Media Location and Political Influence∗ Ramon Xifré-Oliva† October 2007

Abstract An incumbent , whose type is not known with certainty, is running for an election. The incumbent knows his type but voters and a media outlet do not. Voters are heterogenous ex-ante; they differ in their prior assessment of the incumbent’s type. The media outlet observes a verifiable signal about the incumbent’s type and decides which message to send and the segment of voters whom to send it. The outlet’s profits are increasing in the change its message causes on voters’ assesment of the incumbent’s type. Before informing voters, the incumbent makes an offer to the outlet proposing a message and a segment of voters to inform in exchange for a monetary transfer. In absence of political influence, we show the outlet has a tendency to inform those extremist voters more reluctant with the message. This aligns outlet’s and incumbent’s interest partially in equilibrium. If the outlet’s quality of information is not good enough, it may accept incumbent’s offer to conceal adverse signals in equilibrium. Keywords: media outlet, politics, location, polarization. JEL classification numbers: D72, D82.

∗

I wish to thank Marco Celentani for continued suggestions and insights. I also wish to thank Luis Corchón, Riccardo Martina, Andreu Mas-Colell, Marc Möller, Sven Rady, Pablo Ruiz-Verdú and Klaus M. Schmidt for comments on previous drafts. I also thankfully acknowledge financial support from the Spanish MCYT through project SEJ2006-09993/ECON, European Commision’s Marie Curie Fellowship Programme under contract HPMT-CT-2000-00184 and the Barcelona Economics Program of CREA. The usual disclaimer applies. † Escola Superior de Comerç Internacional (ESCI) - Universitat Pompeu Fabra. Pg. Pujades, 1. 08003 Barcelona (Spain). [email protected]

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1

Introduction

The importance of a free, independent press for the proper functioning of democratic governments and institutions is vital. Media play a unique role in transmitting information to mass audiences and they supply most of the information people use when voting (Bartels, 1993; Delli Carpini and Keeter, 1996; and Popkin, 1994). The collusion between government and media, however, can undermine this crucial role (Freedom House, 2001). In this paper we explore the link between media’ and government’s interests. A requisite for elections to genuinely play their role is that voters are properly informed about the nature and consequences of all alternatives or candidates. The information needed to vote correctly is usually costly to acquire and for this reason many voters delegate on media outlets the function of acquiring and processing information. Most media, in turn, have a more or less defined political standpoint and do not report objective information only but also subjective opinion and target specific groups or certain ideological positions. This paper also tries to explain how a profit-driven outlet, who is exogenously restricted to inform only a segment of voters, chooses a ‘location’ for its message in the electorate. A basic ingredient of our model is that voters are heterogenous. There is an incumbent running for an election against a challenger. The incumbent’s ability to make successful public policy decisions is not known with certainty by voters, and it can be larger or smaller than the challenger’s; i.e., incumbent’s type can be good or bad. Voters are distributed in the 0-1 line and have different ex-ante assessments of the incumbent’s type. We assume that priors in the electorate favour the incumbent so if no additional information were available the incumbent would be reelected. We characterize the electorate by the polarization of their prior opinion, that is, how certain are extremists (incumbent’s supporters and detractors) that their beliefs about the incumbent’s type are true ex-ante. Before voting, a media outlet observes a verifiable signal about the incumbent’s type and then sends a message to a segment of voters. The incumbent also observes the signal. With respect to the content of the message we assume the outlet cannot fabricate signals and send them as messages: it can only conceal information or reveal it truthfully to voters. Concerning the segment of voters, we assume that it is optimal for the outlet not to inform the entire electorate but rather just a segment of a given, exogenous size. Before 2

informing voters, the incumbent makes an offer to the outlet consisting of a message, a segment of voters and monetary transfer. The incumbent commits to pay the transfer to the outlet if the latter sends the proposed message to the proposed segment of voters. Finally, the outlet decides whether to accept or reject the incumbent’s offer and sends a message to a segment of voters. The outlet is characterized by the quality, or accuracy, of its information, i.e., how able it is to obtain correct information about the incumbent’s type. Both the polarization in the electorate and the quality of outlet’s information are publicly observable. We make a critical assumption on the outlet’s profits. We assume that the outlet’s profits are increasing in the change its message causes in voters’ assessment of the incumbent. The idea behind this assumption is that sending more ‘shocking’ or relevant information to voters creates larger value for the outlet. This is related to some recent theories of communication (Dewatripont and Tirole, 2004) that consider that the quality of communication is increasing in the sender’ persuasion and the receiver’s absorption efforts. In our context, the application of this theory (for the particular case of strategic complementarity between both efforts), would suggest that voters, when confronted with new evidence that may lead them to sharply change their assessment of the incumbent — and possibly their vote —, intensify their absorption effort which, in turn, renders the outlet’s persuasion efforts more productive and profitable. Our main result is that the outlet’s message is more influential when addressed to extremist voters reluctant to accept it. Thus the outlet raises more profits when it sends an adverse message about the incumbent to its supporters, and a favourable one to its detractors. Beyond that, the outlet’s tendency to inform extreme positions is reinforced when the quality of its own information is high and the polarization in the electorate is low, i.e., when the outlet is relatively more persuasive. To understand that notice that, because voter’s beliefs about the incumbent are updated with the Bayes’ rule, the marginal change of opinion due to a message against the priors is larger in extreme locations than in more central ones. This suggests that the outlet tends to inform relatively undecided voters when the quality of its information is low or the initial polarization in the electorate is high. In terms of the relationship between the incumbent’s and the outlet’s interests we

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find that they are partially aligned in equilibrium. This means that the outlet’s optimal choice of message and location favour the incumbent’s reelection interests and, therefore, the latter needs not to make any offer to the former. We also study the conditions under which the incumbent buys the outlet’s silence in equilibrium. We find that the outlet is more likely to conceal information in equilibrium when the incumbent’s rents of holding office are larger and the outlet’s information quality, lower. Models of media firms date back, at least, to Steiner (1952) and have been mainly circumscribed in the industrial organization literature, e.g. Spence and Owen (1977) and Anderson and Coate (2000). There is now an emerging literature that specifically studies the interaction between media and public policy, including Besley and Burgess (2001), Strömberg (2001 and 2004), Larcinese (2002 and 2003), Chan and Suen (2004), Prat (2004) and Besley and Prat (2004). Some of them (Strömberg 2001, Larcinese 2002 and 2003) focus mainly on the implications of media activity on redistribution. Others (Chan and Suen, 2004, Strömberg 2004 and Besley and Prat 2004) concentrate attention on the information transmission process between media and voters and the implications in the political arena. This paper belongs to this second category. Chan and Suen (2004) model information transmission between media and voters in a Downsian model. In their model, voters actively acquire information about the party policies and media are ideologically biased. They find that voters are more likely to vote for a party when it receives positive media coverage and, as a result, parties adopt more centrist policies in order to compete for positive media coverage. In our model, voters’ only role is to vote and it is the outlet who decides to conceal or transmit information; and, in the second case, also whom to send it. Strömberg (2004) studies the incentives of the media to deliver news to different groups in a model that combines mass media competition and political competition. He makes voters’ information endogenous with respect to other models of political competition, like Lindbeck and Weibull (1987), Grossman and Helpman (1996) or Baron (1994), who assumed voters were exogenously informed. One of the main features of Strömberg (2004)’s model is that mass media operate under increasing-returns-to scale. This induces profit motivated media to provide more news to large groups. Our modelling of the outlet’s technology is simpler as we take the length of the optimal segment of informed voters

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to be exogenous. We focus rather in the outlet’s location decision as a function of the quality of its information. Our theoretical model of information transmission between the outlet and voters is related to Besley and Prat (2004). They also assume that the political incumbent has the technology to ‘buy the silence’ of media and show the actual freedom of press is endogenous in equilibrium. In contrast to our paper, however, they build a model in which all voters (and outlets) are identical. Because of this, they find two extreme equilibria of the media market: either the media industry is free or completely captured. We focus rather on the ‘spontaneous’ alignment of interests between the outlet and the incumbent in a setup where the electorate is heterogenous.

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The model

There is an incumbent running for an election whose type (ω) can be good (G) or bad (B). A bad incumbent yields −1 to all voters, and a good one, 1. The incumbent knows his type, but voters and a media outlet do not. There is a challenger that yields 0 in expected terms to all voters. Voters vote for one or the other (there is no abstention) and in case of indifference we assume voters prefer, on the basis of previous performance, the incumbent. The voting rule is by majority. Voters differ ex ante in their assessment of the incumbent’s type. They are uniformly distributed in the 0-1 segment and characterized by their location x ∈ [0, 1] which we relate to their prior estimate that the incumbent’s type is good. In particular, we will assume that voters located at x believe a priori that Pr(ω = G)x = g(x) and therefore Pr(ω = B)x = 1 − g(x). Without loss of generality, assume that voters can be ordered so that g(x) is a decreasing function; voters at x = 0 are optimistic about the incumbent’s type and voters at x = 1 are pessimistic. Although all voters have the same (contingent) preferences over the incumbent, for lighter wording we may refer to optimistic voters as incumbent’s ‘supporters’ and to pessimistic ones as ‘detractors’. Assumption 1 g(x) is linear and symmetric around 1/2 The role of this assumption is help to get a closed-form solution for the equilibrium location. Linearity is dispensable without altering the main results of the paper on

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outlet’s location. Symmetry is a more delicate issue. Small asymmetries that favour the incumbent may not change our basic results. In general, to the extent that g(x) is not symmetric, the outlet’s equilibrium location may change, most likely tending to exacerbate the extremism we find in the paper. However, to properly deal with such a generalized model, the challenger’s role would need to be reconsidered, specially if the asymmetry plays in his favour. For a voter located at x we denote his expected value of voting for the incumbent by I(x) = g(x) − (1 − g(x)) = 2g(x) − 1. We normalize the function g(x) in such a way that I(0) = p, I(1/2) = 0 and I(1) = −p, where we take p ∈ (0, 1) to be a measure of the initial polarization of opinion, or confidence in the prior information, in the electorate. That is, when p is large, the incumbent’s supporters (detractors) are more satisfied (regretful) with his election. As a result of the normalization we have that, for any exogenous p, g(x) = 1/2 + p (1/2 − x) ∈ [(1 − p)/2, (1 + p)/2]. Voters located at x vote according to I(x); they vote for the incumbent if I(x) ≥ 0 and for the challenger if I(x) < 0. By construction of the model, the incumbent would be reelected if there were no additional information because his supporters are located in [0, 1/2]. As noted before, allowing g(x) not to be symmetric so that I(x′ ) = 0 for x′ > 1/2, would also preserve this status quo and would not change our results significantly. Before voting there is new information available about the incumbent which may be relevant or not for the election. Voters lack direct access to this information and they must rely on a media outlet. The outlet receives a signal s ∈ {G, B, ∅} about ω. With probability ε the signal is void, s = ∅, and we assume that both types of incumbent are equally likely to produce void signals. As a result, a void signal is not informative for voters to infer incumbent’s type and, therefore, useless. In case of receiving new, relevant information, this could go in favour, s = G, or against, s = B, the incumbent. More specifically, we assume that

Pr(s = G|ω = G) = Pr(s = B|ω = B) = (1 − ε)µ, Pr(s = B|ω = G) = Pr(s = G|ω = B) = (1 − ε)(1 − µ), Pr(s = ∅|ω = G) = Pr(s = ∅|ω = B) = ε, where µ ∈ (1/2, 1) and ε ∈ (0, 1) are exogenous and common knowledge. Our results hold 6

for any value of ε. The parameter µ captures the quality of the outlet’s information and it is restricted to be larger than 1/2 only for tractability reasons. A larger µ corresponds to a situation in which the outlet receives the right signal more often. The outlet, after receiving s, informs voters by sending a message m. To rule out delicate signalling considerations, we assume that the incumbent also observes the signal s and that the outlet can send verifiable messages only. This means that the outlet, upon receiving an informative signal s ∈ {G, B}, has only two choices for the message: send it, m = s, or send no information, which we denote by m = ∅. If the outlet receives the void signal, its only possibility is to send it, m = ∅. The outlet does not only choose which message to send but also whom to send it, i.e., which voters to inform. For a given, exogenous length L ∈ (0, 1), the outlet chooses a center point c in the electorate and informs voters located in the segment [c − L/2, c + L/2]. It is important to clarify that voters in the segment have different priors on the incumbent’s type but all receive the same message from the outlet. Assumption 2 L = 1/2. The length of the segment may be interpreted as the result of the outlet’s (unmodelled) trade-off between costs and revenues from informing a large number of voters, both likely to be increasing in the size of the audience. The size of L is not critical to obtain our results but there are two important restrictions implicit in this assumption that are indeed necessary. First, the outlet cannot split the interval; the rationale for this is that it is surely more affordable for the outlet to cover the same number of voters in case voters’ views are relatively similar among themselves than rather in case they are disperse. Second, the size of the interval does not depend on its location; this restriction seems neutral as modelling otherwise would imply some type of outlet’s ideological bias. The incumbent, who has observed signal s, makes a take-it-or-leave-it offer to the outlet before informing the voters. The incumbent indicates a message mb and a center point cb and commits to pay t to the outlet if it sends message mb to voters centered around cb . We assume the incumbent has full commitment power and exclude renegotiation. Let R denote the incumbent’s revenues from holding office and we assume that he has no external opportunities.

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With respect to the outlet’s profits, we adopt the principle that more ‘shocking’ information leads to higher profits. One rationale for this is that voters are more inclined to incur the cost of absorbing and buying information if it is relevant enough for them. Voters at x, after receiving outlet’s message m, update the probability that the incumbent is good and, as a result, the expected value of voting for him. Eventually, for some locations the orientation of the vote (i.e., the sign of I(x)) may change after the outlet sends the message. We assume that the outlet’s profits of informing position x correspond to the change in voters’ expectations over the incumbent due his message m, π(x, m) = |I(x) − I(x|m)| . We write the absolute value of the difference between I(x|m) and I(x) because in case of a good message we have I(x|G) > I(x) and in case of a bad message we have I(x|B) < I(x). If we adopt this specific assumption on the profit function we can solve the model explicitly, but any other specification increasing in the distance |Pr(G) − Pr(G|m)| would preserve our qualitative results. The time structure can be summarized as follows. t = 1 The incumbent’s type ω is realized and learned privately by him. The outlet and the incumbent observe signal s about ω. t = 2 The incumbent makes an offer (t, mb , cb ) to the outlet t = 3 The outlet decides whether to accept or reject the offer (t, mb , cb ) and then sends message m centered at c. t = 4 Voters observe the message and vote. In the next section we study the outlet’s optimal communication decisions supposing the incumbent is passive, i.e., is not making any offer. In section 4 we use these results to solve for the equilibrium of the entire game that incorporates the incumbent’s intervention and analyze the alignment of both parties’ interests.

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Optimal location

In this section we study the outlet’s optimal choices of message and location that maximize its profits for each signal it mat receive, supposing that the incumbent makes no offers. 8

The analysis is easy in case the outlet receives the void signal. It has no information to publish and voters will not change their estimate of the incumbent’s type; therefore, the outlet makes no profits regardless of any location it may choose for the message. Because the outlet can only publish verifiable messages, it has only two options upon receiving an informative message: to send it or to conceal it. It is easy to see that, in absence of political influence, the outlet will never opt for concealing information as that would imply no audience and no profits. Suppose the outlet receives the good signal, then it will send the good message and it has to decide which segment of voters to inform. Voters at any location x ∈ [0, 1] will improve their assessment of the incumbent’s type after receiving the good message. That is, for any location x, because Pr(ω = G|m = G) > Pr(ω = G), the posterior expected value of voting for the incumbent I(x|G) is larger than the prior one I(x). Indeed, there is a set of locations for which I(x) was negative before receiving the message and were voting for the challenger that now have a I(x|G) positive and will vote for the incumbent. Figure 1 represents I(x), I(x|G) and I(x|B). Notice that the votes for the incumbent correspond the locations for which the function is positive. The question for the outlet is which voters would be mostly responsive to the good message about the incumbent. Given voters differ ex-ante in their assessment of the incumbent’s type and the continuity of our setup, there will be an optimal segment of voters to inform that will depend on the parameters of the model: the degree of polarization p and the quality of outlet’s information µ. This is the segment for which posterior and prior voters’ expectations over the incumbent’s value will differ more from each other. The outlet looks for the optimal location c around which it will send message m solving the following problem
c+L/2
π(x, m)dx ⇔ max max c

c−L/2

c

c+1/4

|I(x|m) − I(x)| dx.

c−1/4

The following proposition characterizes the solution to this problem. Proposition 1 For a given p and µ, define  2 − p2 + 4µ(1 − µ)(4 − p2 ) ∗ d (p, µ) = 4p(2µ − 1) and consider only informative signals. 9

1. If the outlet sends m = G, then (a) if µ ≥ 1/2(1 + p), then the outlet informs voters in [1/2, 1], (b) otherwise the outlet informs voters centered at 1/2 + d∗ (p, µ). 2. If the outlet sends m = B, then (a) if µ ≥ 1/2(1 + p), then the outlet informs voters in [0, 1/2], (b) otherwise, the outlet informs voters centered at 1/2 − d∗ (p, µ). 3. Let E ≡ {(p, µ) : µ < 1/2(1 + p)}. We have ∂d∗ (p, µ)/∂p < 0 and ∂d∗ (p, µ)/∂µ > 0 for any (p, µ) ∈ E. The optimal location of the outlet’s message follows two principles. First, the outlet’s message is more influential when addressed to extremist voters reluctant to accept it. Second, this tendency to extremism is weakened when the accuracy of outlet’s information is low and polarization in electorate is high. The reason why the outlet makes more profits sending the bad message to the incumbent’s supporters and the good one to his detractors is that voters update incumbent’s type through the Bayes’ rule and this is a non-linear transformation. By assumption, the incumbent’s prior expected value I(x) is a linear function. The application of the Bayes’ rule transforms voters’ expectation on the incumbent’s value after a good message I(x|G) in a concave function and voters’ expectation after a bad message I(x|B) in a convex function. This is illustrated in Figure 1. Thus the outlet’s profit π(x, m) = |I(x) − I(x|m)| is a concave function independently of the message it sends, m ∈ {G, B}, as it is illustrated in Figure 2. At this is point it is worth clarifying that this result is preserved if g(x) is not linear; the result is driven by the fact that the Bayes’ rule increases the curvature of the I(x|m) function. Further, as Figure 2 illustrates, the function π(x, m) is not symmetric around x = 1/2. The appendix shows that π(1, G) = π(0, B) > π(0, G) = π(1, B). Indeed, if one defines  1 − 2 µ(1 − µ) δ(µ, p) = > 0, 2p (2µ − 1) the outlet maximizes π(x, G) when informing an incumbent’s detractor located at 1/2 + δ(µ, p) and maximizes π(x, B) when informing an incumbent’s supporter located at 1/2 − 10

δ(µ, p) as it appears in Figure 2. The formula for d∗ (p, µ) differs from δ(µ, p) because the former maximizes profits pointwise while the latter for an interval of length 1/2 centered at 1/2 + d∗ (p, µ). Concerning the dependence of the distance d∗ (p, µ) on the parameters it is important to notice that the properties hold only inside the set E, i.e., when the outlet’s accuracy is small relative to the polarization. In particular, values of p and µ inside E ensure that d∗ (p, µ) ∈ [0, 1/4]. Notice that d∗ (p, µ) is a measure of the outlet’s extremism; when d∗ (p, µ) is small the outlet’s locates its message close to the center of the electorate; and when d∗ (p, µ) attains its maximum value of 1/4 the outlet informs the a priori supporters (or detractors) only. Under the restriction that (p, µ) ∈ E, we find that the outlet’s extremist tendency decreases with the polarization in the electorate and increases with the quality of his information. Both effects share a common intuition that has to do with the outlet’s relative persuasion power. Outlet’s persuasion chances depend negatively on the degree of confidence voters’ have about their own prior views (approximated by polarization) and positively on its (commonly known) ability to get the right information. As it becomes harder for the outlet to persuade electorate, either because extreme voters are more severely entrenched or because its information is not good enough, it is rational not to target ‘difficult’, extreme locations of voters but rather focus on more ‘affordable’ positions where voters’s changes of view are less important but more likely to happen.

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Political Influence

We now turn to study the interaction between the outlet’s location decision and the incumbent’s interest for reelection. By construction of the model, the incumbent would be reelected if no additional information were supplied to voters. This section shows that the incumbent’s interests for reelection and the outlet’s tendency to maximize profits are partially aligned. Proposition 2 In equilibrium, 1. If s ∈ {G, ∅}, the incumbent makes no offer and wins the election. 2. If s = B, there exists a value µ∗ (p, R) such that,

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(a) if µ ≤ µ∗ (p, R), the incumbent makes the offer mb = ∅ for any cb and t < R which is accepted by the outlet, and the incumbent wins the election; (b) if µ > µ∗ (p, R), the incumbent makes no offer and loses the election. For two out of the three possible signals there is no need for the incumbent to make an offer. If the outlet receives the void signal, it has no information to publish and therefore voters will remain with their priors which favour the incumbent. If the outlet receives the good signal it maximizes profits, as we have seen in the previous section, sending it to incumbent’s detractors because it is more informative for them rather than for the supporters. This, in turn, serves the incumbent’s interests as there is a change of opinion in a segment of the electorate which had adverse priors towards him. In other words, there is no need for the incumbent to make any offer to the outlet because outlet’s optimal location ensures his reelection. In these two cases, both parties are perfectly aligned. Note that we do not need g(x) to be symmetric around 1/2 for these two results to hold. They hold in general if priors are sufficiently favourable to the incumbent, i.e., if g(x) is symmetric around any x larger than 1/2. When there is a bad signal, both parties’ interests are not aligned any more because the outlet’s tendency is to inform incumbent’s supporters of the bad signal would make the incumbent lose the election. Figure 1 shows that in case m = B there is a majority of voters for which I(x|B) is negative. Given the outlet cannot fabricate a good signal, the incumbent can only ‘buy the silence’ and offer a transfer t to the outlet in exchange for concealing information in equilibrium and sending message mb = ∅ at any location. The incumbent therefore has to compensate the outlet for concealing information. Cases (a) and (b) of the second part of the above proposition refer to the cases in which this compensation is affordable or not for the incumbent, respectively. Recall that R denotes the incumbent’s rents from holding office. On the other hand, it is easy to see (and proven in the appendix) that the outlet’s revenues from sending an informative signal are increasing in the quality of its information, µ. For this reason, given p and R, there is a critical value µ∗ (p, R) such that if the outlet has a µ > µ∗ (p, R) its revenues from informing incumbent’s supporters exceed the latter’s rents from holding office. In this case, case (b), the minimum offer the outlet would accept to conceal information is larger than the maximum one affordable by the incumbent. The outlet 12

accepts no offer in equilibrium and: voters get the actual, bad signal; the majority changes in favour of the challenger; and the incumbent loses the election. Notice that this happens when the quality of outlet’s information is sufficiently high and suggests that ‘reliable’ media, because they lose more when concealing information, are harder to influence by the political environment. Conversely, in case (a), if the outlet receives the bad signal and the quality of his information is not good enough, the incumbent offers a transfer t < R, the outlet accepts it and conceals information in equilibrium. As a result, voters are deprived from relevant political information and they reelect the incumbent when the challenger is their optimal candidate. As the threshold µ∗ (p, R) is increasing in R, the political distortion of information is more likely to happen, ceteris paribus, when the rents of holding office are large and the outlet’s information quality is low. As a final comment, notice that a rough, simple measure of the coincidence of both parties’ interests is the probability that the incumbent needs not to offer a transfer in equilibrium. In our simple setup, this is equivalent to the probability that the observed signal about the incumbent is the bad one or the void one (part 1 of the proposition). This probability can easily computed as Pr(s ∈ {∅, B}) =

(1 − ε)µ (1 − ε)(1 − µ) 1 ε + +ε= + 2 2 2 2

which is increasing in ε. Therefore, it is more likely that both parties’ interests are aligned if the outlet’s probability of receiving irrelevant signals is high. This result is related to the intuition that the incumbent is more comfortable with the media in case the noise (useless information) is more pervasive.

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Conclusion

In this paper we study how a media outlet, who may have relevant, verifiable evidence about the unknown type of a political incumbent, decides which voters to inform. Voters are heterogenous and, in particular, they differ ex-ante in their assessment of the incumbent’s type. We also investigate to which extent the outlet’s interest of maximizing profits and the incumbent’s interest of being reelected are aligned in equilibrium. Our results are based on a crucial assumption about the outlet’s profits: the outlet makes

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more profits when it provokes a more intense change in voters’ expectations on the incumbent. The model takes two parameters as primitives: the prior degree of polarization of opinion in the electorate (how certain voters are of their respective intention for voting ex-ante) and the quality of outlet’s information (how accurate is its evidence about the incumbent). For the sake of simplicity we only allow the outlet, after receiving relevant political information, to send it or conceal it and we rule out the possibility that it fabricates unobserved signals. We find that the outlet, in absence of political pressure, never conceals information and prefers to inform those voters which are sceptic with respect to the observed signal: the incumbent’s supporters when the evidence is adverse, and his detractors, when favourable. If the quality of information is sufficiently high and the polarization sufficiently low, this tendency is exaggerated and the outlet informs sceptic, extremist voters only. The model thus suggests that high quality of information may give the outlet certain incentives to abandon the ‘opinion center’. Or alternatively, holding information quality fixed, we find that extremism in the electorate and in the outlet’s message play against each other: when the outlet perceives a more polarized electorate opts for targeting centrist voters and viceversa. In terms of alignment of journalistic and political interests, this paper predicts that ‘spontaneous’ alignment is more likely to happen in setups where the outlet receives politically irrelevant information more often. Concerning the incumbent’s active pressure on the outlet to conceal adverse evidence, we find this is bounded up by the quality of the outlet’s information. That is, it is more difficult for the incumbent to buy the outlet’s silence when the latter’s information is more reliable, and thus, more profitable to publish. Further work includes developments in two directions. First, the reconsideration of the assumptions on the voters’ priors and the exploration of certain generalizations of the outlet’s profit function. Second, the study of a richer strategic setup allowing both for a second outlet and the challenger to play also a role. In this respect, the present paper is a preparation for the full analysis of the interaction between political and media competition.

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[13] Popkin, S. (1994). The Reasoning Voter: Communication and Persuasion in Presidential Campaigns. Chicago: Chicago University Press. [14] Prat, A. (2004). Rational Voters and Political Advertising. mimeo. [15] Spence, M. and B. Owen (1977). Television Programming, Monopolistic Competition and Welfare. Quarterly Journal of Economics, 91, 103-126. [16] Steiner, P. O. (1952). Program Patterns and Preferences, and the Workability of Competition in Radio Broadcasting. Quarterly Journal of Economics, 66, 194-223. [17] Strömberg, D. (2001). Mass Media and Public Policy, European Economic Review, 45. [18] Strömberg, D. (2004). Mass Media Competition, Political Competition, and Public Policy, Review of Economic Studies, 71.1, 265-284.

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6

Appendix - Proofs

Proof of Proposition 1 Consider first the case of m = G. Start by noting that from the Bayes’ rule if voters at x receive m = G they believe that µg(x) and µg(x) + (1 − µ)(1 − g(x)) (1 − µ)(1 − g(x)) Pr(ω = B|m = G) = . µg(x) + (1 − µ)(1 − g(x)) Pr(ω = G|m = G) =

Therefore the posterior expected value of the incumbent for voters at x is I(x|G) =

µg(x) − (1 − µ)(1 − g(x)) g(x) + µ − 1 = µg(x) + (1 − µ)(1 − g(x)) g(x)(2µ − 1) − µ + 1

which, if one substitutes g(x) by the expression 1/2 + p (1/2 − x), it can be rewritten as

I(x|G) =

2px − p − 2µ + 1 . (4µ − 2) px + p(1 − 2µ) − 1

The case of the bad signal is analogous and we find that

(1 − µ)g(x) and (1 − µ)g(x) + µ(1 − g(x)) µ(1 − g(x)) Pr(ω = B|m = B) = , (1 − µ)g(x) + µ(1 − g(x))

Pr(ω = G|m = B) =

and, similarly, after m = B the posterior expected value of the incumbent for voters at x is I(x|B) = =

(1 − µ)g(x) − µ(1 − g(x)) g(x) − µ = (1 − µ)g(x) + µ(1 − g(x)) g(x)(1 − 2µ) + µ 2px − p − 1 + 2µ . (2 − 4µ) px − p(1 − 2µ) − 1

Recall that the prior expected value of the incumbent is I(x) = Pr(ω = G) − Pr(ω = B) = p(1 − 2x) and it is easy to check that I(x|G) ≥ I(x) ≥ I(x|B), for any x. It can be checked, as noted in the text, that 17

(2µ − 1)(1 − p2 ) > (2µ − 1) p + 1 (2µ − 1)(p2 − 1) π(0, G) = π(1, B) = . (2µ − 1) p − 1 π(1, G) = π(0, B) =

Now, to solve max c




c+ 14

c− 14

|I(x|m) − I(x)| dx

for m = G, B, we denote the indefinite integral of the first term by
α(x) = I(x|m)dx   µ(1 − µ) ln ((2x − 1) p(2µ − 1) − 1) 1 x+2 = 2µ − 1 p (2µ − 1) and the indefinite integral of the second term is β(x) = px (1 − x) . Then, for the case of m = G, define γ(c) = α(c + 1/4) + β(c − 1/4) − (α(c − 1/4) + β(c + 1/4)). We solve ∂γ(x)/∂c = 0 and keep the relevant root, which is  1 2 − p2 + µ(1 − µ)(16 − 4p2 ) 1 c= + = + d∗ (p, µ). 2 4p(2µ − 1) 2 For the case of m = B, define γ(c) = α(c − 1/4) + β(c + 1/4) − (α(c + 1/4) + β(c − 1/4)), solve ∂γ(x)/∂c = 0 and keep the relevant root,  1 1 2 − p2 + 4µ(1 − µ)(4 − p2 ) c= − = − d∗ (p, µ). 2 4p(2µ − 1) 2 With respect to the derivatives, we find that  8µ(1 − µ) − p2 + 4µ(1 − µ)(4 − p2 ) ∂d∗  = ∂p 2 p2 + 4µ(1 − µ)(4 − p2 )p2 (2µ − 1)  2 − p2 + 4µ(1 − µ)(4 − p2 ) ∂d∗ =  ∂µ p2 + 4µ(1 − µ)(4 − p2 )p (2µ − 1)2

Now, we find that ∂d∗ /∂p < 0 and ∂d∗ /∂µ > 0, for all (p, µ) ∈ E.


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Proof of Proposition 2 If the outlet receives the void signal, then m = ∅ and I(x|∅) = I(x) and it makes no profits. If the outlet receives signal G then, by previous proposition, we know that it will send m = G to incumbent’s detractors. From the expression for I(x|G) above, we have that I



 1 2µ − 1 + |G = 0 2 2p

where (2µ − 1)/2p > 1/2. This means there is a majority of votes for the incumbent after the outlet sends m = G and the incumbent wins the election. If the outlet receives the bad signal and sends m = B, from the expression for I(x|B) we have that I



1 2µ − 1 − |B 2 2p



= 0,

and, therefore, the incumbents loses the election if the outlet sends the message. Taking advantage of the proof of the previous proposition, we know that the outlet’s profits in case of sending m = B are γ(c, p, µ) = α(c∗ −1/4)+β(c∗ +1/4)−(α(c∗ +1/4)+β(c∗ −1/4)) with 1 2− c = − 2 ∗

 p2 + 4µ(1 − µ)(4 − p2 ) . 4p(2µ − 1)

The function β does not depend on µ and one can check that the difference α(c∗ − 1/4) − α(c∗ + 1/4) is increasing in µ.


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0





















1 I(x|G) I(x) I(x|B)

Figure 1. Expected value of voting for the incumbent

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π(x, G)

π(x, B) 0

1 1 2

1 2

−δ

+δ

Figure 2. Outlet’s profits of sending m = G and m = B

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