
,
C
A
y
=
max
U
A
y
−
b
A
,
0
.

The constants

(5)
−
γ
−
y
A
2
+
C
A
y
A
=
−
γ
−
y
∗
2
+
C
P
y
∗
+
C
A
y
∗
,
−
γ
−
y
P
2
+
C
P
y
P
=
−
γ
−
y
∗
2
+
C
P
y
∗
+
C
A
y
∗
.

Plugging eq. (4) into eq. (5) yields

where the first line is lobby

The equilibrium policy level is equal to

The first-order condition of this maximization problem amounts to

The second-order condition is satisfied and so

If lobby

The first-order condition is given by

The second-order condition is satisfied and therefore

Likewise, if lobby

The first-order condition amounts to

The second-order condition is satisfied and so

According to Proposition 1, the lobbies’ equilibrium contributions are equal to

Plugging

and

The threshold rule

Plugging in the expression for

(6)
−
γ
1
+
α
2
−
π
2
+
2
γ
2
2
+
α
−
π
2
+
γ
2
1
+
α
2
−
π
2
+
2
γ
2
2
+
α
−
π
−
1
3
γ
3
.

The first derivative of eq. (6) with respect to

(7)
γ
1
−
α
4
+
α
+
2
γ
+
2
α
π
−
π
2
1
+
α
−
π
α
−
γ
+
π
2
2
+
α
−
π
3
.

The first derivative (7) is strictly positive for all

Evaluating it at the critical points yields that the second-order condition holds for

For

The threshold rule

Plugging in the expression for

(8)
−
1
−
γ
1
+
α
2
−
π
2
+
2
γ
2
2
+
α
−
π
2
+
1
−
γ
2
1
+
α
2
−
π
2
+
2
γ
2
2
+
α
−
π
−
1
3
1
−
γ
3
.

The first derivative of eq. (8) with respect to

(9)
1
−
γ
1
+
2
γ
+
α
−
π
2
−
4
π
1
−
α
2
+
α
1
+
γ
−
1
+
γ
−
π
π
2
2
+
α
−
π
3
.

The first derivative (9) is never strictly positive for all

–

–

–

The second derivative of eq. (8) is equal to

Evaluating it at the critical points yields that the second-order condition holds for

For

I find next the equilibrium threshold rules

for

for

for

for

This can be summarized as follows. For

For

I show first that given the rules

The equilibrium policy level is equal to

The aggregate utility of anti-policy individuals from the policy outcome

Plugging in the expressions for

which is a decreasing function of

I show next that given the rules

The equilibrium policy level is equal to

The aggregate utility of pro-policy individuals from the policy outcome

Plugging in the expressions for

which is an increasing function of

The first derivatives of

These derivatives are such that

When the government is biased in favor of low policy levels, i. e.,

It follows that

Lobby

When the government is biased in favor of high policy levels,

It follows that

Lobby

When the government in unbiased,

The government utility in equilibrium is equal to

It is non-negative, increases in

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