Media E¤ects on Policy Choice
Scott Ashworthy
Kenneth W. Shottsz
May 3, 2007
Abstract
A policy-maker sometimes has an electoral incentive to pander, i.e., to implement
a policy that voters think is in their best interest, despite the fact that she has information indicating that it probably isn’t in their best interest. Incentives to pander
are typically reduced when voters learn, prior to the next election, whether the policy
chosen by the incumbent truly was in their best interest. This suggests that the media
can improve accountability by reporting to voters information about the whether an
incumbent made good policy choices. We show that media monitoring sometimes eliminates the incumbent’s incentive to pander, but sometimes aggravates the problem of
pandering. Furthermore, in some circumstances incumbent incentives are better when
the media suppresses some information and acts as a "yes man."
New title needed? Rough draft. Please do not circulate or cite without permission. Comments very
much appreciated. We thank seminar audiences at Berkeley and Princeton for useful comments.
y
Assistant Professor of Politics, Princeton University.
Princeton, NJ 08544.
Phone: (609) 258-2153. Email:
sashwort@princeton.edu.
z
Associate Professor, Stanford Graduate School of Business. 518 Memorial Way, Stanford CA 94305-5015. Phone:
(650) 725-4510. Email: kshotts@stanford.edu.
I am persuaded myself that the good sense of the people will always be found to be
the best army. They may be led astray for a moment, but will soon correct themselves.
The people are the only censors of their governors: and even their errors will tend to keep
these to the true principles of their institution. To punish these errors too severely would
be to suppress the only safeguard of the public liberty. The way to prevent these irregular
interpositions of the people is to give them full information of their a¤airs thro’the channel
of the public papers, & to contrive that those papers should penetrate the whole mass of
the people. The basis of our governments being the opinion of the people, the very …rst
object should be to keep that right; and were it left to me to decide whether we should
have a government without newspapers or newspapers without a government, I should not
hesitate a moment to prefer the latter.
Thomas Je¤erson, 1787 letter to Edward Carrington
1
Introduction
What is the role of the media in a democracy? Je¤erson suggests one possible, and important role –to
educate the public about the merits of particular policy choices. Since politicians in a democracy are
accountable to voters, it is important that the public be well-informed, lest the government respond
to mistaken voter impulses. Thus, as Je¤erson notes, the media may be crucial to the functioning of
a democracy.
We develop a formal model to analyze this claim. In the model, politicians are accountable to
voters, who are potentially misinformed about their true interests; in Je¤erson’s terms it is possible
that “the opinion of the people” is not right. Elected o¢ cials in our model have better information
than voters do about optimal policy choices, and thus may have an incentive to pander to public
opinion if voters misperceive their interests. In particular, an o¢ cial may implement a policy that
voters think is in their best interest, despite the fact that she has information indicating that it
1
probably isn’t in their best interest.
We …rst present a baseline model in which no media is present, and then compare that model’s
predictions to the predictions of two variants of a model with a media. The media has private
information about what policy best serves voters’ interests, and it functions as a commentator,
making statements about what policy choice is correct.
In the …rst variant, the media makes its
announcement simultaneously with the incumbent’s policy choice. In the second, the media gets to
observe the policy choice before making its announcement; this timing means that if the media sees
a weak signal indicating that the incumbent chose the wrong policy it may herd on the incumbent’s
choice, acting as a yes man.1
In both variants of the model, the media’s statement is made before the next election and consequently is relevant for voters’decision about whether to re-elect the incumbent. Incumbents, who are
partially electorally-motivated, anticipate the media’s behavior. Thus the media plays a role in the
process of holding incumbents accountable for their actions, and the prospect of media commentary
can potentially discipline an incumbent’s policymaking.
The key question we ask is how the existence of the media a¤ects the incumbent politician’s
propensity to pander. A reasonable ex ante conjecture, building on the intuition expressed by
Je¤erson, is that since the media gives voters information about whether the policy chosen by an
incumbent was truly in their best interest, politicians will have less incentive to pander in the presence
of a media. In particular, if at the time of the next elections voters will be perfectly informed about
whether the incumbent’s policy choice promoted their interests, then the incumbent has no incentive
to pander.
Thus one might reasonably conjecture that the presence of an informative, though
sometimes mistaken, media would improve accountability by reducing pandering.
Our model produces several interesting results, some of which are consistent with this conjecture
and others of which contradict it.
1
Although the details of imitation in our model di¤er from those in Pendergast (1993), the underlying intuition of
conformity is similar.
2
1. In both the simultaneous and sequential variants of the model, there are circumstances where
the presence of the media eliminates the incumbent’s incentives to pander. Somewhat surprisingly, in the simultaneous variant the media is most e¤ective at reducing pandering precisely in
situations where pandering is most prevalent in the baseline model, i.e., when the incumbent is
in a close electoral race with her challenger.
2. Although the media can sometimes reduce the incumbent’s incentives to pander, it does not
completely eliminate them. In fact, there are circumstances where the incumbent would not
pander in the baseline no-media model, but will pander in the model with a media.
3. In the sequential variant of the model, where the media observes the incumbent’s policy choice
before strategically deciding what public statements to make, the media is biased towards being
a yes man, in the sense of supporting the incumbent’s policy choice. However, this yes man
behavior is not always a bad thing.
In fact–and quite surprisingly–there are circumstances
where a yes man media is more e¤ective than the truthful media in reducing pandering.
Some of these results are counter-intuitive, since they imply that more information does not
necessarily improve accountability. In our model, perfect information is best, i.e., if voters always
learn before the election whether an incumbent’s policy choice was correct, the incumbent never has
an incentive to pander. But an informative yet noisy signal is not always a good thing. Obviously
the potential for errors by the media may make information less useful in reducing an incumbent’s
incentives to pander. Even worse, the potential for errors can also give the incumbent an incentive
to pander.
For example, suppose that an incumbent is running ahead of the challenger, and consider two hypothetical scenarios. In the …rst scenario, the public will only observe the incumbent’s policy choice,
whereas in the second scenario the public observes not only the policy choice but also commentary
by a partially-informed media about whether this policy choice served their interests. If the incumbent’s lead over the challenger is su¢ ciently large, then in the absence of media commentary, he has
3
some ‡exibility to choose a policy that goes against public opinion, i.e., to not pander if he believes
the public misperceives its true interests. However, if he faces the possibility of media commentary,
he must consider the fact that if he goes against public opinion, and is criticized by the media, this
combination will be su¢ cient to cause him to lose o¢ ce. Thus, even if the media generally makes
accurate statements, as long as there is a chance that the media will engage in mistaken criticism,
the incumbent can have an electoral incentive to pander.
Thus in our model, although there are
some circumstances where the presence of the media reduces pandering there are also circumstances,
like the one just outlined, in which the presence of the media induces pandering.
The paper proceeds as follows. Section 2 discusses theoretical issues and related literature.
Section 3 sets up the model, and Section 4 presents a few useful results about voter behavior.
Section 5 presents the baseline model in which no media is present, and Sections 6 and 7 extend this
model to examine the variants with simultaneous and sequential media announcements. Sections 8
and 9 compare incentive e¤ects and electoral selection in the simultaneous and sequential variants
of the model.
2
Theoretical issues
The media’s role in democratic accountability has received much recent attention, particularly by
scholars focusing on media bias and competition among media outlets can a¤ect the quality of
information available to voters. For example, Page (1996) argues that since any single media outlet
may be biased, it is important to have a wide range of media outlets to provide information as the
basis for democratic deliberation. Baron (2004) develops a theoretical model of media bias when the
pool of available reporters is biased. Groseclose and Milyo (2005) develop an empirical technique for
measuring the relative liberalism or conservatism of di¤erent media outlets, based on their citation
of think tank experts.
Arnold (2004) studies the e¤ects of economic competition on the quality of coverage of members
4
of Congress, and …nds that competition can induce newspapers to focus on ‡u¤ stories rather than
in depth substantive reporting on politics. Gentzkow and Shapiro (2006) analyze how competition
a¤ects the media’s propensity to pander to consumers by con…rming their prior beliefs.
In the analysis that follows we will set aside all issues related to bias and competition, i.e., we
analyze a model with a single, unbiased, media outlet. The reason for this is not that we …nd bias
and competition uninteresting; on the contrary, we think they are quite important.
However, for
purposes of our analysis, it is important to use a “best case” model of the media as a pure provider
of information. Ultimately, our goal is to assess a very simple, and seemingly-compelling intuition
– that by providing information the media reduces incentives for pandering.2 Our most surprising
results have to do with the fact that this intuition often fails. Even in the best-case scenario, with
an unbiased media, the presence of the media does not necessarily eliminate pandering, and indeed
it can sometimes aggravate the problem. We want to make it clear that these results are not driven
by assumptions that the media is biased or corrupt.
3
The Basic Setting
Policies and Preferences
In each of two periods, a policy is selected from the set fA; Bg. The
optimal policy in a period depends on the state of the world in that period, ! 2 fA; Bg. A representative voter gets payo¤ 1 for each period in which the policy matches the state, and 0 for each period
in which policy does not match the state. The state of the world is independent for the two periods,
and in each period state A is more likely: Pr(! = A)
2
> 1=2. We do not introduce additional
Although, as far as we know, there does not exist any formal model that analyzes the question of whether the
presence of a media reduces politicians’ incentives to pander, there has been some formal work on other aspects of
accountability. Besley and Prat (2006) analyze whether the media can discipline kleptocratic tendencies in government
o¢ cials. Egorov, Guriev, and Sonin (2007) analyze the tradeo¤s facing an autocrat who can use a free media to acquire
information about bureaucrats’performance but is concerned that a media might instigate a revolution by informing
voters that he himself has performed badly.
5
notation to distinguish the policies for the two periods, since almost all of the action in the model
occurs in the …rst period.
In period 1, an incumbent policy-maker chooses policy xI 2 fA; Bg. At the end of period 1 the
voter can either reelect the incumbent or replace her with a challenger. A politician gets a payo¤
> 0 for matching her policy choice to the state, plus an ego rent of 1 for each period in which she
holds o¢ ce.3
After the …rst period policy choice, a media commentator makes an announcement xM ; declaring
which state of the world he believes is more likely. The media maximizes the probability that its
announcement matches the true state, i.e., it is intrinsically motivated to give the voter its best
assessment of the state.4
Information Structure At the beginning of each period, the voter has no information about the
state, aside from the prior, but the policy maker and the media each get a private, informative signal
about the state, sI and sM respectively. The quality of the signal depends on the type, , of the
recipient. Each can be high or low quality:
2 fH; Lg. A high-quality type learns the true state:
Pr(s = ! j
= H) = 1:
A low-quality type receives an imperfect signal:
Pr(s = ! j
3
= L) = q > :
Note that politicians do not care about policy when they are not in o¢ ce. This assumption ensures that a low-
quality incumbent does not want to lose o¢ ce in the hopes of being replaced by a higher-quality o¢ cial.
4
Gentzkow and Shapiro (2006) suggest a di¤erent possible model of media motivations, in which the media is
concerned about potential customers’beliefs about its quality. Given that our primary focus is on the e¤ects of media
behavior, rather than the media behavior itself, we use the simpler assumption that the media is motivated by a desire
to report the truth.
6
The restriction that q >
ensures that even a low-type’s signal outweighs the prior, since by Bayes’s
Rule
Pr(! = B j s = B; = L) =
(1
(1
)q
) q + (1
1
> :
q)
2
Each player knows her own type, but not anyone else’s. The prior probabilities for each player
(incumbent, challenger, and media) being a high-quality type are:
Pr(
I
= H) =
I
Pr(
C
= H) =
C
Pr(
M
= H) =
M:
We say that the election is competitive if
I
and
C
are close together.
With probability , uncertainty about the correct …rst period policy resolves before election day
and the voter learns the true state; otherwise he must make his voting decision based only on the
policy choice xI ; and media announcement (if any). Formally, the voter’s signal is sV 2 fA; B; g,
where
means “no information”. If uncertainty resolves then sV = !: We interpret a low
as
meaning that either the election is imminent – so there is little time for information to be publicly
revealed – or that the policy being chosen is unlikely to produce any short run e¤ects that can be
easily assessed.
Timing Our goal is to explore the impact of the media’s announcement on the incumbent’s incentives to take the correct action in the …rst period. To highlight the role of the media, we start with
a baseline model without a media. This is a simpli…ed variant of Canes-Wrone, Herron, and Shotts
(2001).
We then analyze two di¤erent variants of the model; in the simultaneous variant, the media makes
its announcement at the same time that the incumbent chooses policy, whereas in the sequential
variant, the media’s announcement is made after the incumbent has chosen policy. The latter variant,
with sequential communication, is perhaps more interesting substantively, since we typically think of
7
the media observing and then commenting on the incumbent’s policy decisions. But considering two
timings for the media announcement allows us to isolate the causal mechanisms that lead to changed
incentives when a media is present. With simultaneous communication, the only change is that the
media’s announcement provides an additional, imperfect, public signal about whether the incumbent
chose the correct policy. In the model with sequential communication, the media can herd on the
incumbent’s choice, acting as a yes man. This last possibility turns out to be important.
Another reason to consider simultaneous communication is that we can interpret the equilibrium
as what happens with sequential announcements if the media is nonstrategic, in the sense that it is
duty-bound to announce its signal without trying to learn from the policy choice and the incumbent’s
equilibrium strategy. This is because there is no possibility of herding in a simultaneous moves model.
We focus on perfect accountability equilibria, in which the incumbent matches her action to her
signal. This sort of equilibrium is normatively desirable, since the incumbent uses her information
optimally to promote the voter’s policy interests. With this focus, we can sharpen our main question:
does the presence of a commentator make the existence of a perfect accountability equilibrium more
or less likely? And how does the existence of a perfect accountability equilibrium depend on factors
such as the competitiveness of the election (j
C j)
I
and the probability that uncertainty resolves
( )? When perfect accountability equilibria do not exist, there exist pandering equilibria, in which
a low quality incumbent sometimes chooses an action that matches voters’ prior beliefs about the
correct policy, but that does not promote their interests. We characterize such equilibria in the
appendix [to be written].
4
Preliminary Results
Before characterizing perfect accountability equilibria in the di¤erent variants of our model, we
provide some results that are useful in all three cases.
8
4.1
Second Period Policy and Continuation Values
As usual, we start solving our the game from the end. Because the second period is identical in each
model, we give a uni…ed treatment here.
As there are no subsequent periods, the period 2 policy-maker is concerned only with the immediate impact of her policy choice. Since she gets utility
> 0 from matching the state and zero
otherwise, she will choose the policy corresponding to the state she believes more likely, given her
signal. Since q >
, even the low type believes that her signal is probably correct. Thus, in the
second period, the policy-maker has a dominant strategy to follow her signal.
Given this second-period behavior, we can derive the optimal election rule. The voter wants
second-period policy to match the state. And he knows that whoever he elects will follow her signal
in the second period. Thus the voter elects whichever candidate he believes is more likely to be a
high quality type. If we write (h) for the voter’s assessment of the probability that the incumbent
is a high type given history h, then the optimal election rule is:
reelect the incumbent if and only if (h)
where
C
C
is the probability that the challenger is high quality.5
Given voter behavior and second period concerns, we can derive an expression for the incumbent’s
indirect payo¤ function for period 1. She gets an immediate payo¤ of
if she picks the correct policy,
xI = !; in period 1.
In addition, she gets a positive payo¤ if she is re-elected:
v( )
1 + (I[
I
= H] + qI[
I
= L]) ;
where I[p] is the indicator function for the proposition p. The …rst term, 1, is the direct ego rent
5
To be precise if
(h) =
C
(h) >
C
the voter must re-elect, if
(h) <
C
the voter must remove the incumbent, and if
the voter is indi¤erent. Perfect accountability involve pure strategies for other actors so only for knife-edge
parameter values will it be the case that
(h) =
C:
9
from holding o¢ ce, while the second re‡ects the probability that the incumbent will choose the right
action if she is reelected. Note that the second term depends on the incumbent’s type.
Thus, an incumbent with type
max
xI 2fA;Bg
I
who sees signal sI in period 1 picks policy xI to solve:
Pr(xI = ! j sI ) + v( ) Pr[ (h)
C
j xI ; sI ]:
The …rst part of this expression is the incumbent’s utility directly from her …rst period policy choice
and the second term is her re-election payo¤ weighted by her probability of re-election given her
policy choice.
4.2
Simplifying voter beliefs
Since the incumbent’s re-election chances depend on voter beliefs about her quality, these beliefs,
especially the posterior
(h) ; play a central role in our analysis. Particularly in the cases where the
media commentator gets to make an announcement, this direct calculation of this probability can
become quite complicated, because it depends on the media’s strategy, the incumbent’s strategy, and
their actions. Fortunately, our focus on perfect accountability equilibria means we can substantially
simplify these calculations.
By Bayes’s rule, the voter’s posterior belief about incumbent quality after history h is
(h) =
Pr(h j
I
Pr(h j I = H) Pr( I = H)
= H) Pr( I = H) + Pr(h j I = L) Pr(
I
= L)
:
Updating is particularly easy when uncertainty resolves and the voter observed the true state, sV = !.
In this case, the voter knows for sure whether the incumbent’s policy choice was correct. If the
incumbent chose the wrong policy, then the voter’s conjecture that the incumbent follows her signal
and the fact that only the low type can get a wrong signal combine to imply that the incumbent has
probability 0 of being high quality.
On the other hand, if the incumbent chose the correct policy and uncertainty resolves, then the
voter knows that xI = !: There are two ways this can happen: the incumbent is high quality or she
10
is low quality and got the right signal. Thus by Bayes’s rule, the voter’s belief about the probability
that the incumbent is high quality is
I
I
+ q(1
I)
:
What if the voter does not observe the true state? Since high ability types never make mistakes we
can write the posterior in a simple form.
Lemma 1 Assume that the incumbent matches her action to her signal. Then (h) = Pr(! = xI j
h) :
Intuitively, the voter …rst revises his beliefs about the true state of the world, and then uses those
beliefs about the state as weights to form beliefs about the incumbent’s type as a weighted average
of the best case (the incumbent is know to be correct) and the worst case (the incumbent is known
to be wrong).
5
Baseline Model
We can now analyze the incumbent’s policy choice in the …rst period of our baseline model. In this
baseline, recall, there is no media. Thus the timing is:
Inc learns
I ; sI
Inc chooses
xI 2 fA; Bg
Voter sees
xI ; sV
Election
Since we focus on existence of perfect accountability equilibria, we follow a simple procedure to
characterize all such equilibria for each variant of our model. First we assume that the incumbent
follows her signal, and calculate the voter’s posterior beliefs. We then use these posterior beliefs to
determine the voter’s optimal reelection rule given the information available to the voter at the time
of the election. Finally, we determine whether the incumbent actually prefers to follow her signal,
given voter behavior.
11
Updating
Recall that (h) is the voter’s assessment of the probability that the incumbent is high
quality, given history h. In the baseline model, h is just (xI ; sV ), so we write
(xI ; sV ) for the
posterior given …rst-period policy xI , public signal sV ; and given that in a perfect accountability
equilibrium the incumbent’s strategy is to choose xI = sI .
Using Lemma 1, we can calculate these posteriors for every history that the voter might observe.
For our purposes, the key aspect of these posteriors is their ordinal ranking. This is given as:
Lemma 2 In the baseline model, 0 =
(A; B) =
(B; A) <
(B; ) <
(A; ) <
(A; A) =
(B; B) < 1:
Proof The beliefs follow from a straightforward application of Bayes’s Rule. The only nontrivial
part is the inequality (B; ) < (A; ). By Lemma 1, this inequality is equivalent to
Pr(! = B j xI = B) < Pr(! = A j xI = A)
where Pr(! = B j xI = B) =
(1
(1
and Pr(! = A j xI = A) =
)[
)[
I +q(1
I +q(1
[
[
I +q(1
I )]
(1 q)(1
I )]+
I +q(1
I )]+(1
I)
I )]
)(1 q)(1
I)
: Substituting in and simplifying, the
inequality reduces to
1
1+
which is holds because
(1 q)(1
[ I +q(1
I)
I )] (1
1
<
1+
)
(1 q)(1
[ I +q(1
I)
(1
)
I )]
> 1=2.
2
As in several other recent papers (Canes-Wrone, Herron, and Shotts 2001; Gentzkow and Shapiro
2006; Prat 2005) the inequality (B; ) < (A; ) is the source of incentives for pandering— i.e., an
incumbent choosing a policy that voters believe is optimal even though she has information indicating
that it is not. Consider a low-quality incumbent who observes signal sI = B. Because q > , even
the low quality incumbent’s signal outweighs the prior, so unlike the voters she believes that xI = B
is the correct policy. But if uncertainty does not resolve (sV = ), then policy B leads voters to have
a worse posterior belief about her quality, because (B; ) < (A; ).
12
Figure 1 summarizes conditions under which a perfect accountability equilibrium exists, depending on the parameters of the model. The horizontal axis is the challenger’s probability of being high
quality,
C;
while the vertical axis is the probability of uncertainty resolution . Lemma 2 divides
the horizontal axis into several regions, and in each region voters will use a di¤erent optimal election
rule in a perfect accountability equilibrium. Our next step is to derive those rules and determine
whether it is optimal for the incumbent to follow her signal given these rules.
Reelection and policy choice Based on Lemma 2, there are four cases to consider. Note that
the incumbent’s …rst period policy motivations do not depend on either
or
C
–other things being
equal she always prefers to follow her signal –so we focus on variation in electoral incentives across
di¤erent parameter values.
1.
C
(B; ). The incumbent wins re-election unless uncertainty resolves and her choice was
wrong. Since the event of uncertainty resolution is independent of her action and signal, she
has an electoral incentive to choose the policy that she thinks is most likely correct. Because
her signal is informative, she has a strict incentive to follow her signal, setting xI = sI . Thus,
there is a perfect accountability equilibrium in region 1 of Figure 1.
2.
(A; ) <
(A; A). The incumbent wins only if uncertainty resolves and her choice was
C
correct, so she has an electoral incentive to choose the policy that she believes is more likely to
match the state.
3.
(A; A) <
C.
Because the voter wants to elect the candidate more likely to be high quality,
the incumbent can never win in this region. Thus her payo¤ is a¤ected only by the policy choice
in the …rst period so she strictly prefers to follow her signal. Along with the previous case, this
shows that there is a perfect accountability equilibrium in region 3 of Figure 1.
4.
(B; ) <
C
(A; ). This is the most interesting case. If uncertainty resolves, the incum-
bent wins re-election if and only if her choice was correct. If uncertainty does not resolve, she
13
wins if and only if she chose xI = A: How does this pattern of electoral incentives a¤ect the
incumbent’s policy choice?
If the incumbent chooses A then her total payo¤ for the two periods is
Pr(! = A j sI ) + v( ) (1
+ Pr(! = A j sI )) :
If she chooses B then her total payo¤ is
Pr(! = B j sI ) + v( ) Pr(! = B j sI ):
Choosing A is thus optimal if and only if
v( )(1
) + ( + v( ) ) (Pr(! = A j sI )
If sI = A, then the di¤erence (Pr(! = A j sI )
Pr(! = B j sI ))
Pr(! = B j sI )) is positive, and xI = A is opti-
mal. Thus the incumbent always wants to follow an A signal.
(Pr(! = A j sI )
Pr(! = B j sI )) =
0:
If sI = B and
I
= H, then
1, and for it to be optimal for the incumbent to follow her
signal and play xI = B requires
v(H)(1
Finally, if sI = B and
B
I
)
( + v(H) )
= L, then (Pr(! = A j sI )
Pr(! = A j sI = B;
I
0:
Pr(! = B j sI )) = 2
= L) =
(1
(1 q)
q) + (1
)q
B
1, where
< 1=2:
Thus for the incumbent to follow her signal and play xI = B requires
v(L)(1
)
( + v(L) ) + 2
B(
+ v(L) )
0:
The …nal simpli…cation will come from the fact that the low type always has the strongest incentive
to pander.
Lemma 3 In the baseline model, for any parameters at which a low quality incumbent wants to
follow a B signal, a high quality incumbent also wants to follow a B signal.
14
From Lemma 3, the hardest incumbent to deter from choosing the wrong policy is the low type
who gets signal B. She follows her signal if and only if
v(L)(1
)
( + v(L) ) + 2
B(
+ v(L) )
0
or
(2 B 1) + v(L)
2v(L)(1
B)
For
not too big,
:
(1)
> 0.6
We summarize these results as:
Proposition 1 In the baseline model, there is a perfect accountability equilibrium if one of the
following conditions holds:
1.
C
< (B; ), i.e., challenger reputation is worse than incumbent who chooses xI = B.
2.
C
(A; ), i.e., challenger reputation is better than incumbent who chooses xI = A.
3.
6
, i.e., uncertainty resolution is likely.
Simultaneous Media Announcements
Now we allow the media to make an announcement without knowledge of the incumbent’s action.
The timing is:
Inc learns
I ; sI
Media learns
M ; sM
6
If
Inc chooses
xI 2 fA; Bg
Media says
xM 2 fA; Bg
1
2 B
1+q
then
Voter sees
xI ; sV
Election
< 0 and there always exists a perfect accountability equilibrium.
15
Media Behavior
The media wants to maximize the probability that its announcement matches
the true state. If we let
M (sM ; M )
be the media’s posterior probability that the state is A, then
it’s easy to see that the media announces A if
M
> 1=2 and announces B if
M
< 1=2. Because we
assume that q > , even the low type’s signal outweighs the prior:
M (B; L)
<
1
<
2
M (A; L):
Thus the media always announces its true signal, xM = sM .
The probability that the media’s announcement matches the state, unconditional on its type, is
thus
qM
Updating
M
+ (1
M )q:
As before, (h) is the voter’s assessment of the probability that the incumbent is high
quality, given history h. With a media announcement, h is (xI ; xM ; sV ), and we use ~ (xI ; xM ; sV ) to
denote the voters’s posterior given …rst-period policy xI , media announcement xM and public signal
sV , if the incumbent’s …rst period strategy is to set xI = sI :
Using Lemma 1, we can calculate these posteriors for every history that the voter might observe.
For our purposes, the salient aspect of these posteriors is again their ranking.
Lemma 4 With simultaneous media announcement,
0 = ~ (A; xM ; B) = ~ (B; xM ; A) < ~ (B; A; ) < ~ (A; B; )
< ~ (B; B; ) < ~ (A; A; ) < ~ (A; xM ; A) = ~ (B; xM ; B) < 1:
The lemma is straightforward to derive using Bayes’s Rule. For our purposes, the key inequalities
are ~ (B; A; ) < ~ (A; B; ) and ~ (B; B; ) < ~ (A; A; ): The intuition behind these inequalities is
straightforward. Suppose that xM 6= xI ; and the voter does not learn the true state of the world.
16
Since the voter’s prior belief is that A is the more likely state of the world, an incumbent who chose
xI = A and was criticized by a media who announced xM = B is more likely to be high quality
than an incumbent who chose xI = B and was criticized by a media that announced xM = A; thus
~ (B; A; ) < ~ (A; B; ): Similarly if the media announces that the incumbent chose the correct
policy, the incumbent is more likely to be high quality if this policy matched the voter’s prior, so
~ (B; B; ) < ~ (A; A; ):
Figure 2 shows how the parameters of the model a¤ect the existence of perfect accountability
equilibrium. The horizontal axis is the challenger’s probability of being high quality, while the vertical
axis is the probability of uncertainty resolution. Lemma 4 divides the horizontal axis into several
regions, each of which has a di¤erent optimal election rule in a perfect accountability equilibrium.
To explain the pattern of perfect accountability equilibria in Figure 2, we derive the voters’s
optimal behavior given that the incumbent follows her signal, and determine whether it is optimal
for the incumbent to follow her signal given this voter behavior.
Reelection and policy choice As in the baseline model, the incumbent’s …rst period policy
incentives do not vary as a function of
1.
C
C
or : Based on Lemma 4, there are six cases to consider.
~ (B; A; ). The incumbent wins unless uncertainty resolves and her choice was wrong.
Since choosing the policy that matches her signal minimizes the chance of a policy mistake, she
has an electoral incentive to choose xI = sI : Thus there is a perfect accountability equilibrium
in region 1 of Figure 2.
2. ~ (A; B; ) <
C
~ (B; B; ). The incumbent wins if uncertainty resolves and her choice
was correct, or if uncertainty does not resolve and the media agrees with the policy choice.
Conditional on uncertainty resolving, the incumbent needs to match the state, so she wants
to choose the state she thinks is more likely. Conditional on uncertainty not resolving, the
incumbent needs to match the media’s announcement. Because the media just announces its
signal, the incumbent wants to choose the policy most likely to be the media’s signal. And since
17
q M > 1=2, this means the incumbent wants to set xI = sI in this event also. Thus there is a
perfect accountability equilibrium in region 3 of Figure 2.
3. ~ (A; A; ) <
C
~ (A; xM ; A). The incumbent wins only if uncertainty resolves and her choice
was correct: xI = sV . Since the event of uncertainty resolution is independent of her action
and signal, she just wants to match the state she considers most likely. Because her signal is
informative, she has a strict incentive to match her signal.
4. ~ (A; xM ; A) <
C.
Because the voter always wants to elect the candidate more likely to be
high quality, the incumbent can never win in this region. Thus her payo¤ is a¤ected only by
the policy choice in the …rst period, and her payo¤ is greater if that choice matches the state,
so she strictly prefers to follow her signal. Along with the previous case, this shows that there
is a perfect accountability equilibrium in region 5 of Figure 2.
5. ~ (B; B; ) <
C
~ (A; A; ). The incumbent wins only if either uncertainty resolves and her
choice was correct, or if uncertainty does not resolve and both the incumbent’s policy choice
and media announcement are A:
6. ~ (B; A; ) <
C
~ (A; B; ). The incumbent wins unless uncertainty resolves and her action
was wrong or uncertainty does not resolve, the incumbent chooses B and the media announces
A:
The last two cases are the most interesting, as there are nontrivial pandering incentives. Conveniently, the two cases lead to the same incentive constraints for incumbent behavior.
Consider …rst the case where the incumbent wins if she is proved correct or if she chooses A and
the media agrees. Then choosing A gives payo¤
( + v( )) Pr(! = A j sI ;
I)
+ (1
)v( ) Pr(sM = A j sI ;
while choosing B gives payo¤
( + v( ))(1
Pr(! = A j sI ;
18
I )):
I );
Thus the incumbent chooses A if and only if
( + v( )) (2 Pr(! = A j sI ;
I)
1) + (1
)v( ) Pr(sM = A j sI ;
I)
0:
(2)
Consider next the case where the incumbent wins is she is proved correct, if she chooses A, or is she
chooses B and is backed up by the media. Then choosing A gives payo¤
( + v( )) Pr(! = A j sI ;
I)
+ (1
)v( );
while choosing B gives payo¤
( + v( ))(1
Pr(! = A j sI ;
I ))
+ (1
)v( )(1
Pr(sM = A j sI ;
I )):
This leads to the same incentive constraint: choose A if and only if
( + v( )) (2 Pr(! = A j sI ;
I)
1) + (1
)v( ) Pr(sM = A j sI ;
I)
0:
(3)
Thus, since equations 2 and 3 are identical we have reduced the two cases to one.
As in the baseline model, there is no incentive problem for an incumbent who sees signal A. Such
an incumbent has a posterior Pr(! = A j sI = A;
I)
> 1=2, and the incentive constraint is satis…ed.
The case of signal si = B is more interesting. For both types, the …rst term in the inequality is
negative, since Pr(! = A j sI ;
I)
< 1=2: Thus this …rst term gives the incumbent an incentive to
follow her signal. However, the second term creates an incentive in the direction of pandering.
We now work out the algebra for the incentive constraints in this case. Consider the case where
the incumbent wins if and only if uncertainty resolves and the policy is correct, or xI = xM = A.
The high type who gets signal B will follow her signal if and only if
( + v( )) (2 Pr(! = A j sI = B;
I
= H)
1) + (1
19
)v( ) Pr(sM = A j sI = B;
I
= H)
0
Since Pr(! = A j sI = B;
1
I
= H) = 0 and Pr(sM = A j sI = B;
I
= H) = Pr(sM = A j ! = B) =
q M ; we rewrite the inequality as
)v(H) 1
qM
0
) (1 + ) 1
qM
0
qM
0:
( + v(H)) + (1
( + (1 + )) + (1
(1 + ) + (1
qM
) 1
+ (1
) 1
For the low type who gets signal B we use the notation
Note that
=
Bq
M
+ (1
B)
qM > 1
1
(4)
Pr(xM = A j sI = B;
I
= L) < 1=2:
q M : The low type who gets signal B will follow her
signal if and only if
( + v(L)) (2 Pr(! = A j sI = B;
I
= L)
1) + (1
)v(L) Pr(sM = A j sI = B;
I
= L)
0
Substituting in, the inequality becomes
( + (1 + q )) (2
(1 + q) (2
B
1) + q(1
B
)
1) + (1
+ (2
B
)(1 + q )
1) + (1
)
0
0:
(5)
The …nal simpli…cation will come from the fact that the low type always has the strongest incentive
to pander.
Lemma 5 With simultaneous announcements, for any parameters at which a low quality incumbent
wants to follow a B signal, a high quality incumbent also wants to follow a B signal.
This means that the hardest incumbent to deter from choosing the wrong policy is the low type
who gets signal B. She follows her signal if and only if
( + v(L)) (2
B
1) + (1
(2
B
)v(L)
0
1) + v(L)
v(L)(1
2
B)
+ v(L)
or
(2
2v(L)(1
B
1) + v(L)
B)
20
v(L) 1
~:
(6)
We summarize these results as:
Proposition 2 In the simultaneous model, there is a perfect accountability equilibrium if one of the
following conditions holds:
1.
C
< ~ (B; A; ), i.e., challenger reputation is worse than an incumbent who chooses xI = B and
is criticized by the media, which announces xM = A.
2.
C
3.
C
2 [~ (A; B; ); ~ (B; B; )], i.e., the election is competitive.
~ (A; A; ), i.e., challenger reputation is better than an incumbent who chooses xI = A
and is supported by the media, which announces xM = A.
4.
6.1
> ~, i.e., uncertainty resolution is likely.
Comparing the Models
Now that we know the conditions for existence of perfect accountability equilibrium in each case, we
can compare the incentives. We …rst note an e¤ect that makes good behavior more likely with a
media.
Fact 1 The probability of uncertainty resolution needed to ensure perfect accountability is lower with
a media than without a media: ~ < .
Proof Note that from Equation 1,
=
is obtained by simply subtracting v(L) 1
pression for : Thus, since
(2 B 1)+v(L)
2v(L)(1 B )
and from Equation 6, ~ =
(2
2v(L)(1
B
1)+v(L)
B)
v(L)(1
from both the numerator and denominator in the ex-
< 1, ~ < :
2
There is another fact that points in the direction of less pandering with a media. When the
race is very close, i.e.,
C
2 (~ (A; B; ); ~ (B; B; )) as in region 3 of Figure 2, there is a perfect
accountability equilibrium in the simultaneous media model. This stands in sharp contrast to the
21
)
baseline model, where the incentives for pandering are worst in close races.7 Why is pandering
eliminated here? If uncertainty is not resolved then the incumbent wants to choose the policy that
will be favorably evaluated by the media. Because the media’s signal tends to be correct, this means
the incumbent has an incentive to choose the policy that he thinks is most likely to be correct. In
contrast, in the baseline model, if uncertainty is not resolved the incumbent has an incentive to
choose the policy that the voters believe is correct, i.e., she has an incentive to pander.
Based on what we’ve seen so far, it might seem that a media unambiguously reduces pandering.
That’s false. A media that dutifully reports the information that it observes doesn’t always promote
better policy-making; in some circumstance it actually makes things worse.
Using the expressions used to derive Equations 1 and 4, it is straightforward to show that
~ (B; A; ) <
(B; ) and
(A; ) < ~ (A; A; ). This is not surprising; for example, ~ (B; A; ) <
(B; ) means that if a voter sees the incumbent choose B and the media later reports that A is
the correct policy, then the voter updates downwards about the incumbent’s quality as a result of
the media’s announcement.
This means that there exist parameter values–for example,
< ~ and
C
2 (~ (B; A; ); (B; ))–
for which pandering occurs in the simultaneous media model but not in the baseline model. Why
does this happen? In this example the incumbent starts with a substantial advantage over the
challenger. In the baseline model, she knows that even if she chooses xI = B, she will not be
removed if uncertainty does not resolve, since
C
< (B; ). In the simultaneous announcements
media model, however, she knows that if she chooses xI = B and the media announces xM = A,
then she will lose o¢ ce. Thus she has an incentive to pander.
7
The mixed strategy rate of pandering in the baseline model is highest when
22
I
=
C:
7
Sequential Announcements
Now we consider what happens if the media moves with knowledge of the incumbent’s policy choice.
The timing is:
Inc learns
I ; sI
Media learns
M ; sM
Inc chooses
xI 2 fA; Bg
Media Behavior
Media says
xM 2 fA; Bg
Voter sees
xI ; sV
Election
The …rst important observation about this timing is that the truthful media
behavior we described in the previous section is not part of any perfect accountability equilibrium
with sequential announcements. In particular, the media will sometimes want to be a yes man,
ignoring its own signal and simply following the incumbent’s lead.
Consider a low-quality media who gets signal B but observes policy xI = A. In a perfect
accountability equilibrium, this media is able to infer that the incumbent’s signal was A, so the
two signals are split. Furthermore, the low-quality media knows that the incumbent signal is more
accurate (on average) than its own, because the incumbent might be a high type. Thus the net
impact of the signals is to tilt the media’s posterior towards ! = A. Combined with the prior bias
towards A, this ensures that the media’s assessment of the probability that ! = A is greater than
1=2. And since the media wants to match its announcement to the state, it will ignore its signal and
announce xM = A.
In what follows, we want to explore the implications of herding in the simplest possible case.
Thus we assume that the incumbent is su¢ ciently likely to be high quality, and hence surely correct
in its policy choice, to induce a low-quality media to be a yes man even when the incumbent’s policy
choice is B. The following assumption is su¢ cient.
Assumption 1
I
q(2
q(2 1)
1)+(1
):
23
Without this assumption, conditions for the existence of a perfect accountability equilibrium will
look like a mixture of the conditions we derive below and those for simultaneous communication. We
leave the details to the interested reader.
Lemma 6 Under Assumption 1, in any perfect accountability equilibrium of the sequential move
game, the media is a partial yes man.
Regardless of its signal, a low quality media says that the
incumbent was right, xM = xI : A high quality media announces its signal, xM = sM .
Proof Recall that the media seeks to maximize the probability that xM = !. Thus the claim
follows from two observations. First, the high quality media knows that it’s signal is correct with probability 1, so it announces its signal truthfully. Second, the low quality media’s signal is outweighed
by the incumbent’s signal, which is truthfully revealed in a perfect accountability equilibrium. To
see this last point, use Bayes’s rule to write the media’s posterior as
Pr(! = A j sI = B; sM = A;
M
= L) =
(1
I ) (1
(1
q) q + (1
which is less than or equal to 1=2 because, under Assumption 1,
Updating
I
I ) (1
q) q
) [ I + (1
q(2
q(2 1)
1)+(1
I ) q] (1
):
q)
2
As before, (h) is the voter’s assessment of the probability that the incumbent is high
quality, given the history h. With a media announcement, h is (xI ; xM ; sV ), so we use ^ (xI ; xM ; sV )
to denote the posterior given …rst-period policy xI , media announcement xM and public signal sV ,
if the incumbent’s …rst period strategy is to set xI = sI :
Using Lemma 1, we can calculate these posteriors for every history that the voter might observe.
For our purposes, the salient aspect of these posteriors is again their ranking.
Lemma 7 With sequential media announcement,
0 = ^ (A; xM ; B) = ^ (B; xM ; A) = ^ (B; A; ) = ^ (A; B; )
< ^ (B; B; ) < ^ (A; A; ) < ^ (A; xM ; A) = ^ (B; xM ; B) < 1:
24
The main interesting part of this lemma, is the fact that ^ (B; A; ) = ^ (A; B; ) = 0; in contrast
to the simultaneous moves model, where 0 < ~ (B; A; ) < ~ (A; B; ): The reason for this di¤erence
is that with sequential moves, the media will only disagree with the incumbent’s policy choice if it
receives a high-quality signal indicating that the incumbent chose the wrong policy choice. Thus, if
xM 6= xI it must be the case that xI 6= !; and since a high-quality incumbent never chooses xI 6= !;
the voter thus knows for sure that the incumbent is low quality.
Figure 3 shows how the parameters of the model a¤ect the existence of a perfect accountability
equilibrium. The horizontal axis is the challenger’s probability of being high quality, while the vertical
axis is the probability that uncertainty resolves. Lemma 7 divides the horizontal axis into several
regions, each of which has a di¤erent optimal election rule in a perfect accountability equilibrium.
Our next step is to derive those rules and determine whether it is optimal for the incumbent to
follow her signal given these rules.
Reelection and policy choice Based on Lemma 7 , there are four cases to consider.
1.
C
^ (B; B; ). The incumbent wins unless uncertainty resolves and her choice was wrong
or the media announces that she chose the wrong policy. The only way either of these events
can happen is if she actually chose the wrong policy, since only a high quality media, who
knows for sure that the incumbent’s policy choice was wrong, will ever disagree with her policy
choice. Thus she has a strict incentive to match her signal, choosing policy xI = sI . So we have
established that there is a perfect accountability equilibrium in region 1 in Figure 3.
2. ^ (A; A; ) <
^ (A; xM ; A). The incumbent wins only if uncertainty resolves and her choice
C
was correct: xI = sV ; so she just wants to match the state she considers most likely. Because
her signal is informative, she has a strict incentive to match her signal.
3. ^ (A; xM ; A) <
C.
Because the voter always wants to elect the candidate more likely to be high
25
quality, the incumbent can never win in this region. Thus her payo¤ is a¤ected only by the
policy choice in the …rst period, and her payo¤ is greater if that choice matches the state. Thus
she strictly prefers to follow her signal. Along with the previous case, this shows that there is
a perfect accountability equilibrium in region 5 in Figure 3.
4. ^ (B; B; ) <
^ (A; A; ). The incumbent wins unless she is proved wrong, either by the
C
state revealing as di¤erent than the policy or by being contradicted by the media.
The last case is the most interesting, as there are nontrivial pandering incentives. However, the
relevant incentive constraint is easy to get— we just need to reinterpret the case of simultaneous
media announcements. The key to seeing this is to notice that it is still the case that pandering
only works if the media follows with a con…rmatory message. The only di¤erence from before is
that, with a partial yes-man media, this has become more likely. Instead of the expression from the
simultaneous model,
Pr(xM = A j xI = A; sI = B;
I)
=
(sI ;
I) q
M
+ (1
(sI ;
I ))(1
q M );
we now have
Pr(xM = A j xI = A; sI = B;
where
(sI ;
I)
= Pr (! = AjsI ;
I) :
I)
=
(sI ;
I)
+ (1
(sI ;
I ))(1
M)
Thus we can simply copy the previous argument to get the no
pandering constraint as
^
where
=
B
+ (1
B )(1
(2
2v(L)(1
1) + v(L)
B
B)
v(L) 1
(7)
M ).
We summarize these results as:
Proposition 3 In the sequential model there is a perfect accountability equilibrium if one of the
following conditions holds:
26
1.
C
< ^ (B; B; ), i.e., challenger reputation is worse than an incumbent who chooses xI = B
and is supported by the media, which announces xM = B.
2.
C
^ (A; A; ), i.e., challenger reputation better than an incumbent who chooses xI = A and
is criticized by the media, which announces xM = A.
3.
> ^, i.e., uncertainty resolution is likely.
The sequential model provides insight into media behavior. If the media is low quality then it is
a complete yes man, in the sense that it always says that the incumbent chose the correct policy. A
high-quality media, in contrast, is not a yes man but rather reports its true signal. Taken as a whole,
the media, which can be either high or low quality, a partial yes man. Thus the model predicts that
media commentators sometimes suppress evidence that incumbents have made policy mistakes. It
is particularly interesting to get this result in a model in which the media’s sole objective is to give
accurate information about the state of the world. In particular, the result is not driven by collusion
or sidepayments since in our model there is no possibility for the media to be bought o¤ by the
incumbent.8
8
Comparison of Models: Incentives
The primary goal of this paper is to assess how the media a¤ects the incumbent’s incentives to
pander. One might intuitively think that a partial yes man media is worse than a media that
truthfully reports its signal. And in one sense this is true. A simple modi…cation of the argument
ranking the cutpoints
from the baseline model and ~ from the simultaneous model shows that the
cutpoint for a partial yes man media is in between those cutpoints, i.e., from equations 1, 6 and 7,
it is straightforward to con…rm that ~ < ^ < . This …ts with the intuition that the more honest
the media is in reporting its signal, the more bene…cial will be the e¤ects on policy choice. Thus
8
For a model in which incumbents may buy o¤ the media, see Besley and Prat (2006).
27
if we focus solely on the probability of uncertainty resolution, we …nd that the set of
values for
which pandering is possible is smallest for the simultaneous/nonstrategic media model, intermediate
for the sequential yes man media model, and largest for the baseline no media model.
However, focusing solely on
lenger quality,
C,
misses part of the story. Incentives to pander also depend on chal-
and there are some
C
values for which pandering can occur in the simultaneous
model but not in the sequential model. Speci…cally, (~ (B; A; ); ~ (A; B; )) [ (~ (B; B; ); ~ (A; A; ))
from Proposition 2 is neither a strict superset nor a strict subset of (^ (B; B; ); ^ (A; A; )) from
Proposition 3. Thus, at least some of the time, a partial yes man media actually makes things better
than a nonstrategic media that truthfully reports xM = sM :
This is not what we expected ex ante. But it actually makes sense. The problem with the
nonstrategic media is that the incumbent fears that a low-quality media will criticize her, thereby
causing her to lose o¢ ce. If the low quality media is a yes man and
C
^ (B; B; ) this problem
is removed, but the incumbent still faces the disciplining e¤ects of potential criticism from the high
quality, accurate, media that reports the true state of the world after she has chosen the wrong
policy. Thus she wants to pick the policy that maximizes the probability that xI = !, and she has
no incentive to pander.
One additional interesting result is that if the media is su¢ ciently likely to be high quality,
speci…cally
M
>
(2
1)
, then ^ (B; B; ) >
I,
i.e., in a perfect accountability equilibrium, when
xI = B and xM = B the voter’s belief about the incumbent’s probability of being high quality goes
up from the prior
C
I
for incumbent quality. Because, as shown in Proposition 3, challenger quality
must be greater than ^ (B; B; ) to get pandering in the sequential announcement model, this
means that there can be no pandering unless
C
>
I.
Given that incumbents are more likely than
challengers to be high quality, due to selection e¤ects of repeated elections (Ashworth and Bueno
De Mesquita 2006), this means that as long as the media is su¢ ciently likely to be high quality, a
partial yes man strategic media will do a great job of eliminating pandering. A nonstrategic media,
28
in contrast, will fail to eliminate pandering for some
C
2 (~ (B; A; ); ~ (A; B; )) and ~ (A; B; ) <
9
C
<
I
because there is pandering when
I.
Which Timing Leads to Better Reelection Decisions?
The bulk of this paper has focused on the question of when perfect accountability equilibria exist
under di¤erent assumptions about the media. It would be tempting to conclude that the preceding
analysis is su¢ cient for welfare comparisons across media types: if, for some parameters, one media
arrangement leads to perfect accountability and the other does not, isn’t the former better for the
voter? Not necessarily, since we also need to take into account the probability that the winner of
the election is high quality. And this is nontrivial, because, surprisingly, either information structure
can be more informative, in the Blackwell sense. Rather than undertake an exhaustive analysis, we
just present two examples to show that the informativeness ranking is ambiguous.
Example 1: Simultaneous superior
and
Suppose that
C
2 (max f~ (B; B; ); ^ (A; A; )g ; ~ (A; A; ))
> ~: For either type of media, there is a perfect accountability equilibrium under these para-
meter values. If uncertainty resolves, selection of a second period executive works the same way in
either model; the incumbent is re-elected if and only if xI = !. So from here on we focus solely on
what happens if uncertainty does not resolve.
If uncertainty does not resolve, selection of the second period executive works di¤erently in the
two models. In the sequential media model, the incumbent never wins re-election when uncertainty
does not resolve, since
quality is simply
C.
C
> ^ (A; A; ), so the probability that the second period executive is high
In the simultaneous media model, in contrast, the incumbent wins re-election
if and only if xI = A and xM = A; in which case the probability that the incumbent is high quality
is ~ (A; A; ). When the incumbent does not win re-election, the probability that the second period
executive is high quality is
C,
and thus since ~ (A; A; ) >
29
C;
the probability that the second period
executive is high quality is strictly greater than
C.
Thus, in this example a simultaneous media is more e¤ective than a sequential media at helping
the voter choose a high-quality executive for the second period.
Example 2: Sequential superior
Suppose that
C
2 (0; ~ (B; A; )). For either type of media,
there is a perfect accountability equilibrium under these parameter values. If uncertainty resolves,
selection of a second period executive works the same way in either model; the incumbent is reelected if and only if xI = !. So from here on we focus solely on what happens if uncertainty does
not resolve.
If uncertainty does not resolve, selection of the second period executive works di¤erently in the
two models. In the sequential media model, the incumbent wins re-election unless xI 6= xM ; in which
case the incumbent is surely low quality, and gets replaced by a challenger who is high quality with
probability
greater than
C
> 0: Thus the probability that the second period executive is high quality is strictly
I:
In the sequential media model, the incumbent is always re-elected when uncertainty
does not resolve, so the probability that the second period executive is high quality is just
I:
Thus, in this example a sequential media is more e¤ective than a simultaneous media at helping
the voter choose a high-quality executive for the second period.
10
Conclusion
To be written...
11
Appendix: Proofs
Proof [Lemma 1] Consider the following learning process. The voter …rst learns h, and then learns
the true state. (The second step may or may not be redundant.) The voter’s belief at the election
corresponds to the intermediate stage of this process.
30
At the …nal stage of the process, the voter’s belief about incumbent quality is either 0 or . Since
a probability of an event is just the expected value of an indicator function, the martingale property
of Bayesian updating implies
(h) = Pr(
I
= H j h) = E(Pr(
I
= H j h; !));
where the expectation is with respect to the realization of the …nal stage of learning. But the
expectation is just
Pr(! = A j h) Pr(
I
= H j h; ! = A) + Pr(! = B j h) Pr(
I
= H j h; ! = B);
which gives the result.
2
Proof [Lemma 3] Write the di¤erence between a low type’s gain from choosing A rather than
B; conditional on sI = B and the high type’s gain, as
v(L)(1
=
At
(1
)
( + v(L) ) + 2
q)(2
1) + 2
B
B(
+ v(L) )
(v(H)(1
)
( + v(H) ))
( + (1 + q) ) :
= 0, this di¤erence is equal to
(2
B
(1
q)) :
We claim that this di¤erence is positive. Substitute for
B
to see that the expression is positive if
and only if
2 (1 q)
(1 q) + (1
)q
2
Since
> 1=2,
> (1
q) + (1
> 1
>
q
(1
q) + (1
)q:
)q, and thus the inequality holds.
Next, di¤erentiate the expression for the di¤erence with respect to
0
( ) = 2 (1
q) + 2
31
B (1
+ q) > 0:
to get
Thus the di¤erence is positive at
= 0 and increasing in , so it is positive everywhere. This means
that if the low type’s incentive constraint is satis…ed (the gain is negative), then the high type’s
incentive constraint is also satis…ed.
2
Proof [Lemma 5] Considering term-by-term the expressions for the high and low types in equations 4 and 5 , we show that if the high type weakly prefers to play A after seeing a B signal, the low
type must strictly prefer to do so. For the last term, (1
For the penultimate term
Since
> 1
(2
B
1) >
since
(1 + q) (2
B
1) + q(1
)
> (1
) 1
q M since
>1
qM :
> 0: For the …rst term we need
B
) >
(1 + ) + (1
) 1
qM
q M it is su¢ cient to show that
(1 + q) (2
1 + + (1 + q) (2
B
1)
B
1) + q(1
(1
q) (1
) 1
qM
>
) 1
qM
> 0:
(1 + ) + (1
) 1
qM
And since q M > q it is su¢ cient to show that
1 + + (1 + q) (2
This expression is linear in
and when
1)
B
q)2 (1
(1
= 1 it is positive since
2 + (1 + q) (2
1) > 2
B
(1 + q) > 0:
Thus all we need to show is that the expression is positive when
1 + (2
B
1)
(1
(1
(1 q)
q) + (1
B
)q
2
which holds since
>
(1
q)2 and
= 0; i.e.,
q)2 > 0
2
2
) > 0:
> (1
q)2
> (1
q)2
>
> 1=2 > (1
32
(1
q)2 + (1
q) q (1
):
q) (1
)q
2
References
[1] Ashworth, Scott O., and Ethan Bueno de Mesquita. 2006. “Electoral Selection and the Incumbency Advantage.” Princeton Typescript.
[2] Baron, David P. 2004. “Persistent Media Bias.” Stanford Typescript.
[3] Bernhardt, Dan, Stefan Krasa, and Mattias Polborn. 2006. “Political Polarization and the
Electoral E¤ects of Media Bias.” Illinois typescript.
[4] Besley, Timothy, and Andrea Prat. 2006. “Handcu¤s for the Grabbing Hand? The Role of the
Media in Political Accountability.” American Economic Review 96(3):720-736..
[5] Canes-Wrone, Brandice, Michael C. Herron, and Kenneth W. Shotts. 2001. “Leadership and
Pandering: A Theory of Executive Policymaking.” American Journal of Political Science
45(3):532-550.
[6] Carpenter, Daniel. 2002. “Groups, the Media, Agency Waiting Costs, and FDA Drug Approval.”
American Journal of Political Science 46 (3):490-505.
[7] Egorov, Georgy, Sergei Guriev, and Konstantin Sonin. 2007. “Media Freedom, Bureaucratic
Incentives, and the Resource Curse.” New Economic School Typescript.
[8] Gentzkow Matthew and Jesse M. Shapiro. 2006. “Media Bias and Reputation.” Journal of
Political Economy 114(2):280-316.
[9] Groseclose, Tim, and Je¤rey Milyo. 2005. “A Measure of Media Bias.” Quarterly Journal of
Economics 120(4):1191-1237.
[10] Page, Benjamin I. 1996. Who Deliberates?. Chicago: The University of Chicago Press.
[11] Prat, Andrea.
2005.
“The Wrong Kind of Transparency.” American Economic Review
95(3):862-877.
[12] Prendergast, Canice. 1993. “A Theory of ‘Yes Men.’” American Economic Review 83(4):757770.
33
[13] Stromberg, David. 2004. “Mass Media Competition, Political Competition, and Public Policy.”
Review of Economic Studies 71:265-284.
34
12
Appendix: For Referees only
This appendix contains proofs for referees only. First we show Bayes’s Rule can be used to calculate
voter beliefs –since these calculations are just a matter of straightforward algebra, they are omitted
from the main text. Second, we state and prove mixed strategy pandering equilibria for parameter
values such that no perfect accountability equilibrium exists. Even stating these equilibria is highly
tedious, so they are omitted from the main text.
Proof [Lemma 4 - Simultaneous Beliefs] The only nontrivial steps are the inequalities involving
. First consider the inequality , ~ (B; A; ) < ~ (A; B; ). For these beliefs, the voter knows that one
of the two actors – the incumbent and the media – received a correct signal and the other received
an incorrect signal. By Lemma 1, this inequality is equivalent to
Pr(! = B j xI = B; xM = A) < Pr(! = A j xI = A; xM = B)
where Pr(! = B j xI = B; xM = A) =
A; xM = B) =
[
[
I +(1
I +(1
I )q]
q M )+(1
(1
I )q](1
(1
qM
)(1
(1 )[ I +(1 I )q](1 q M )
)[ I +(1 I )q](1 q M )+ (1 I )(1 q)q M
)
I )(1
q)q M
and Pr(! = A j xI =
: Substituting in and simplifying, the inequality
reduces to
1
1+
(1
[ I +(1
q)
qM
M ) (1 q M ) (1
)q](1
q
I
1
<
I )(1
1+
)
(1
[ I +(1
q)
(1 q M ) (1
M)
)q](1
q
qM
I
I )(1
)
which holds because q M > :
Next we show that ~ (A; B; ) < ~ (B; B; ). By Lemma 1, this inequality is equivalent to
Pr(! = A j xI = A; xM = B) < Pr(! = B j xI = B; xM = B):
Writing out the expression using Bayes’s Rule and rearranging terms yields
1
1+
(1 q)(1
[ I +q(1
qM 1
M
I )] 1 q
I)
1 qM
qM
which is true because q M > :
35
1
<
1+
(1 q)(1
[ I +q(1
I)
I )] 1
;
Finally, we show that ~ (B; B; ) < ~ (A; A; ). By Lemma 1, this inequality is equivalent to
Pr(! = B j xI = B; xM = B) < Pr(! = A j xI = A; xM = A):
Writing out the expression using Bayes’s Rule and rearranging terms yields
1
1+
1
>
qM
I)
M 1
I )] 1 q
(1 q)(1
[ I +q(1
1+
;
1 qM 1
M
I )] q
(1 q)(1
[ I +q(1
I)
which is true because q M > :
2
Proof [Lemma 7 – Sequential Beliefs] For the equalities in the …rst line, the key is that only a
high quality media will disagree with an incumbent, and a high quality media always sees sM = !
and announces xM = sM : This fact, combined with the fact that only a low quality incumbent will
choose xI 6= !; means that when the media and the incumbent disagree it must be the case that the
incumbent is low quality.
The only other non-trivial step is ^ (B; A; ) < ^ (A; B; ), for which we need
Pr(! = B j xI = B; xM = B) < Pr(! = A j xI = A; xM = A)
where Pr(! = B j xI = B; xM = B) =
A; xM = A) =
[
[
I +(1
I +(1
I )q]+(1
(1
(1
)[
I +(1
I )q]
)(1
I )(1
q)(1
M)
)[
I +(1
I )q]+
(1
I )q]
I )(1
q)(1
M)
and Pr(! = A j xI =
: Substituting in and simplifying, the inequality
reduces to
1
1+
which is true because
(1
q)(1
I +(1
I )q
I )(1
1
<
M)
(1
1+
)
> 1=2.
(1
I )(1
I +(1
q)(1
I )q
M)
(1
)
2
36
Figure 1: Baseline No-Media Model
=Regions for perfect accountability Eq’m
1
2
ρ
Probability
of uncert
resolution
1
3
0
μ ωx ==B
φ
0
κI
I
μ ωx ==φA
1
I
KC = Challenger quality (probability of being high qual)
Figure 2: Nonstrategic Media Model
1
2
Probability
of uncert
resolution
4
1
3
5
ρ~
0
0
μ~x = B
I
xM = A
μ~x = A
I
xM
=B
μ~x = B
I
xM
=B
μ~x = A 1
I
xM = A
KC = Challenger quality (probability of being high qual)
=Regions for perfect accountability Eq’m
Figure 3: Strategic Media Model
1
2
Probability
of uncert
resolution
1
ρ̂
3
0
0
μ̂ x = B
I
xM = B
μ̂ x = A
I
xM = A
1
KC= Challenger quality (probability of being high qual)