Congruence Among the Voters and
Contributions to Political Campaigns.∗
Elena Panova†
February 28, 2006
Abstract
This paper builds a theory of political campaign contributions.
Interest groups can engage in non-directly informative political advertising in order to signal their private information on the valence of
candidates. The paper’s key insights are: (a) campaign contributions
can be rationalized by interest groups signalling benefits; (b) political campaigns are cheaper, the more congruent the voters; (c) higher
campaign receipts by incumbents can be explained by better information available to interest groups that seek re-election; (d) campaign
contributions increase the voters welfare.
Key words: campaign contributions, voter information, incumbency advantage, electorate diversity.
JEL codes: D72, D82, M37.
1
Introduction.
Political campaign contributions play an important role in elections.1 While
this role varies across democracies, some patterns are common: political ad∗
This paper is based on the first chapter of my Ph.D. dissertation. I am extremely
grateful to my supervisor Jean Tirole for his guidance. I thank Mattias Dewatripont
and Andrea Prat who refereed my dissertation, and made many useful suggestions. I am
also grateful to David Dreyer Lassen, Nicolas Marceau, Louis Phaneuf, Cristian Shultz,
Peter Norman Sørensen, Julia Shvetz, John Sutton, and Etienne Wasmer for their helpful
comments.
†
GREMAQ, Université des Toulouse-1, CORE at UCL, and UQAM.
1
See surveys by Morton and Cameron (1992), Prat (1999, 2004), and Stratmann (2005).
1
vertising is expensive (although these expenses are small compared to stakes
of public policies); the vast majority of campaign contributions comes from
private sources, winners of elections (mostly incumbents) receive more contributions than losers.
These patterns clearly appear in US Congressional races (see our review
in the Appendix). During the last two decades, US Congressional candidates
raised and spent on average more than a billion of 2003 US dollars per election cycle. Around 80% of these contributions came from Political Action
Committees or directly from individuals. An incumbent candidate received
on average about 6 times more contributions than a challenger candidate.
Incumbents won on average more than 90% of House races and about 80%
of Senate races.
Given that private campaign financiers may pursue different objectives,
these observations raise the following inter-related issues: what are the incentives to contribute to electoral campaigns, and why does political advertising
influence the election? Furthermore, why do campaign contributions disproportionately benefit incumbent candidates?
In order to address these issues, we build a model where interest groups
signal private information they hold about the valence of candidates for office
by financing political advertising. Specifically, there are two interest groups.
Each interest group is a uniform constituency of voters who benefit from
group-specific public policy. There are two candidates competing for office:
the incumbent and the challenger.
Each candidate has a type that depends on her valence with different
interest groups. We make an important distinction between an unbiased
candidate, whose valence with differen interest groups is the same, and a
biased candidate, who is valent with one interest group but nonvalent with
the other. When there is a positive correlation between the valence of a
candidate with different interest groups, more weight is put on the event
that a candidate is unbiased. This correlation the most important parameter
in our model. It measures the congruence between the interest groups in
their preferences regarding the candidates.
The interest groups do not observe a candidate’s type when they vote.
However, before the election each interest group receives private signal on
whether the incumbent is valent with it or not. This signal depends on benefits by this interest group from group-specific public policy. These benefits
are either high, or moderate, or else null. Positive benefits signal that the
incumbent is valent, while no benefits signal that the incumbent is nonvalent.
2
Hence, in isolation the beneficiaries vote for the incumbent, while nonbeneficiaries vote for the challenger.
The quality of private information that is relevant to the vote may differ
between the interest groups. More precisely, private signal on the incumbent’s type held by an interest group is stronger, the higher its benefits from
group-specific public policy. Therefore, when the incumbent delivers policy
benefits to only one interest group, information about these benefits encourages nonbeneficiaries to vote for her if sufficiently high prior weight is put on
the event that a candidate is unbiased.2 Hence, both interest groups potentially benefit from information sharing before the election: nonbeneficiaries
may increase the efficiency of their vote, while the beneficiaries may increase
the probability of re-election.
The interest groups can share information in two ways. The first way is
cheap-talk: the interest groups can endorse the candidate for re-election. The
second way is costly signalling: the interest groups can contribute money
to electoral campaigns. Political advertising is not directly informative.3
However, its intrinsic costs create an opportunity for the interest groups to
burn money in public. We consider when and how the voters share their
private information depending on the congruence between them.
An opportunity to finance political advertising is useless for the interest
groups in two extreme cases. Specifically, if the prior weight of the event
2
In other words, better informed beneficiaries convince “swing” nonbeneficiaries to vote
for the incumbent. Lupia (1994) shows that indeed preferences by better informed voters
can be an important information for the vote by less informed citizens. He analyses survey
data on voting behavior in insurance reform initiatives of 1998 in California, and finds that
poorly informed voters “used their knowledge of insurance industry preferences to emulate
the behavioral of those respondents who had relatively high level of factual knowledge.”
3
There are three reasons for this assumption. The first reason is that lying during
electoral campaigns is feasible. In the United States legal system does not punish lie in
political advertising (in contrast with commercial advertising). Also, selective reporting
(“slanting”) allows to reshape information without lying directly, as described in the literature on communications. The second reason is that according to experimental evidence
by Ansolabehere and Iyengar 1996, political advertising is effective even if it contains no
direct information. The third reason is that alternative assumption generates the following
contradiction. Suppose that political advertising directly provides information about candidates to voters. Then, political advertising expenditures as well as the election outcomes
depend on the advertising prices. The largest item of expenditures on electoral campaigns
is television advertising (Prat 1999). However, Ansolabehere, Gerber, and Snyder 2001,
find that higher prices of television advertising have no effect on total campaign spending
levels or vote margins in Congressional elections.
3
that a candidate is unbiased lies below a lower congruence threshold, benefits
received by one interest group is useless information for the other interest
group. Hence, political advertising is ineffective, and the interest groups do
not spend money on it. If the prior weight of the event that a candidate is
unbiased lies above an upper congruence threshold, the vote is coherent if the
interest group share their private information: if nonbeneficiaries learn that
the incumbent has delivered some policy benefits to the other interest group,
they vote for her. Therefore, the beneficiaries have no incentives to lie about
the size of their benefits. Hence, cheap-talk is an available option for credible
communication between the interest groups.
The focus of our paper is the case where the prior weight of the event
that a candidate is unbiased lies between the thresholds.4 In this case, the
vote is not perfectly coherent if the voters honestly disclose policy benefits
delivered to them by the incumbent. Indeed, nonbeneficiaries vote for the
incumbent if and only if they learn that she has delivered high benefits to
the other interest group, because the signal on her type generated by this
information is sufficiently strong. Hence, when an interest group receives
moderate benefits, it wants to claim that its benefits are high in order to
avoid tie in the election. At the same time, when an interest group indeed
receives high benefits, it seeks to overcome the suspicions, and to signal in
a credible way its high eagerness to re-elect the incumbent. To that goal, it
contributes to electoral campaigns a sum that it would not have contributed
if its benefits were moderate. Hence, we rationalize campaign contributions
by interest groups signalling benefits.5 This is the main insight of our paper.
Notice, that more prior weight is put on the event that a candidate is
unbiased, less money the beneficiariaries need to burn in public in order to
credibly signal private information they hold about the incumbent’s valence.
Hence, we predict that electoral campaigns are cheaper, the more congruent
the voters.
Furthermore, our model allows to explain why do incumbents receive
more contributions. When the interest groups signal their private information by financing campaign of a candidate they seek to elect,6 one candidate
4
The upper congruence threshold lies above the lower congruence threshold, because
moderate policy benefits generate a weaker signal on the incumbent’s type than high policy
benefits.
5
We explain the novelty of our argument in the next section.
6
The interest groups can signal their benefits by financing campaign of either candidate.
Hence, we do not rule out split contributions.
4
(promoted by better-informed interest groups) receives more contributions.
Hence, we explain higher campaign receipts by incumbents with better information available to interest groups that seek re-election (in our model, the
beneficiaries from public policies).
Intensive debate about social costs and benefits from campaign contributions that takes place both in the academic literature and in press, encourages us to adress these issues in our paper. We compare the sum of campaign
contributions to the informational benefit that they generate - a higher coherence of the vote. Because contributions are smaller than policies at stake,
we find that campaign contibutions increase the voters welfare. This increase
is larger, more congruent the interest groups.
We suggest, however, to interpret this insight cautiously as far as regulation issues are concerned, at least because we do not consider how does
information sharing between the interest groups affect the incentives by the
incumbent. We make, however, two general remarks. First, if the voters lack
an opportunity to signal their private information by contributing to electoral
campaigns, they might search other ways for credible communication. This
may lead to even larger inefficiencies than the waste of money on political
advertising. Second, this waste could be diminished by reducing a voter’s
uncertainty regarding the preferences by the rest of the electorate.
The paper is organized as follows. The next section discusses our contribution to the literature. Section 3 presents the model. Section 4 considers
a “thought experiment” in which all information about the candidates available to the voters is public, and forms thereby the basis for Section 5, that
describes how do campaign contributions and the vote depend on the congruence between the interest groups. Section 6 considers the impact of campaign
contributions on the efficiency of the election. Section 7 summarizes the main
insights, and suggests some directions for future research.
2
Related literature.
A sizeable literature in economics views campaign contributions as a payment
for policy favor from informed lobbies to candidates, and explicitly assumes
that uninformed voters are more eager to elect a candidate who raises more
contributions. These papers do not explain why politicians get away with
corruption, because they do not model the asymmetry of information that
generates a signal-extraction problem for the voters or judges.
5
Starting with Austen-Smith 1987, a growing number of studies points at
this drawback, and builds models where political campaigns provide information about the quality of candidates to rational voters. Although these
models keep assuming that political advertising is financed by informed lobbies that promote candidates who would bias future policies towards their
interests, in equilibrium candidates who run more expensive campaigns are
more suitable for the voters.
The reason for that result depends on whether it is assumed that political
advertising provides direct information to the voters or not. Some theories
(including Ashworth 2003, and Coate 2003) assume that political campaigns
directly inform the voters about the quality of candidates. Therefore, the
candidates whose policy platforms better fit the voter’s preferences advertise
more, because they generate higher returns from campaign advertising.7 In
other papers (Prat 1999, 2002a, 2002b, 2004; and Potters, Sloof, and van
Winden 1997), political advertising is not directly informative. Expensive
campaigns signal high quality of a candidate, because lobbies have stronger
incentives to give money to valent candidates. The argument by Potters,
Sloof, and van Winden is reminiscent of Milgrom and Roberts 1986, except
that candidates outsource financing for political advertising.
For three reasons already discussed in introduction, we assume that political campaigns convey no direct information to the voters. Our theory of
campaign contributions is the most closely related to Prat’s paper 2004. In
his paper, the voters benefit from electing a valent candidate. An interest
group with no electoral weight holds private information about the valence
of candidates. It proposes to a candidate a contribution to her electoral campaign. If the candidate accepts this offer, she credibly promises in exchange
a future policy favour. High-quality candidates receive more contributions,
because they have higher chances to win the election. The reason is that with
a small probability voters themselves learn the valence of the candidates for
office. Hence, in equilibrium expensive campaign of a candidate signals high
7
In Coate’s model political parties with preferences at the extremes of one-dimensional
political spectrum compete by proposing their candidates to swing voters with “moderate”
ideology. Interest groups observe the candidate’s platforms, and support campaigns of
like-minded candidates. Their contributions help the swing voters to learn the candidates’
platforms. Because “moderate” platforms attract more votes, campaign contributions
encourage the parties to pick the candidates whose ideology is more centrist than that of
the median party member.
6
valence of this candidate to the voters.8 Notice, that the lobbyist cannot
endorse a candidate.
In our model information transmission takes place between the interest
groups that vote. We assume that interest groups can simultaneously use
two ways of communication: cheap-talk and costly signalling via campaign
finance, and describe circumstances where costly signalling is the only way
for credible communication. Hence, we view campaign contributions as a way
of information transmission from better- to less informed voters, and not as
a payment for a future policy favour (although, we find that in equilibrium
with campaign contributions there is a higher probability to elect a politician who is biased towards interest of groups that contribute more, than in
equilbrium without contributions).9 This view may allow us to consider a
game with multiple interest groups without making additional assumptions
on the nature of bargaining between lobbies and candidates.
This is reminicent of Battaglini and Bénabou 2003, where several agents
lobby the politician who can take an action that benefits them. The politician’s decision depends on the state of nature that she does not observe. The
lobbyists hold imperfect private information about the state. Battaglini and
Bénabou find that if the expected degree of policy disagreement between the
principal and the agents is low, lobbying activity by each agent is high. The
reason is that an agent anticipates confirmation provided by other agent’s
lobbying.
In our model, well-informed interest group “lobbies” the other interest
group in campaign financing stage in attempt to avoid tie in the election.
In contrast with Battaglini and Bénabou, the stakes of such lobbying are
endogenous. As a result, when the voters are more congruent, an individual
interest group has weaker (and not stronger) incentives to lobby. Indeed,
when more prior weight put on the event that a candidate is unbiased, this
generates two coherent effects. First, it decreases the probability of the event
that there is tie in the election with independent vote. Second, it decreases
the expected benefits by one interest group from changing the vote by the
other interest group in case of such a tie.
8
This informational benefit may be lower than costs of the future policy bias.
Ansolabehere, de Figueiredo, and Snyder 2002, provide a range of facts to illustrate
that campaign contributions are not a form of policy-buying.
9
7
3
The model.
Consider a two-period economy led by an elected official - the politician.
The election takes place at the end of the first period.10 There are two
candidates competing for office: the incumbent and the challenger. The
electorate is constituted by two interest groups. Each interest group is a
uniform constituency of voters. If there is a tie in the election, either interest
groups is equally likely to be pivotal.
There are two public projects indexed by i (i = 1, 2). Project i is specific
to interest group i. That is, interest group i receives return ri from project
i, while costs of the project normalized to 1 are split equally between the
interest groups.
Return from project i is stochastic: it can be null, moderate, or high:
ri ∈ {0, r, R} , where 0 < r < R.
It depends on the politician’s valence with interest group i, that is measured
by random variable
v, with probability 12
vi =
0, with probability 12
We say that the politician is valent with interest group i if vi = v, and
nonvalent with interest group i if vi = 0. When the politician is valent with
interest group i, more weight is put on more successful outcomes of project
i:

 R, with probability vi ,
r, with probability vi + l,
(1)
ri =

0, with probability 1 − l − 2vi ,
where variable l is a positive constant (l stands for “luck”). Since l is positive,
the politician may generate moderate returns from project i even if she is
nonvalent with interest group i. Notice however, that the politician need to be
valent with interest group i in order to be able to generate high returns from
project i. Furthermore, we assume that the politician might fail project i
(that is, deliver no returns from the project) even if she is valent with interest
group i: l + 2v < 1.
Hence, the politician has type (v1 , v2 ) that depends on her valence with
different interest groups, as illustrated by Table 1. We make an important
10
Timing of the game is summarized at the end of this section.
8
distinction between an unbiased politician, who is either valent with both
interest groups or nonvalent with both interest groups; and a biased candidate, who is valent with one interest group but nonvalent with the other
interest group.
Table 1: The politician’s type.
v2 = v
v2 = 0
biased
(towards interest group 1)
v1 = v
valent
v1 = 0
biased
(towards interest group 2)
nonvalent
We denote by ρ correlation between the politician’s valence with different
interest groups:
Pr (vi = v | v−i = v) = Pr (vi = 0 | v−i = 0) = ρ,
where index −i denotes a number from {1, 2} that is distinct from i. In
these notations, the distribution of the politician’s type is as follows. With
probability ρ the politician is unbiased (this weight is split equally between
the event that the she is a valent type and the event that she is a nonvalent
type). With probability 1 − ρ the politician is biased (again, this weight is
split equally between the two cells that lie on the main diagonal of table 1).
Correlation ρ is the most important parameter in our model. When it
is positive, more weight is put on the event that the politician is unbiased.
Hence, parameter ρ measures the congruence between the interest groups in
their preferences regarding the candidates competing for office. We focus on
cases where there is some congruence between the interest groups, that is
1
< ρ 1. Later, it will become clear why the complementary cases are out
2
of our interest.
The distribution of the politician’s type is a common knowledge. However, the type itself is known by the politician, but not by the constituencies.
This informational asymmetry is important for the following reason. At the
beginning of each period, a project can be either undertaken, or shut down.
This choice is nontrivial, because the projects are costly, and their outcome
is stochastic (in particular, there is a positive probability of a project failure). We assume that if the only information available for that choice is the
9
distribution of the politician’s type, it is efficient to undertake the projects:
lr +
v
(r + R) > 1.
2
(2)
However, if it is known that the politician is nonvalent with an interest group,
it is efficient to shut down the group-specific project: lr < 1. Trivially,
assumption (2) implies that if the politician is valent with an interest group,
it is efficient to undertake the group-specific project.
The decision whether to undertake the projects or not is made by the
politician. Her objectives are two-fold. First, she receives benefits per period in office. Second, she attaches infinitely small value to picking efficient
policies. The first objective creates re-election concerns. We focus on perfect
Bayesian equilibrium in which these concerns encourage the politician to undertake both projects in the first period regardless of her type (we explain
in section A.2 of the appendix why such equilibrium exist). In the second
period, however, the politician has no re-election concerns. Therefore, she
picks efficient policies, in line with her second objective. Specifically, she undertakes project i if and only if she is valent with interest group i.11 Hence,
in the election each interest group has strict preferences regarding the type
of the winner.
The information available to the voters is as follows. An interest group
holds private signal on the incumbent’s type. This signal is generated by
the first period return that the interest group receives from group-specific
project. In order to illustrate the main insights in the most transparent way,
we assume that the signal is stronger, the higher the return:12
3l + 2v < 1.
(3)
Hereafter, we say that an interest group is a beneficiary if it receives a positive return from group-specific policy. Otherwise, we say that an interest
11
Delegation of the decision about whether or not to undertake the projects to the
politician in office does not affect the efficiency of the first period policies (as implied by
assumption (2)), and increases the efficiency of the second period policies.
12
Assumption (3) is equivalent to inequality
Pr (vi = v | ri = r) −
1
1
> − Pr (vi = 0 | ri = 0) .
2
2
That is, moderate returns generate a stronger signal than no returns. High returns generate
stronger signal than moderate returns according to the system of equations (1).
10
group is a nonbeneficiary.13 Hence, the beneficiaries hold more precise private
information than nonbeneficiaries.
The interest group can exchange the information they hold in two ways.
The first way is cheap-talk: an interest group can simply endorse the candidate for re-election. The second way is costly signalling. An interest group
may contribute any positive sum to the incumbent’s campaign or/and to the
challenger’s campaign. A contribution strategy by interest group i is a pair
of contributions (cC (ri ), cI (ri )) for each outcome ri , where cI (ri ) are interest
group’s i contributions to the incumbent’s campaign, and cC (ri ) are interest
group’s i contributions to the challenger’s campaign. Political advertising
is not directly informative. However, campaign contributions become public
before the election. This allows the interest groups to revise their beliefs
about the incumbent’s type.
The timing of the game is as follows.
Date 1.
a. Random state of nature determines the type (v1 , v2 ) of the politician.
This type is unobserved by constituencies.
b. The incumbent undertakes both projects.
c. The first-period returns from the projects realize. Interest group i
privately observes return ri from group-specific project i, and updates its
beliefs about the incumbent’s type.
d. Interest groups may exchange the information they hold. There are two
ways available for this exchange: cheap-talk and costly signalling: an interest
group may contribute any positive sum to the incumbent’s campaign or/and
to the challenger’s campaign.
e. Campaign contributions become public, and the interest groups revise
their beliefs about the incumbent’s type (political advertising is not directly
informative).
f. The election takes place.
Date 2.
The winner of the election undertakes the projects or not depending on
her type.
13
The first period benefits by interest group i are equal to ri −1. Assumption (2) implies
that r > 1.
11
4
The vote with fully shared information.
In order to understand how do the interest groups exchange information at
date 1.d, we have to find how do they vote when this exchange has already
taken place. To this goal, we consider in this section a “thought experiment”
in which the first period returns from both projects are public. We start by
describing the interest group’s posterior beliefs about the incumbent’s type.
4.1
Posteriors.
Recall, that we focus on perfect Bayesian equilibrium in which at date 1.b the
incumbent undertakes both projects regardless of her type. In this equilibrium, the voters update their beliefs about the incumbent’s type depending
on the first-period returns from the projects. We denote by
prri−i (ρ) = Pr (vi = v | r1 , r2 )
the posterior probability which the voters assign to the event that the incumbent is valent with interest group i.
If project i has high return, the interest groups infer that the incumbent
is valent with interest group i regardless of the outcome of project −i:
pR
r−i (ρ) = 1 for any r−i .
Trivially, posetrior pR
r−i (ρ) does not depend on correlation ρ:
∂ pR
r−i (ρ)
= 0.
∂ρ
(4)
(5)
If project i has moderate return or no return at all, some uncertainty is
left about the valence of the incumbent with interest group i. Specifically,
if both projects fail, then the posterior probability of the event that the
incumbent is valent with interest group i is equal to
p00 (ρ) =
Pr (ri = 0, r−i
Pr (ri = 0, r−i = 0 | vi = v)
,
= 0 | vi = v) + Pr (ri = 0, r−i = 0 | vi = 0)
according to standard Bayesian updating. By full probability rule we find
Pr (ri = 0, r−i = 0 | vi = v) =
1
(1 − l − 2v) (1 − l − 2vρ) ,
2
12
and
Pr (ri = 0, r−i = 0 | vi = 0) =
1
(1 − l) (1 − l − 2v (1 − ρ)) .
2
Hence,
p00 (ρ) =
(1 − l − 2v) (1 − l − 2vρ)
.
2 (1 − l)2 − 2v (1 − l) + 2ρv 2
(6)
In a similar way, we find the posteriors
p0r (ρ) =
(1 − l − 2v) (l + vρ)
,
2l (1 − l − v) + v (1 − l − 2ρv)
ρ (1 − l − 2v)
,
1 − l − 2ρv
(l + v) (1 − l − 2vρ)
pr0 (ρ) =
,
2l (1 − l − v) + v (1 − l − 2ρv)
p0R (ρ) =
and
prr (ρ) =
(l + v) (l + vρ)
,
2l (l + v) + ρv 2
(7)
(8)
(9)
(10)
ρ (l + v)
.
(11)
l + ρv
Because a priori more weight is put on the event that the incumbent
is unbiased, a positive return from a project signals not only her valence
with the beneficiaries from that project, but also her valence with the other
voters. Similarly, no return from a project generates negative signals on the
incumbent’s valence with both interest groups. An outcome of a project’s
affects the posterior beliefs about the incumbent’s valence with the voters
who do not benefit from this project more, the stronger correlation ρ, that
is, the more congruent the interest groups. Hence, when return from project
−i is positive, the posterior probability of the event that the incumbent is
valent with interest group i monotonically increases with ρ. Otherwise, this
probability decreases with ρ (see section A.3 of the appendix):
prR (ρ) =
∂
pri (ρ)
∂ pri (ρ)
∂ pr0i (ρ)
<0< r
< R
for any ri < R.
∂ρ
∂ρ
∂ρ
(12)
Inequalities (5) and (12) imply
Lemma 1 (congruence among the voters and posteriors) Suppose
that outcomes of both projects become public before the election. Then, the
13
posterior probability prri−i (ρ) of the event that the incumbent is valent with
interest group i is nondecreasing with ρ if return from project −i is positive,
and nonincreasing with ρ otherwise.
An important implication of Lemma 1 for the remaining is monotonicity
of the posteriors in ρ.
4.2
The vote.
We are now prepared to describe how do the interest groups vote when they
share information about their first-period benefits.
Recall, that in the second period the politician in office picks efficient
policies because she has no re-election concerns. That is, she undertakes
project i if and only if she is valent with interest group i. Therefore, in the
election an interest group has the following preferences regarding the type of
the winner. It prefers a candidate who is valent with itself to a candidate
who is nonvalent with itself, regardless of her valence with the other interest
group. The reason is that the stakes of public policies are sufficiently high,
see assumption (2). Between two candidates who have the same valence
with itself, an interest group prefers the one who is nonvalent with the other
interest group, because an interest group shares the costs of both projects.
However, the voters cannot just pick a candidate who better fits their
preferences, because they hold imperfect information about the valence of
the candidates. More precisely, they know the distribution from which both
candidates’ type is drawn. This is the only information available to the
voters about the challenger’s type. They receive additional signal about the
incumbent’s type from the first-period outcomes r1 and r2 of the projects
(this signal depends on correlation ρ).
The vote by interest group i depends on this signal. We introduce notai
i
tion Irr−i
(ρ) to describe this vote: if Irr−i
(ρ) > 0 interest group i votes for the
incumbent, otherwise it votes for the challenger. In order to see how does the
i
(ρ) in terms
vote depend on the posteriors, it is convenient to express Irr−i
of the expected future return from project i if the winner of the election is
valent with interest group i:
S = (l + v) r + vR,
where “S” stands for the future stakes of public policies. In these terms,
the expected future payoff by interest group i if the challenger picks policies
14
at date 2 is equal to S−1
. Hence, its expected benefits when the incumbent
2
rather than the challenger picks policies at date 2 are equal to
r
i
Irr−i
(ρ) =
S prri−i
prri−i (ρ) + pr−i
S−1
i (ρ)
−
.
(ρ) −
2
2
(13)
Equation (13) describes how do the posteriors influence the vote. The
i
(ρ) increase in the
expected benefits by interest group i from re-election Irr−i
r
−i
ri
posterior pr−i (ρ), and decrease in the posterior pri (ρ). That is, re-election
is more attractive outcome for interest group 1, the more posterior weight is
put on the event that the incumbent’s type belongs to upper cells of table
1, and the less weight is put on the event that it belongs to the left cells
of the table (the first consideration being more important than the second).
Similarly, interest group 2 is more eager to vote for the incumbent, the more
skewed the posterior distribution of the her type towards the left and down
in table 1.
Because we already have established how do the posteriors depend on the
congruence ρ between the interest groups (see lemma 1), we can find how
does the vote depends on ρ. We will achieve this goal in two steps. On
the first step, we will describe the vote in two extreme cases: in case where
there is no correlation between the politician’s valence with different interest
groups, that is, ρ = 12 (independent vote), and in case where the politician’s
valence with different interest groups is the same, that is, ρ = 1 (coherent
vote). On the second step, we will consider cases where there is a positive but
imperfect correlation between the politician’s valence with different interest
groups, that is, 12 < ρ < 1. In order to describe the vote in these case, we will
refer to the vote in two extreme cases, and use the following monotonicity
argument, that is implied by lemma 1 and equation (13):14
Lemma 2 (monotonicity of the vote in congruence among the
i
(ρ) by interest group i is monotonous in ρ for any r1 ,
voters) The vote Irr−i
r2 .
In section A.4 of the appendix we describe precisely how does the vote
depend on the congruence between the interest groups.
14
When the outcomes of both projects become public before the election, lemma 2 is
impled by lemma 1 that establishes monotonicity of posteriors prri−i , and equation (13),
accrding to which the expected benefits from re-elction are a linear combination of thses
posteriors. Trivially, lemma 2 also holds when the first-period outcomes of the projects
are private (then, the posteriors do not depend on ρ).
15
Independent vote. Suppose that the prior beliefs about the politician’s type are fully diffused, that is, ρ = 12 . In particular, the same weight
is put on the event that the politician is biased as on the event that she is
unbiased. Then, the posterior beliefs about the incumbent’s valence with
interest group i do not depend on the outcome of project −i. Specifically,
if project i fails, the interest groups assign a higher posterior probability to
the event that the incumbent is valent with interest group i than the prior:
1
1 − l − 2v
1
0
pr−i
=
< for any r−i ,
(14)
2
2 (1 − l − v)
2
while if project i has a positive return, the voters increase their expectations
of that event more, the higher the return:
l+v
1 R
1
1
r
=
= 1 for any r−i .
> , pr−i
(15)
pr−i
2
2l + v
2
2
We now use equation (13) to describe the vote. We start with the vote by
nonbeneficiaries. If both projects fail, everyone votes for the challenger:
v (S − 1)
1
0
I0
< 0.
=−
2
2 (1 − v − l)
Nonbeneficiaries have even stronger incentives to vote for the challenger when
the other interest group receives benefits, because in this case the expected
future costs
1 of 0public
1 projects that nonbeneficiaries will pay are higher. That
0
is, Ir−i 2 < I0 2 for any r−i > 0. To summarize, nonbeneficiaries vote for
the challenger regardless of the benefits that the incumbent delivers to other
voters:
1
1
1
0
0
0
IR
< Ir
< I0
< 0.
(16)
2
2
2
We now describe the vote by the beneficiaries. If both project have the
same positive return, both interest groups vote for the incumbent (see equations (2) and (13)):
1
v (S − 1)
r
=
> 0,
(17)
Ir
2
2 (2l + v)
S −1
1
R
> 0,
(18)
=
IR
2
2
16
The beneficiaries have even stronger incentives to vote for the incumbent
when she delivers lower benefits to the other interest group then to themselves, because in this case the expected future costs of public projects that
they pay are lower:
1
1
r
r
0 < Ir
< I0
,
(19)
2
2
1
1
1
R
R
R
< Ir
< I0
.
(20)
0 < IR
2
2
2
However, when the beneficiaries receive return r that is smaller than return
R held by the other interest group, their vote depends on how strong is the
signal on the incumbent’s type generated by moderate return from a project.
If and only if this signal is sufficiently strong, an interest group that holds
moderate benefits votes for the incumbent despite it knows (from the fact
that she has delivered high return to the other voters) that in the future she
will charge it the costs of the project that is not group-specific:
1
r
IR
>0
(21)
2
if and only if
v (S − 1) > l.
(22)
In order to illustrate the main insights in the most transparent way, we
assume hereafter that parameters of the model satisfy inequality (22). Then,
inequalities (16)-(20) imply
Lemma 3 (independent vote) Suppose that there is no correlation
between the politician’s valence with different interest groups, that is, ρ = 12 .
Then, the beneficiaries vote for the incumbent, while nonbeneficiaries vote
for the challenger.
Trivially, the insight of lemma 3 holds regardless of whether the voters
share information before the election or not. We will use this insight in
section 6 where we compare the efficiency of the election with and without
contributions.
Coherent vote. Suppose that the politician is unbiased, that is, ρ = 1.
Then, the interest groups vote coherently. Specifically, if the incumbent
17
delivers high return from at least one project, the interest groups infer that
she is a valent type, and vote for her:
S −1
(23)
> 0 for any r1 , r2 .
2
Suppose now, that none of the projects has high return. Then, some
uncertainty is left about whether the incumbent is a valent type or she is a
nonvalent type. If both projects have moderate return r, the voters assign a
higher posterior probability prr (1) to the event that the incumbent is a valent
type then the prior (see inequalities (12) and (15)), and vote for her:
1
r
r
Ir (1) = pr (1) −
(S − 1) > 0.
(24)
2
IRri (1) = IrR−i (1) =
while if both projects fail, they assign a lower posterior probability p00 (1) to
that event (see inequalities (12) and (14)), and vote for the challenger:
1
0
0
I0 (1) = p0 (1) −
(S − 1) < 0.
(25)
2
When one project has high return, while the other project fails, the voters
assign a higher posterior probability to the event that the incumbent is a
valent type than the prior:
pr0 (1) =
(l + v) (1 − l − 2v)
1
> ,
2l (1 − l − v) + v (1 − l − 2v)
2
and vote for her:
1 S−1
r
> 0.
(26)
(1) = p0 (1) −
2
2
The reason is that according to assumption (3), moderate return from a
project generates a stronger signal on the politician’s type than the failure
of a project.
To summarize inequalities (23), (24), and (26), if at least one project has
a positive return, the interest groups vote for the incumbent:
I0r
i
(1) > 0 for any ri > 0 and any r−i .
Irr−i
(27)
Lemma 4 (coherent vote) Suppose that outcomes of the projects become public before the election, and the politician has the same valence with
different interest groups. Then, the vote is coherent. Both interest groups
vote for the incumbent if at least one project has a positive return. Otherwise, they vote for the challenger.
18
Congruence between the interest groups and the vote. We now
describe the vote in cases where there is a positive but imperfect correlation
between the politician’s valence with different interest groups, that is, 12 <
ρ < 1. In these cases, the politician a priori may be biased. However, more
weight is put on the event that she is unbiased.
If both interest groups receive coherent signals on the incumbent’s type
(that is, they both receive some benefits, or both receive no benefits), then
the posterior distributional weight is further reallocated towards the event
that the politician is unbiased as compared to the prior. Hence, the vote
when the interest groups share information is the same as their independent
vote described by lemma 3.
Specifically, when both interest groups benefit before the election, they
shift the posterior distributional weight towards the event that the incumbent
is a valent type as compared to the prior. Similarly, when both interest groups
receive no return from public projects before the election, they reallocate the
distributional weight towards the event that the incumbent is a nonvalent
type, and vote for the challenger. More precisely, lemmas 2-4 imply that if
i
(ρ) > 0 for any ρ; and I00 (ρ) < 0 for any ρ,
both ri > 0 and r−i > 0 then Irr−i
as depicted on Figure 1. (see section A.4 of the appendix).
From now on, we focus on more interesting cases where one interest group
benefits before the election while the other does not. Recall, that according to
assumption (3), the beneficiaries hold more precise signal on the incumbent’s
type than nonbeneficiaries. Hence, the beneficiaries vote fore the incumbent.15 In contrast, nonbeneficiaries informed about the benefits received by
the other interest group may decide to vote for the incumbent.
To be more precise, suppose that at date 1.c the incumbent delivers benefits to interest group 1, but not to interest group 2. Then, the posterior
distributional weight is shifted towards upper cells of table 1 as compared to
the prior. Hence, the impact of information about benefits received by interest group 1 on the vote by interest group 2 is controversial. On one hand,
these benefits signal that the incumbent is a valent type, and thereby encourage interest group 2 to vote for re-election. On the other hand, however, they
also signal that the incumbent is biased towards interest group 1, and hence,
provide the incentives for interest group 2 to vote for the challenger. Hence,
interest group 1 votes for the incumbent if and only if the first consideration
15
Our model can be easily extended for more general case where the signal on the
incumbent’s type held by nonbeneficiaries is useful for the beneficiaries.
19
I rr−i i (1 / 2 )
I 0R (1 / 2 )
1
money burned
I (1 / 2 )
I (1 / 2 )
I (1 / 2 )
R
r
R
R
r
0
r
r
r
R
0.75
0.5
I (1 / 2 )
ρ = ρ R0
I (1 / 2 )
I
ri
r−i
0.25
(1 / 2 ) = 0
0.5
0.6
0.7
0.8
I rr (1)
I 0r (1)
ρ
0.9
I (1 / 2 )
-0.25
I r0 (1 / 2 )
-0.5
0
0
I rR−i (1) =
= I Rri (1)
I 00 (1)
I R0 (1 / 2 )
ρ = 1/ 2
ρ = ρ R0
ρ = ρ r0
ρ =1
Figure 1: Congruence among the voters and benefits from re-election.
is more important than the second, that is, if and only if the prior weight ρ
of the event that the politician is unbiased is sufficiently high.
Indeed, if the prior distribution of the politician’s type is diffused, that
is ρ = 12 , interest group 2 votes for the challenger (lemma 3), while if the
incumbent is unbiased, that is ρ = 1, interest group 2 votes for re-election
(lemma 4). Lemma 2 implies that the expected benefits by interest group
i from the re-election increase with ρ. Thick red curve, and dashed green
curve on Figure 1 illustrate this dynamics. Thick red curve corresponds to
the case where project 1 has high return, while dashed green curve depicts
the case where project 1 has moderate return. High return from a project
generates a stronger signal on the politician’s type than moderate return.
Therefore, thick red curve is steeper than dashed green curve. For each
return from project 1 there exist a threshold, such that nonbeneficiaries vote
for the incumbent if and only if correlation ρ between the politician’s valence
with different interest groups lies above this threshold.
Specifically, there exist a lower congruence threshold ρ0R , such high return
from project 1 convinces interest group 2 to vote for the incumbent despite
the failure of project 1, if and only if the prior weight ρ of the event that
the politician is unbiased lies above this threshold. That is, IR0 (ρ) > 0 if and
20
only if ρ > ρ0R , where
ρ0R =
(1 − l) S
.
2(1 − v − l)S − (1 − 2v − l)
(28)
Similarly, there exist an upper congruence threshold ρ0r , such that any positive
return from project 1 convinces interest group 2 to vote for the incumbent if
and only if correlation ρ lies above that threshold. That is, Ir0 (ρ) > 0 if and
only if ρ > ρ0r , where
ρ0r =
(1 + l) S
.
2(1 − v − l)S − (1 − 2v − 3l)
(29)
Because high return from a project generates a stronger signal on the
politician’s type than moderate return, the upper congruence threshold ρ0r
exceeds the lower congruence threshold ρ0R (see equations (28) and (29)).
These considerations are summarized by the following
Lemma 5 Suppose that outcomes of the projects become public before
the election. Then, the vote is as follows.
1. The beneficiaries vote for the incumbent.
2. Nonbeneficiaries vote for the incumbent in one of the following two
circumstances.
a. If she delivers high return R to the other voters, and the prior weight
ρ of the event that the politician is unbiased lies above the lower congruence
threshold ρ0R given by equation (28).
b. If she delivers moderate return r to the other voters, the other voters
receives moderate return r , and the prior weight ρ of the event that the
politician is unbiased lies above the upper congruence threshold ρ0r given by
equation (29).
Hence, the vote depends on the prior weight ρ of the event that the
politician is unbiased. If ρ lies below the lower congruence threshold ρ0R ,
the vote by the interest groups is independent; if it lies above the upper
congruence threshold ρ0r , the vote is coherent. Otherwise (that is, if ρ lies
between the thresholds), there is a tie in the election if and only if one interest
group receives moderate return while the other interest group receives no
return. This motivates the following
Definition The congruence between the interest groups is low, if ρ < ρ0R .
21
The congruence between the interest groups is moderate, if ρ0R < ρ < ρ0r .
The congruence between the interest groups is high, if ρ > ρ0r .
Stakes of public policies, the voters’ information and the congruence between the interest groups. As we already have discussed,
an interest group is more eager to vote for a candidate, the higher probabilily is assigns to the event that the candidate is valent with itself, and the
lower probability it assigns to the event that she is valent with the other
voters. The higher the stakes of public projects as compared to their costs,
more important is the first consideration as compared to the second. Hence,
the congruence among the voters is nondecreasing in the efficiency of public
projects. That is, both thresholds ρ0R and ρ0r decrease in S.
Another factor that is important for the coherence of the vote is the
precision of information held by the interest groups. While the signal on
the incumbent’s type generated by high return from a project has a given
precision, the strength of signals generated by two other possible outcomes
of a project depends on variables v and l (see equations (1)).
Indeed, variable v measures how important is valence of the politician
with an interest group for avoiding the failure of the group-specific project.
Hence, higher v, stronger is the signal on the incumbent’s type generated
by the failure of a project. Consequently, more difficult it is to convince
nonbeneficiaries to vote for the incumbent. Hence, threshold ρ0R increases
with v. The impact of variable v on threshold ρ0r is two-fold, because the
signal on the incumbent’s type generated by moderate return from a project
is stronger at higher values of v. However, this effect is minor as compared
to the effect that variable v has on the precision of the signal generated by
the failure. The reason is that the incumbent can succeed a project in two
ways: by delivering high returns from the project and by delivering moderate
returns. At the same time, there is only one way in which she fails a project.
Hence, threshold ρ0r also increases with v though slower than threshold ρ0R .
Moderate return from a project generates stronger signal on the incumbent’s type, the lower the probability that the politician who is nonvalent
with an interest group delivers moderate return from group-specific project
by luck. This luck is measures by variable l. Hence, the higher l, weaker
is the signal on the incumbent’s type generated by moderate return from a
project. At the same time, stronger is the signal generated by the failure.
Hence, both thresholds ρ0R and ρ0r increase in l (threshold ρ0r increases faster
22
than threshold ρ0R ).
These considerations are summarized by the following.
Remark 1 Both thresholds ρ0R and ρ0r decrease in S, increase in v, and
increase in l.
The formal proof of this statement is moved to section A.5 of the Appndix.
5
Campaign contributions and the vote.
In this section we use the insights of lemma 5 to describe when and in which
way do the voters exchange information before the election when the firstperiod return from a project is privately known by the interest group that
holds this return.
Recall, that there are two ways available to the interest groups for this
exchange: cheap-talk and costly signalling via electoral campaign finance. A
contribution strategy by interest group i is a pair of contributions (cC (ri ), cI (ri ))
to the candidate’s campaigns for each outcome ri , where cI (ri ) denote interest group’s i contributions to the incumbent’s campaign, and cC (ri ) stand
for interest group’s i contributions to the challenger’s campaign.
We focus on symmetric Perfect Bayesian Equilibria in pure strategies in
which first, an interest group contributes to electoral campaign of a candidate
whom it is eager to elect (that is, contributions are promotional), second, political advertising is the least expensive. We call equilibria that satisfy these
refinements CPAPC equilibria, where CPAPC stands for “cheapest political
advertising with promotional contributions”.
We consider separately the cases of low-, moderate-, and high congruence
between the interest groups as defined in the previous section. In order to
decribe contributions and the vote in each of these cases, we use the fact that
in equilibrium an interest group’s campaign contributions strategies shall be:
- first, informative (since they are costly);
- second, incentive compatible;
- third, individually rational with respect to the vote they generate.
5.1
Low congruence between the interest groups.
When the prior weight ρ of the event that the politician is unbiased lies below
the lower congruence threshold ρ0R , return ri is a sufficient statistics for the
23
vote of interest group i (lemma 5). Because contributions have no impact
on the election outcome, no positive contributions are individually rational.
The vote is independent.
Proposition 1 When the prior weight ρ of the event that the politician is
unbiased lies below the lower congruence threshold ρ0R , the interest groups do
not contribute to electoral campaigns. Their vote is independent: the benefciaries vote for the incumbent, while nonbeneficiries vote for the challenger.
5.2
High congruence between the interest groups.
When the prior weight ρ of the event that the politician is unbiased lies
above the upper congruence threshold ρ0r , the vote is coherent. Specifically,
the interest group vote for the incumbent if and only if she deliveres positive
return from at least one project (lemma 5). Therefore, it suffices for the
beneficiaries to simply announce their benefits, in order to convince nonbeneficiaries to re-elect the incumbent. Hence, there is an equilibrium in which
the voterst exchange information at date 1.d via cheap-talk. Obviously, this
is the unique CPAPC equilibrium.16
Proposition 2 When the prior weight ρ of the event that the politician is
unbiased lies above the upper congruence threshold ρ0r , there is the unique
CPAPC equilibrium in which an interest group truthfully announces its firstperiod benefits before the election, and the vote is coherent: the interest group
vote for the incumbent if she has delivered a positive return from at least one
project, and for the challenger otherwise.
5.3
Moderate congruence between the interest groups.
We now consider more intersting case where the prior weight ρ of the event
that the politician is unbiased lies between the lower congruence threshold
ρ0R and the upper congruence threshold ρ0r . In this casen, when the interest
groups honestly disclose their first-period benefits there is a tie in the election
16
Other symmetric Perfect Bayesian Equilibria in pure strategies are associated with
positive costs of political advertising. Any contrbutions that satisfy informativeness constraint that requires either cC (ri ) = cC (0) or cI (ri ) = cI (0), and individual rationality
constraints that require cI (ri ) + cC (ri ) 12 Pr (r−i = 0 | ri ) I0ri for any ri , constitute a
symmetric Perfect Bayesian Equilibria in pure strategies. Incentive compatibility does not
impose any additional constraints.
24
if and only if one interest group receives moderate return while the other
interest group receives no return (see lemma 5). This creates moral hazard
in the campaign finance stage (at date 1.d). Indeed, if an interest group
receives moderate return r, it has the incentives to claim that it has received
high return R in order to convince nonbeneficiaries to vote for the incumbent.
The expected gains from such a lie are equal to
1
c = I0r (ρ) Pr (r−i = 0 | ri = r) =
2
=
v (S (l + 1) − ρ (2S (v + 2l) + 1 − 2v − 3l))
4 (v + 2l)
(30)
Because there is a hazard of this lie, cheap-talk is not credible.
At the same time, if an interest group holds high return, it is eager to
credibly communicate this information to the other voters. It may achieve
this goal by costly signalling. We now assume that interest group i receives
high return at date 1.c, and describe its campaign contribution strategy
that satisfy three constraints: informativeness, incentive compatibility, and
individual rationality.
Informativeness constraint requires that campaign contributions signal
high return:
for any ri < R either cC (R) = cC (ri ) or cI (R) = cI (ri ).
(31)
When campaign contributions are informative, the interest groups vote
as described by lemma 5. That is, the beneficiaries vote for the incumbent,
while nonbeneficiaries vote for the incumbent if campaign contributions signal that she delivered high return to other voters, and vote for the challenger
otherwise. Hence, incentive compatibility requires that interest group i contibutes the sum that it would have contrubuted that the beneficiries who
hold moderate return do not contribute so as if the return they hold was
high:
C
(32)
c (R) + cI (R) − cC (r) + cI (r) c,
where threshold c is given by equation (30).
Individual rationality requires that contributions by an interest group to
political advertising do not exceed the expected benefits from contributing.
These benefits come from the impact that they have on the election outcome.
Hence, an interest group may benefit from contributing if and only if it holds
25
Suppose that project i has high return. At date 1.f, interest group i
assigns a positive probability to the event that project −i fails. In this case,
by signalling big success of project i, interest group i convinces interest group
−i to vote for the incumbent. This provides interest group i with expected
future benefits equal to
1
S (1 − l) − ρ (2v (S − 1) + 1 − l)
c = I0R (ρ) Pr (r−i = 0 | ri = R) =
. (33)
2
2
Individual rationality requires:
cC (R) + cI (R) c,
(34)
where threshold c is given by equation (33), and
cC (ri ) + cI (ri ) 0 for any ri < R.
(35)
The latter inequality implies that an interest group that receives less than
high return does not finance political advertising. Hence, the informativeness
constraint (31) is equivalent to
cC (R) + cI (R) > 0,
(36)
while the incentive constraint (32) is equivalent to
cC (R) + cI (R) c.
(37)
Recall, that we pick an equilibrium in which electoral campaigns are the
least expensive, and contributions to a candidate’s campaigns help her to win
the election. Minimization of campaign expenditures cC (R) + cI (R) subject
to constraints (34), (36) and (37) implies that constraint (37) is satisfied as an
equality. The beneficiaries contribute so as to help the incumbent candidate
to win the election, which implies that cC (R) = 0. Hence,
Proposition 3 When the prior weight ρ of the event that the politician is
unbiased lies between the lower congruence threshold ρ0R and the upper congruence threshold ρ0r , there is the unique CPAPC equilibrium in which campaign
contributions and the vote are the following.
1. An interest group contributes to the incumbent’s campaign sum c that
is given by equation (30) if it receives high return. Challenger receives no
contributions.
26
2. The beneficiaries vote for the incumbent regardless of total contributions received by the candidates. nonbeneficiaries vote for the incumbent
candidate if the sum contributed to her electoral campaign is at least as big
as threshold c. Otherwise, they vote for the challenger.
Proposition 3 tells that political advertising by the incumbent has to
be sufficiently expensive to be credible. Hence, we rationalize campaign
contributions by the interest groups signalling benefits.
Money burned in electoral campaigns and congruence among
the voters. Proposition 3 implies that the lower limit of expected contributions to the incumbent’s campaign is equal to
M B = v(1 − l − vρ)c =
=
v 2 (1 − l − vρ) (S (l + 1) − ρ (2S (v + 2l) + 1 − 2v − 3l))
,
4 (v + 2l)
(38)
where “MB” stands for money burned in political advertising. This sum
decreases with correlation ρ. The reason that the higher prior weight of
the event that a candidate is unbiased, lower probability the beneficiaries
assign to the event that the other interest group receives no benefits, and
also lower is their expected gain from convincing nonbeneficiaries to vote for
the incumbent.
At the same time, the sum given by equation (38) increases with policy
stakes S: the higher the stakes, larger the expected gain by the beneficiaries from avoiding tie in the election, hence, stronger are their incentives to
exaggerate the size of their benefits. We summarize these considerations as
Corollary When the prior weight ρ of the event that the politician is
unbiased lies between the lower congruence threshold ρ0R and the upper congruence threshold ρ0r , the lower campaign spending thershold is given by equation (38). This threshold increases with policy stakes S and decreases with
the congruence between the interest groups ρ.
Incumbency advantage. Propositions 3 predicts that campaign contributions are skewed towards the incumbent. The reason is the beneficiaries
hold more precise private information than nonbeneficiaries. Of course, the
prediction of the proposition that the challenger receives no contributions
27
is not realistic. The reason is that in our model the strength of a signal
on the incumbent’s type generated by a policy failure is given, and this signal is weak (and therefore, useless for the beneficiaries). In a more general
version of our model, the challenger receives contributions to her campaign.
However, as long as more precise private information is available to the beneficiaries than to nonbeneficiaries, challenger receives less contributions than
the incumbent.17
6
Campaign contributions and voter welfare.
The election is more efficient when the expected valence by the official in
office at date 2 with an interest group is higher, and the costs of political
advertising are lower. Campaign contributions have no impact on the efficiency of the election when the congruence between the interets groups is
low (see propositions 1), and increase this efficiency when that congruence
is high (see proposition 2). We consider now how does the efficiency of the
election depend on the congruence between the interest groups, when the
congruence between the interets groups is moderate. Recall, that we focus
on the upper limit of this efficiency. That is, we assume that costs of creadible
communication are given by equation (38).
Efficiency of the vote. We start by considering how does the expected
future welfare depend on the probability to screen in a certain type of the
politician during the election. The expected future welfare is equal to 2(S−1),
if a valent candidate wins the election; to S − 1, if a biased candidate is in
office at date 2; and to 0, if nonvalent candidate occupies the office in period
2.
When a biased candidate is in office at date 2, the expected second period welfare is equal to S − 1. This is precisely the same as the expected
17
Only if we assume, contrary to what is done in the model, that nonbeneficiaries hold
more precise private information than the beneficiaries, we find that the challenger’s campaign is more expensive. Consider the mirror image of our model where a project has
high return with probability 1 − l − 2v + 2vi , moderate return with probability l + v − vi ,
and no return with probability v − vi . Then, moderate return from project generates a
negative signal on the incumbent’s valence. However, this signal is not as strong as the
one generated by the failure of a project. Hence, the incumbent receives no contributions,
while the lower limits of the challenger’s campaign expenditures are given by equation
(38).
28
future welfare when the incumbent is replaced with the challenger. Hence,
for the parameters that we consider there are no costs of re-electing a biased
incumbent. The election is more efficient the higher the probability to reelect a valent incumbent and the lower the probability to re-elect a nonvalent
incumbent.
We denote by zV the probability to re-elect a valent incumbent, by zS
the probability to re-elect a biased incumbent, and by zI the probability to
re-elect nonvalent incumbent. In this notation, the expected future welfare
is equal to
ρ
(39)
W2 (zV , zS , zI ) = (S − 1) 1 + (zV − zI ) .
2
No contributions benchmark. As a benchmark, we consider the case
where campaign contributions are prohibited. In this case, the interest groups
vote for the incumbent if and only if they benefit before the election. Therefore,
zV = 2v2 + lv + l + v, zS = l + v, zL = l.
(40)
Hence, according to equation (26), the expected second period welfare is
equal to
vρ
W2NC = W2 2v2 + lv + l + v, l + v, l = (S − 1) 1 +
(2v + l + 1) .
2
(41)
Note, that the efficiency of the election without campaign contributions
given by equation (41) increases with vρ and with S. The reason is the
following. Each interest group screens in a candidate with higher expected
valence with itself. The less noisy the voters signals on the incumbent’s type,
more efficient is this screening. Since more prior weight is put on the event
that a candidate is unbiased, the vote by one interest group creates a positive
externality on the future expected utility of the other interest group. These
externality is stronger, the stronger correlation ρ, and more important the
higher the policy stakes S.
W2N C
Welfare benefits from campaign contributions. We now compare
the efficiency of the election with and without campaign contributions.
According to proposition 3, when at least one project has high return at
date 1.c, the incumbent stays in office. She also stays in office if both projects
29
have moderate return. When one project has moderate return, while the
other project fails, she wins the election with probability 12 . Finally, if both
projects fail she has no chance to be re-elected. Hence,
zV = l + 2v, zS = l +
3v lv
− , zI = l.
2
2
(42)
Hence, the expected informational gain from campaign contributions is equal
to
vρ
(1 − 2v − l) .
(43)
IS M C = (S − 1)
2
According to proposition 3, this gain is achieved at the expense of money
burned in electoral campaigns. The lower campaign spending thershold is
given by equation (38). We subtract it from the informational gain given by
equation (43), and find that
Proposition 4 When the prior weight ρ of the event that the politician is
unbiased lies between the lower congruence threshold ρ0R and the upper congruence threshold ρ0r , campaign contributions increase the voters welfare.
The reason is that contributions are of a smaller value than the policies
at stake.
Remark 2 The more congruent the voters, larger their benefits from
campaign contributions.
Indeed, there are two coherent effects. First, the more congruent the
voters, more important is the externality that individual vote imposes on
the future utilities by the other voters. Hence, larger are the benefits from
informaion sharing that increases the extent to which a voter internalizes that
externality. Second, the more congruent the voters, cheaper it is for them
to signal their private information, hence, less money is burned in campaign
advertising.
7
Conclusion.
The paper builds a model of political campaign contributions where the interest groups finance political advertising in order to share their private information about the valence of candidates. The main insights of the model
can be summarized as follows.
30
1. Campaign contributions can be rationalized by interest group’s signalling benefits.
2. One of the candidates (the incumbent) receives more contributions.
3. Political advertising is less expensive when the interest groups are more
congruent.
4. Campaign contributions increase the voter welfare.
The model could be extended to study the policy-costs created by campaign finance. Assume that the information held by the interest groups depends on the politician’s effort. Campaign finance allows the interest groups
to exchange information about the candidate for re-election. This communication may weaken the incumbent’s incentives to exert an additional unit of
effort in order to signal its valence to the voters.1819
The model also allows to investigate how the total amount of money
spent on political advertising depends on diversity of the electorate. On
the one hand, the number of contributing interest groups increases. On the
other hand, however, each interest group is less likely to be influential in the
election. These questions are open for further research.
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18
Along the lines of Holmström 1999.
For instance, if the politician in office can at some costs exert an effort that increases
the probabilty of a policy success, information sharing among the voters may weaken
her incentives to exert an additional unit of effort. This consideration is reminicent of
Holmström 1999.
19
31
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33
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A
A.1
Appendix.
US Congressional Campaigns.
Costs of political advertising. Figure 2 illustrates the US Congressional campaign receipts from 1981-1982 election cycle to 2001-2002 election
cycle in millions of 2003 US dollars.20 On average, this figure stood at 1069
millions with maximum of 1404 millions in 1987-1988 election cycle and minimum of 806 millions in the following 1989-1990 election cycle.21 This sum
is about one half of annual budget of a small state like Wyoming or Dakota,
and it is roughly enough to pay for example total expenditures on higher
education or public assistance from Massachusetts state budget.22 At the
same time, costs of political advertising are negligible compared to stakes
of public policies, as it is pointed out in many papers starting with Tullok
(1972). The figure extensively used in the literature as a benchmark is US
Federal government spending. Indeed, in the last two decades, contributions to the US Congressional races per election cycle constitued on average
0.026% of the Feredal budget receipts during the next 2 years (until the next
election cycle) with minimum of 0.023% in 1990 and maximum of 0.029% in
20
We use the data by Federal Election Commission available at URL
http://www.fec.gov. We deflate them with GDP per capita deflator to find real
2003 figures.
21
Strattman 2005 points that there was a 64% increase in congressional spending in
2003-2004 election cycle compared to 1989-1990 election cycle. However, we remark here
that this figure would stand at only 15% if 1991-1992 election cycle is taken as a reference
point.
22
See State Expenditure Report by National Association of State Budget Officers available at URL http://www.nasbo.org/Publications/PDFs/2004ExpendReport.pdf.
34
millions 2003 US dollars
1600
1400
1200
1000
800
600
400
200
0
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
Congressional Fundraising
Average Congressional Fundraising
Figure 2: Contributions to the US Congressional Campaigns.
1982 and 1986. Ansolabehere, de Figueiredo, and Snyder 2003 refer to many
other facts that illustrate the gap between campaign contributions receipts
and stakes of public policies.
Main sources of Campaign Finance. Most contributions came from
individuals and Political Action Committees (see Figure 3).Ansolabehere, de
Figueiredo, and Snyder 2003 provide a more detailed overview of the sources
and the size of campaign finance.
Incumbency advantage. An incumbent candidate received on average about 6 times more than a challenger candidate (see Figure 4).23 Incumbents
won on average more than 90% of House races and about 80% of Senate races
(in November 2, 2004 General Election, incumbents won 93% of Senate races
and 78% of House races).
23
Electoral campaign by a Senate candidate was about 5.5 more expensive than that of
a House candidate.
35
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
1992
1994
1996
1998
individual contributions
2000
PAC's contributions
2002
2004
Others
incumbent/challenger receipts ratio
Figure 3: Main sources of campaign finance.
12
10
8
6
4
2
0
1992
1994
1996
1998
Senate
Figure 4:
36
2000
House
2002
2004
A.2
Re-election concerns and political activism.
In this section we show that there exist a perfect Bayesian equilibrium in
which at date 1.b the incumbent undertakes both projects regardless of her
type.
Suppose that the interest groups hold the following beliefs. They believe
that at date 1.b the incumbent undertakes both projects regardless of her
type. If project i is undertaken, the voters update their beliefs about the incumbent’s type depending on the first-period return ri according to standard
Bayesian updating, as described by equations (4)-(11). Out-of-equilibrium,
the voters assign probability 1 to the event that the incumbent is nonvalent
with interest group i, if project i is shut down (if at the same time project
−i is undertaken, they update their beliefs about the incumbent’s valence
with interest group −i according to standard Bayesian updating depending
on the first-period return r−i ).
When the voters hold such beliefs, the incumbent indeed undertakes both
projects at date 1.b regardless of her type. The reason is that she may generate moderate returns from project i, even if she is nonvalent with interest
group i. In this case, the probability to be re-elected is higher as compared
to the situation when project i is shut down.
A.3
Congruence among the voters and posteriors.
We derive equations (4)-(11) with respect to ρ:
∂ pR
r−i (ρ)
= 0,
∂ρ
∂ p00 (ρ)
v (1 − l) (1 − v − l) (1 − 2v − l)
=− 2 < 0,
∂ρ
(1 − l)2 − 2v (1 − l) + 2ρv2
∂ p0r (ρ)
v (1 − l) (v + 2l) (1 − 2v − l)
=
> 0,
∂ρ
(2l (1 − l − v) + v (1 − l − 2ρv))2
(1 − l) (1 − 2v − l)
∂ p0R (ρ)
=
> 0,
∂ρ
(1 − l − 2vρ)2
4vl (l + v) (1 − v − l)
∂ pr0 (ρ)
=−
< 0,
∂ρ
(2l (1 − l − v) + v (1 − l − 2ρv))2
37
∂ prr (ρ)
vl (l + v) (2l + v)
> 0,
=
∂ρ
(2l (l + v) + ρv 2 )2
∂
prR (ρ)
l (l + v)
> 0.
=
∂ρ
(l + ρv)2
Note, that these derivatives have all constant sign. Hence, the posterior probability prri−i (ρ) that the incumbent is valent with interest group i is monotonic
in ρ for any r1 , r2 .
A.4
Congruence between the interest groups and the
vote.
In this section we use equations (8)-(11), and (13) to describe how does the
vote depend on congruence between the interest groups that is measured by
correlation ρ.
Suppose first that project i has high return. Then, the voters assign
probability 1 to the event that the incumbent is valent with interest group
i regardless of return from project −i. However, return from project −i is
relevant information for the vote by interest group i because it signals the
expected future policy −i costs that are shared by the voters. If project −i
has high return, then the incumbent is a valent type. Hence, the expected
benefits by an interest group from re-election IRR (ρ) do not depend on ρ
∂IRR (ρ)
= 0.
∂ρ
as depicted by the third curve from the top on Figure 1. However, return
from project −i is lower than R, there is some uncertainty left about the
incumbent’s valence with interest group −i. The posterior probability of the
event that the incumbent is valent with interest group −i increases with ρ.
The reason is that high return from project i generates a strong signal on the
incumbent’s type, that shifts the posterior distribution towards the northwest cell of table 1. Hence, the expected future policy costs paid by interest
group i increase with ρ. Therefore, its benefits from re-election decrease with
ρ:
1 ∂ p0R (ρ)
(1 − l) (1 − 2v − l)
∂I0R (ρ)
=−
=−
< 0,
∂ρ
2 ∂ρ
2 (1 − l − 2vρ)2
38
and
1 ∂ prR (ρ)
l (l + v)
∂IrR (ρ)
=−
=−
< 0,
∂ρ
2 ∂ρ
2 (l + ρv)2
as illustrated by two upper curves on Figure 1.
Suppose now that project i has moderate return. If return from project
−i is positive, the posterior distributional weight is shift towards north-west
of table 1, as compared to the prior. Hence, the expected benefits Irr−i (ρ) by
interest group i from re-election increase with ρ:
∂Irr (ρ)
∂ pr (ρ)
(S − 1) vl (l + v) (2l + v)
> 0,
= (S − 1) r
=
∂ρ
∂ρ
(2l (l + v) + ρv 2 )2
∂IRr (ρ)
2S − 1 ∂ prR (ρ)
(2S − 1) l (l + v)
> 0.
=
=
∂ρ
2
∂ρ
2 (l + ρv)2
as illustrated by the curves that lie in the forth and the fifth positions from
the top at ρ = 12 on Figure 1. If project −i fails, this shifts the posterior
distributional weight towards the event that the politician is nonvalent with
interest group −i. On the one hand, this is good news for interest group i
regarding the expected future policy costs. On the other hand, however, this
signals that the politician is a nonvalent type. The latter consideration is
more important than the first, the more prior weight is put on the event that
the politician is unbiased. Hence, the expected benefits I0r (ρ) by interest
group i from re-election decrease with ρ:
∂ pr0 (ρ) ∂ p0r (ρ)
1
∂I0r (ρ)
(2S − 1)
=
=
−
∂ρ
2
∂ρ
∂ρ
(2S − 1) 4vl (l + v) (1 − v − l) + v (1 − l) (v + 2l) (1 − 2v − l)
< 0,
2 (2l (1 − l − v) + v (1 − l − 2ρv))2
as illustrated by the curve that lies in the third position from the top at
ρ = 12 on Figure 1.
Finally, suppose that project i has no return. If both projects fail, this
generates two signals that shift the posterior distribution of the incumbent’s
type towards the south-east cell of table 1 more, the stronger correlation
ρ. Hence, the expected benefits by an interest group from re-election I00 (ρ)
decrease with ρ:
=−
∂I00 (ρ)
∂ p0 (ρ)
(S − 1) v (1 − l) (1 − v − l) (1 − 2v − l)
= (S − 1) 0
=−
< 0,
2
∂ρ
∂ρ
(1 − l)2 − 2v (1 − l) + 2ρv2
39
as depicted by the curve that lies below zero at ρ = 1 on Figure 1.
The cases were one interest group benefits before the election while the
other does not are discussed in section 4.2 of the main text. Re-election is
more attractive for nonbeneficiaries, the more prior weight is put on the event
that the politician is unbiased:
∂ p0r (ρ) ∂ pr0 (ρ)
1
∂Ir0 (ρ)
(2S − 1)
=
=
−
∂ρ
2
∂ρ
∂ρ
=
v ((2S − 1) (1 − l) (v + 2l) (1 − 2v − l) + 4l (l + v) (1 − v − l))
> 0,
(2l (1 − l − v) + v (1 − l − 2ρv))2
2S − 1 ∂ p0R (ρ)
(2S − 1) (1 − l) (1 − 2v − l)
∂IR0 (ρ)
=
=
> 0.
∂ρ
2
∂ρ
2 (1 − l − 2vρ)2
A.5
Stakes of public policies, the voters’ information
and the congruence between the interest groups.
In this section we prove Remark 1. We derivative the lower and the upper
congruence thresholds given by equations (28) and (29) with respect to S, v,
and l. We find:
∂ρ0R
(1 − l) (1 − 2v − l)
< 0,
=−
∂S
(2S (1 − v − l) − (1 − 2v − l))2
∂ρ0r
(1 + l) (1 − 2v − 3l)
=−
< 0,
∂S
(2S (1 − v − l) − (1 − 2v − 3l))2
2 (S − 1)
∂ρ0R
=
> 0,
∂v
(2S (1 − v − l) − (1 − 2v − l))2
∂ρ0r
2 (S − 1)
=
> 0,
∂v
(2S (1 − v − l) − (1 − 2v − 3l))2
2vS (S − 1)
∂ρ0R
> 0,
=
∂l
(2 (1 − v − l) S − (1 − 2v − l))2
∂ρ0r
2 (2 − v) S (S − 1)
> 0.
=
∂l
(2S (1 − v − l) − (1 − 2v − 3l))2
40