PROFIT-MAXIMIZING MEDIA BIAS◦
(ONLINE APPENDIX)
RYAN Y. FANG♦
Abstract. In this Online appendix to “Profit-Maximizing Media Bias” (henceforth
“the Paper”), we consider a generalized setting in which consumers can differ in their
utility functions as well as their prior beliefs. We characterize the optimal news reports, fixing the production technologies available to the media outlets, to consumers
with different utility functions and beliefs. We then show that the assumption of
homogeneous utility function and heterogeneous prior beliefs made in the Paper is
only a choice of representation: the consumers described in the Paper behave identically as a set of consumers with a common prior and heterogeneous utility functions.
Finally, we show that media bias can lead to political polarization, which can be
socially costly. Thus, social welfare can depend on the balancedness of consumers’
news consumption itself.
JEL Classification: D03; D80; L10; L51; L52
Key Words: Media Bias, Fairness Standards, Endogenous Information Acquisition,
Confirmation Bias, Political Polarization
Date: September 2015 (first version: October 2013).
◦
This research was conducted under the direction of my thesis advisers Roger Myerson, Philip Reny,
and Hugo Sonnenschein and have benefited immensely from their insightful suggestions. I am also
grateful for the valuable comments provided by Simon Board, Edward Green, Priscilla Man, Glenda
Oskar, Jesse Shapiro, Richard Van Weelden, and seminar participants at Brown University, Cheung
Kong GSB, CUHK Business School, Pennsylvania State University, the University of Chicago, and
the 2014 Midwest Economics Association Annual Meeting. All remaining errors are, of course, my
own.
♦
Department of Economics, Pennsylvania State University. Email: [email protected].
1
1. The Generalized Model
1.1. The Generalized Consumer Problem. Let i denote a typical consumer who
faces a choice between three actions: the left action (l), the right action (r), and
abstention (a). As summarized in Table 1.1, i’s utilities after choosing actions l and
r depend on the unknown state of the world, which can be either left (L) or right
(R), whereas her utility after choosing action a is certain and is normalized to 0. The
δi
i
parameters αi , βi , δi , γi are positive real numbers. We assume that αiα+β
< δi +γ
, so
i
i
that action a is a best response to some beliefs of i, who is assumed to be a subjective
expected utility (SEU) maximizer. Let her subjective prior belief over the possible
states, {L, R}, be given by the vector (1 − πi , πi ), that is, she believes that state R
obtains with probability πi . Consumers can have different utility functions and prior
beliefs, hence the dependence of (αi , βi , δi , γi , πi ) on i.
Table 1.1. Consumer i0 s Decision Problem
L
R
l αi −βi
r −δi γi
a 0
0
1.1.1. Default Actions. Let upi (d) denote consumer i’s expected utility when her belief
over {L, R} is given by the vector of probabilities (1 − p, p) and she decides to take
action d ∈ {l, r, a}. Define dbi (p) as her optimal decision given her belief p, i.e., dbi (p) ≡
arg maxd∈{l,r,a} upi (d). Given i’s utility function, dbi (p) is given by:

i

{l},
p ∈ [0, αiα+β
)

i




i

{l, a}, p = αiα+β


i
δi
i
dbi (p) =
.
{a},
p ∈ αiα+β
,
i δi +γi



δi


{a, r}, p = δi +γ

i



δi
{r},
p ∈ ( δi +γi , 1]
Members of dbi (πi ) are referred to as consumer i’s default actions. For expositional
convenience, the consumers with default action l, i.e. all i with dbi (πi ) = {l}, are
referred to as liberals, and those with default actions r and a are referred to as conservatives and moderates, respectively.
1.2. The News Reports. As discussed in the Paper, a news report can be identified
with a composite signal that sends a message mL (respectively, mR ) when any of
2
the right (left) signals returns “left” (“right”), and sends a message mI when all of
the left-biased signals return “left” and all of the right-biased signals return “right”.
Given a media outlet’s reporting strategy (qL , qR ), its news report is characterized by a
pair (σ (qL ) , σ (qR )) ∈ [0, 1]2 , where σ (qL ) and, respectively, σ (qR ) are the conditional
probabilities that the equivalent composite signal sends the messages mL and mR (see
Table 1.2). We refer to (q, 0) and (0, q) as extreme reporting strategies and any other
feasible (qL , qR ) as an interior reporting strategy.
Table 1.2. A News Report
Message \ State
L
R
mL
σ (qR )
0
mI
1 − σ (qR ) 1 − σ (qL )
mR
0
σ (qL )
1.3. The Value of Information to Consumers. In equilibrium, the consumers
form rational expectations about the media outlets’ reporting strategies and update
their beliefs according to Bayes’ rule. Given consumer i’s prior belief, πi , and her
news consumption bundle, identified with a composite signal characterized by σ ≡
(σL , σR ), we can calculate i’s posterior belief upon receiving messages mL , mR , and
mI , respectively, as well as her prior belief of their likelihood. Abusing notation a little,
these can be written as:
pσπi (mL ) = (1 − πi ) σR
pσπi (mR ) = πi σL
pσπi (mI ) = 1 − πi σL − (1 − πi ) σR
pσπi (R | mL ) = 0
pσπi (R | mR ) = 1
pσπi (R | mI ) =
πi (1 − σL )
.
1 − πi σL − (1 − πi ) σR
Let u∗i (p) ≡ max{upi (l) , upi (r) , upi (a)}. Thus, u∗i (p) is the maximum expected utility consumer i can achieve without additional information given her belief (1 − p, p).
u∗i (πi ) is referred to as i’s default utility. Having access to a bundle of news reports
allows the consumer to make her decision contingent on the message she receives.
Thus, with consumption bundle (σL , σR ), the maximum expected utility consumer i
3
can achieve, ex ante, becomes:
Ui∗ (σL , σR , πi ) ≡ pσπi (mR ) u∗i pσπi (R | mR ) + pσπi (mL ) u∗i pσπi (R | mL )
+pσπi (mI ) u∗i pσπi (R | mI )
= πi σL γi + (1 − πi ) σR αi + [1 − πi σL − (1 − πi ) σR ] u∗i pσπi (R | mI ) .
The difference between Ui∗ (σL , σR , πi ) and u∗i (πi ), denoted Vi (σL , σR ), is the net gain
in i’s expected utility brought by the news consumption bundle σ and, hence, is how
much she values the latter.
2. Utility Maximizing News Reports
We want to understand the impact of media bias and the relevant industry regulations on the consumers’ well-being. This comes down to understanding the consumers’
preferences over news consumption bundles. In this section, we ask the following question: fixing a media outlet’s resources and production technology, what is the most
valuable news report it can produce for an individual consumer, given the consumer’s
utility function and prior belief? The answer to this question will also inform our
analysis of the market demand for news below.
δ
α
< δ+γ
, we want to
Formally, let (α, β, δ, γ) be any member of R4++ that satisfies α+β
solve, for each q ∈ (0, 1) and each π ∈ (0, 1), the following problem:
max(qL ,qR ) U ∗ (σ (qL ) , σ (qR ) , π)
s.t.
(2.1)
qL , qR ≥ 0
qL + qR ≤ q,
where the dependence of U ∗ on the vector (α, β, δ, γ) is understood and suppressed in
the notation.
We begin by exploring some properties of the U ∗ function. The following lemma
establishes that U ∗ is monotone in (σL , σR ).
Lemma 1. For any π ∈ (0, 1) and any σL , σL0 , σR , σR0 ∈ [0, 1], such that σL < σL0 and
σR < σR0 :
a) U ∗ (σL , σR , π) ≤ U ∗ (σL0 , σR , π) and U ∗ (σL , σR , π) ≤ U ∗ (σL , σR0 , π); and,
b) U ∗ (σL , σR , π) < U ∗ (σL0 , σR0 , π) ≤ U ∗ (1, σR0 , π) = U ∗ (σL0 , 1, π).
Note that, for b = L, R, reducing σb can be viewed as randomly misreporting the
realizations of b-biased signals. Thus, Lemma 1 a) is essentially a special case of
Blackwell’s (1951) theorem of comparing experiments. It re-iterates the well-known fact
4
that, to an individual facing a non-strategic decision problem, additional information
can never hurt.
Lemma 1 b) further states that there are always some information that are strictly
beneficial to the consumer. In other words, additional resources are always (strictly)
valuable. It follows that any (qL∗ , qR∗ ) that solves (2.1) must satisfy qL∗ + qR∗ = q.
The consumer’s problem involves a tradeoff between the two types of signals. The
nature of the tradeoff depends on the technology for converting resources into information, that is, on σ. As mentioned in the Paper, we impose no restriction on σ beyond
strict monotonicity. In particular, σ may be concave and the marginal rate of transformation between the two types of signals may be diminishing. When this is the case,
our consumer may very well prefer her news to be balanced than biased so that she
receives more signals in total. For example, a news report containing two left-biased
signals and two right-biased signals may be preferable to one containing only three
left-biased signals. The next proposition shows that this is the only reason why any
consumer might prefer her news to be more balanced: when σ is convex, all consumers
prefer their news reports to be extremely biased.
Proposition 1. If σ : [0, 1] → [0, 1] is (weakly) convex, the solution to problem (2.1)
is either (q, 0) or (0, q) for all consumers.
This result may appear to be counter-intuitive at the beginning. Audi alteram
partem: conventional wisdom dictates that a rational individual should always “hear
the other side” too.1 It is beliefs like this that underpin the common concern over
media bias and, in turn, the belief in the necessity of government imposed fairness
standards. The reason why such conventional wisdom fails in this case is because collecting information of any kind costs resources, which are strictly valuable. The next
lemma gives conditions under which information biased to “the wrong side”, although
not harmful to a consumer, cannot provide any value to her either.2
Lemma 2. For any π ∈ (0, 1) andany σL , σL0 , σR , σR0 ∈ [0, 1]:
(σ0 ,σR )
(σ ,σ )
a) If db pπ L R (R | mI ) = db pπ L
(R | mI ) = {r}, then U ∗ (σL , σR , π) =
U ∗ (σ 0 L , σ R , π); and,
1Note
that, we are only examining the merits of Audi alteram partem in the narrow context of
individuals acquiring information in order to make better personal decisions. In particular, we are
not considering it in the context of justice or legal systems, where further complexities arise.
2Lemma 2 is an example of the nonconcavity in the value of information first discussed by Radner and
Stiglitz (1984). The same principle underpins other examples where biased information is preferable
by rational individuals such as those presented in Calvert (1985) and Suen (2004).
5
0
σL ,σR
(
)
(σ
,σ
)
L
R
b) If db pπ
(R | mI ) = db pπ
(R | mI ) = {l}, then U ∗ (σL , σR , π) =
U ∗ (σ L , σ 0 R , π).
Lemma 2 says that if, upon receiving inconclusive evidence (mI ) presented by a news
report (qL , qR ), the consumer’s optimal choice is l (r), then additional signals biased
to the right (left) is not valuable to her, ex ante. Thus, it follows from Lemma 1 that
she must be strictly better off consuming a news report that is extremely biased to the
left (right).
In terms of the example given in the Paper, if, based on her prior information, the
consumer is determined to support the government’s initiative on subsidizing college
education, then she should not waste resources seeking the assessment of a conservative
think tank that cannot credibly persuade her to change her choice. On the other hand,
the assessment of a liberal think tank is valuable: in the possible event that this
think tank suggests that the subsidy does not stimulate economic growth, it has the
credibility to persuade the consumer to oppose the subsidy.
If the consumer is a moderate, to persuade her to choose l (r) with inconclusive
evidence, the news report (qL , qR ) must be strictly biased to the left (right), and it
remains to be determined whether (qL , qR ) or a more balanced news report is more
valuable to her. When σ is convex, the former is always more valuable to the consumer.
This is not generally the case when σ is concave. However, when the consumer is a
liberal (conservative), she chooses l (r) after seeing inconclusive evidence presented
by a perfectly balanced news report or even a news report biased to the right (left).
Consequently, regardless of the shape of σ, the unique optimal news report to a liberal
(conservative) is always extremely biased to the left (right).3
Proposition 2. The unique solution to problem (2.1) is q∗ = (q, 0), if the consumer
is a liberal, and is q∗ = (0, q), if she is a conservative.
Note that, when σ is concave, the extremely biased news report may contain strictly
fewer signals in total than a more balanced report. Nevertheless, the partisan consumers always prefer the former. Studies have shown that consumers of biased news
appear to be less informed than those consume more balanced news.4 This has been
taken by some as evidence that biased news conveys less facts than balanced news.
Proposition 2 shows that, even so, the consumers of biased news are not necessarily
3Note
that Proposition 2 relies on our implicit assumption that the media outlet is equally efficient
in acquiring information biased to either direction. See discussions below for implications of relaxing
this assumption.
4See, e.g., Gentzkow and Shapiro (2004) and Fairleigh Dickinson University’s Public Mind Poll (2011,
2012)
6
worse off, if they do not seek information for its own sake but rather as an instrument
for better decision making.
The present model can also be extended to give the consumers a choice between
any finite number of actions. In this more general case, Proposition 1 goes through
without any modification. Moreover, we can identify the “most liberal consumers”,
whose default action is the “most liberal action”, i.e., db(0), and the “most conservative
consumers”, whose default action is db(1). Proposition 2 still holds in the general model
for the most liberal and the most conservative consumers.
2.1. Proofs of Lemmas 1 and 2 and Propositions 1 and 2. Recall that:
U ∗ (σL , σR , π) = πσL γ + (1 − π) σR α
+ [1 − πσL − (1 − π) σR ] u∗ (p (R | mI )) ,
p(R|m )
p(R|m )
p(R|m )
I
I
I
and that u∗i (p (R | mI )) ≡ max{ui
(l) , ui
(r) , ui
(a)}.
Since [1 − πi σL − (1 − πi ) σR ] is non-negative for all (σL , σR ) ∈ [0, 1]2 , we can rewrite
U ∗ (σL , σR , π) as:
U ∗ (σL , σR , π) = max{πσL γ + (1 − π) σR α
+π (1 − σL ) (−β) + (1 − π) (1 − σR ) α,
πσL γ + (1 − π) σR α
+π (1 − σL ) γ + (1 − π) (1 − σR ) (−δ) ,
πσL γ + (1 − π) σR α}.
Lemma 1 follows from the fact that each of these expressions is non-decreasing in
σL or σR and strictly increasing in σL + σR . Now if either σL or σR is 1, the news
reports are perfectly informative and the consumer can achieve the highest expected
utility possible.
(σ ,σ )
For any (σL , σR ) such that db pπ L R (R | mI ) = r, U ∗ (σL , σR , π) = uπ (r) +
(σ ,σ )
(α + δ) πσR , which clearly does not depend on σL . When db pπ L R (R | mI ) = l,
U ∗ (σL , σR , π) = uπ (l) + (γ + β) πσL , which does not depend on σR . Lemma 2 follows.
The expressions in the curly brackets are all linear in (σL , σR ). Thus, their maximum
∗
U is convex in (σL , σR ). If σ, in addition to being strictly increasing, is also convex,
U ∗ (σ (qL ) , σ (qR ) , π) is convex in (qL , qR ) and the solution to (2.1) must be an extreme
point of the set of feasible reporting strategies. Lemma 1 rules out the extreme point
(0, 0). This proves Proposition 1.
(σ ,σ )
Recall that, for all π ∈ (0, 1), pπ L R (R | mI ) < π, if and only if σL > σR . Therefore,
Lemma 2 implies that, for a liberal, there exists ε > 0, such that any news report
7
(σL , σR + ε) with σL ≥ σR is as valuable to her as the extremely biased news report
(σL , 0). In particular, we have U ∗ (σ (q) , σ (q) + ε, π) = U ∗ (σ (q) , 0, π). On the other
hand, Lemma 1 and the strict monotonicity of σ imply that, for all reporting strategies
(qL , qR ) other than (q, 0), we have U ∗ (σ (qL ) , σ (qR ) , π) < U ∗ (σ (q) , σ (q) + ε, π). It
follows that the unique optimal news report to a liberal (conservative) is (q, 0) ((0, q)).
3. Isomorphic Representation
As alluded to above, the consumers in the simplified model presented in the Paper
behave identically as a set of consumers with a common prior and heterogeneous utility
functions. In this section, we give a proof of this fact. Formally, we show that for any
γ
β
π 0 , π 00 ∈ (0, 1), there exists a vector (α, β, δ, γ) such that, α, β, δ, γ > 0 and δ+γ
< α+β
,
0
and, if consumer i’s utility function is that given in Table 3.1 and her prior belief is π ,
and consumer j’s utility function and prior belief is given by the vector (α, β, δ, γ, π 00 ),
then, for any (σL , σR ) ∈ [0, 1]2 , we have:
(1) dbi (π 0 ) = dbj (π 00 );
(2) Vi (σL , σR ) = Vj (σL ,σR ); and,
(σL ,σR )
(σL ,σR )
b
b
(3) di pπ0
(R | mI ) = dj pπ00
(R | mI ) .
That is, i and j choose the same action before and after receiving any news report,
and are willing to pay the same amount for any news report.
Table 3.1. Consumer’s Simplified Decision Problem
L
R
l 1 − c −1 − c
r −1 − c 1 − c
a
0
0
Proof. It suffices to show that, we can find (α, β, δ, γ), such that, for any (σL , σR ) ∈
[0, 1]2 :
0
00
i) uπi (d) = uπj (d), for d ∈ {l, r, a};
ii) Vi (σL , σR ) = Vj (σL , σR ); and,
iii) for all d, d0 ∈ {l, r, a},
p
(σL ,σR )
ui π0
(R|mI )
(σ ,σ )
p L R (R|mI )
(d) ≥ ui π0
(d0 )
if and only if
p
(σL ,σR )
uj π00
(R|mI )
(σ ,σ )
p L R (R|mI )
(d) ≥ uj π00
(d0 ) .
By definition, ii) holds if i) holds and Ui∗ (σL , σR , π 0 ) = Uj∗ (σL , σR , π 00 ).
8
Let Σ = σL + σR and ω =
(σL , σR ) ∈ [0, 1]2 :
σR
.
Σ
It is easy to verify that, for all π ∈ (0, 1) and all
U ∗ (σL , σR , π) = max{(1 − ω) [uπ (l) + (γ + β) πΣ] + ωuπ (l) ,
(1 − ω) uπ (r) + ω [uπ (r) + (α + δ) (1 − π) Σ] ,
(1 − ω) [γπΣ] + ω [α (1 − π) Σ]}.
It follows that both i) and Ui∗ (σL , σR , π 0 ) = Uj∗ (σL , σR , π 00 ) hold if:


[(1 − π 00 ) α − π 00 β + (γ + β) π 00 Σ] = [1 − 2π 0 − c + 2π 0 Σ]





[(1 − π 00 ) α − π 00 β] = [1 − 2π 0 − c]




[− (1 − π 00 ) δ + π 00 γ] = [2π 0 − 1 − c]


[− (1 − π 00 ) δ + π 00 γ + (α + δ) (1 − π 00 ) Σ] = [2π 0 − 1 − c + 2 (1 − π 0 ) Σ]





[γπ 00 Σ] = [(1 − c) π 0 Σ]




[α (1 − π 00 ) Σ] = [(1 − c) (1 − π 0 ) Σ]
.
Thus, there exists (α, β, δ, γ) such that both i) and ii) hold if the system of linear
equations above has a solution.
1−π 0
π0
1−π 0
π0
It is easy to verify that (α, β, δ, γ) = (1 − c) 1−π
00 , (1 + c) π 00 , (1 + c) 1−π 00 , (1 − c) π 00
is a solution to the system. It is, in fact, the unique solution.
Note that, when the system of equations hold, we also have:
p
(σL ,σR )
ui π0
=
(R|mI )
(σ ,σ )
pπ00L R (R|mI )
uj
(σ ,σ )
p L R (R|mI )
(d) − ui π0
(d) −
(σ ,σ )
pπ00L R (R|mI )
uj
(d0 )
(d0 )
for all d, d0 ∈ {l, r, a}. Thus, iii) is also satisfied.
4. Political Polarization and The Merits of Fairness
4.1. Political Polarization. Two consumers with very similar utility functions and
prior beliefs may prefer their news consumption to contain opposite biases.5 On the
other hand, having received news reports with opposite biases, the posterior beliefs of
two almost identical consumers may end up being quite far apart. Thus, media bias
can cause political polarization, which is defined behaviorally as consumers choosing
more extreme actions in opposite directions.
2c
, and
By way of an example, consider a duopolists’ game with σ (x) ≡ x, q > 1+c
∗
κ ∈ (κ2 , κ). Thus, the consumers consume at most one news report and the two media
5The
set of utility maximizing news reports is upper-hemicontinuous but not lower-hemicontinuous in
the consumer’s utility function and prior belief.
9
outlets offer news reports (q, 0) and (0, q) in equilibrium. Moreover, all consumers
with π < 12 strictly prefer (q, 0) to (0, q), and the opposite is true for consumers with
1
π>
. Therefore, among
2
all moderate consumers, those with prior belief defined by
1−c
, min{ 1−c−κ
, 1}
2
2(1−q) 2
π ∈
choose to consume news report (q, 0), whereas those with
1+c
1−c−κ 1
π ∈ max{1 − 2(1−q) , 2 }, 2 choose to consume news report (0, q).
In the event that both media outlets report inconclusive evidence mI , which occurs with probability 1 − q, all consumers who consume the news report (q, 0) up(q,0)
dates their belief to pπ (R | mI ), and those who consume the report (0, q) updates
(0,q)
(q,0)
2c
their belief to pπ (R | mI ). Because q > 1+c
, we have pπ (R | mI ) < 1−c
for all
2
(0,q)
π < 21 and pπ (R | mI ) > 1+c
for all π > 12 . Therefore, upon learning inconclu2
sive evidence
presented by
their respective media outlets of choice, all moderates with
1−c−κ 1
1−c
, min{ 2(1−q) , 2 } will end up choosing action l, whereas all moderates with
π ∈
2
1
1+c
π ∈ max{1 − 1−c−κ
,
},
will end up choosing action r. As such, media bias leads
2(1−q) 2
2
to political polarization.6
The extent of political polarization depends on the level of news consumption costs
and the degree of competition. In our example, when κ is close to κ, polarization is not
severe, since very few consumers consume any news. As κ ∈ (κ∗2 , κ) falls, more moderates choose to consume the extremely biased news reports and polarization becomes
more severe. However, as κ continues to fall, some moderates find it worthwhile to
consume both (q, 0) and (0, q), which gives them a perfectly balanced news consumption bundle. When presented with inconclusive evidence mI , these consumers do not
change their action. Thus, polarization is mitigated. If κ falls below κ
b , both media
2
q q
outlets choose to produce the perfectly balanced news report 2 , 2 in equilibrium.
Consequently, political polarization is eliminated completely.
On the other hand, even with κ ∈ (0, κ
b2 ), as competition intensifies, the media
outlets eventually choose to produce extremely biased news again. Thus, polarization
can be exacerbated by increase in competition. However, with more media outlets
acquiring information, the chances that conclusive evidence is produced improves, and
so does consumer surplus.
4.1.1. Political Polarization and Social Inefficiency. There are many reasons why political polarization can be socially undesirable. Here, we give an example where externalities associated with consumers’ choices make polarization socially inefficient.
6Note
that, the same messages (mL , mI , mR ) convey different information when they are sent by
different signals (news reports). Therefore, although both denoted by mI , the pieces of inconclusive
evidence presented by the two news reports (q, 0) and (0, q) are not the same.
10
Suppose that, in addition to costing c to the consumers, the partisan actions l and
r also impose an externality on the society, which makes the social cost of these actions equal to c0 > c. Consider the previous example in which news reports (q, 0)
1−c−κ 1
and (0, q) are offered and are consumed by consumers with π ∈ 1−c
,
min{
,
}
2
2(1−q) 2
1−c−κ 1
1+c
respectively. Suppose that the exterand those with π ∈ max{1 − 2(1−q) , 2 }, 2
0
(q,0)
1−c
1−c
nalities
that 2 < pπ (R | mI ) < 2 for some consumer with
are significant so
, min{ 1−c−κ
, 1 } . Thus, if consumer π takes into account the costs her action
π ∈ 1−c
2
2(1−q) 2
imposes on the society, she would not change her action after learning mI . However, in
the absence of any means to ensure that the consumer internalizes all the social costs,
she ends up choosing l, and social welfare is brought down.
4.1.2. Mitigating Political Polarization. Now suppose the government imposes a fairness standard characterized by b ∈ [0, 12 ). When κ is sufficiently high, the media outlets
R
− 12 |≤ b,
choose to produce the most biased news reports (qL , qR ) that satisfy | qLq+q
R
that is, 12 + b q, 12 − b q and 21 − b q, 12 + b q . Consider the consumer in the
0
(q,0)
1−c
, min{ 1−c−κ
, 1 } and 1−c
< pπ (R | mI ) < 1−c
. Re2
2(1−q) 2
2
2
(q ,q )
R
. Therefore, for
call that, fixing qL + qR , pπ L R (R | mI ) is strictly increasing in qLq+q
R
1
1
(( +b)q,( 2 −b)q)
b sufficiently small, we must have pπ 2
(R | mI ) > 1−c
. Thus, this consumer
2
previous example with π ∈
no longer chooses l after learning mI from her media source.
As such, government imposed fairness standards can mitigate political polarization.
Indeed, when b = 0, polarization can be completely eliminated. However, this comes
at a cost of lost consumer surplus. Moreover, as we show in the Paper, when b > 0,
government imposed fairness standards can cause some consumers to consume overall
more biased news bundles.
References
Blackwell, David, “Comparison of Experiments,” in “Proceedings of the Second
Berkeley Symposium on Mathematical Statistics and Probability,” University of California Press, 1951, pp. 93–102.
Calvert, Randall L., “The Value of Biased Information: A Rational Choice Model
of Political Advice,” Journal of Politics, 1985, 47, 530–55.
Fairleigh Dickinson University’s Public Mind Poll, “Some News Leaves People
Knowing Less,” Technical Report, Fairleigh Dickinson University 2011.
, “What You Know Depends on What You Watch: Current Events Knowledge
Across Popular News Sources,” Technical Report, Fairleigh Dickinson University
2012.
11
Gentzkow, Matthew A. and Jesse M. Shapiro, “Media, Education and AntiAmericanism in the Muslim World,” Journal of Economic Perspectives, 2004, 18
(3), 117–133.
Radner, Roy and Joseph E. Stiglitz, “A Nonconcavity in the Value of Information,” in Marcel Boyer and Richard E. Kihlstrom, eds., Bayesian Models of Economic
Theory, Amsterdam: Elsevier, 1984.
Suen, Wing, “The Self-Perpetuation of Biased Beliefs,” The Economic Journal, April
2004, 114, 377–396.
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