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Home , Accuracy in Media, Matthew Rabin, Sendhil Mullainathan

The Market for

By AND *

We investigate the market for news under two assumptions: that readers hold beliefs which they like to see confirmed, and that can slant stories toward these beliefs. We show that, on the topics where readers share common beliefs, one should not expect accuracy even from competitive media: results in lower prices, but common slanting toward reader biases. On topics where reader beliefs diverge (such as politically divisive issues), however, newspapers segment the market and slant toward extreme positions. Yet in the aggregate, a reader with access to all news sources could get an unbiased perspective. Generally speaking, reader heterogeneity is more important for accuracy in media than competition per se. (JEL D23, L82)

Several recent books have accused mainline relies crucially on how one conceptualizes the media outlets of reporting news with a heavy demand for news. political bias. Bernard Goldberg (2002) and In the traditional conception of the demand (2003) argue that the bias is on the for news, consumers read, watch, and listen to left, and provide numerous illustrations of their the news in order to get information. The qual- argument, while Eric Alterman (2003) and Al ity of this information is its accuracy. The more Franken (2003) argue that the bias is on the accurate the news, the more valuable is its right, with equally numerous illustrations. In to the consumer. Pressure from audi- principle, can come from the supply ences and rivals forces news outlets to seek and side, and reflect the preferences of deliver more accurate information, just as mar- (David Baron, 2004), editors, or owners (Besley ket forces motivate auto-makers to produce bet- and Andrea Prat, 2004; Simeon Djankov et al., ter cars.1 2003). Alternatively, it can come from the de- This conception of the news as a source of mand side, and reflect the news providers’ pure information is dramatically different from profit-maximizing choice to cater to the prefer- that of noneconomists studying the media. Ac- ences of the consumers. We examine, theoreti- cording to these scholars, private media want to cally, the determinants of media accuracy in sell newspapers and television programs, as such a demand-side model, focusing specifi- well as advertising space. To do that, they pro- cally on the effects of reader beliefs, reader vide a great deal of pure entertainment. But heterogeneity, and competition on media bias. even with news, audiences want their sources We argue that the analysis of media accuracy not only to inform but also to explain, interpret, persuade, and entertain. To meet this demand, media outlets do not provide unadulterated in- * Mullainathan: Department of , 208 Littauer formation, but rather tell stories that hang to- Center, , Cambridge, MA 02138 (e-mail: gether and have a point of view, what is referred [email protected]); Shleifer: Department of Eco- to in the business as “the narrative imperative.”2 nomics, M9 Littauer Center, Harvard University, Cam- bridge, MA 02138 (e-mail: [email protected]). We are extremely grateful to Alberto Alesina, Daniel Benjamin, , Filipe Campante, Gene D’Avolio, Glenn Elli- 1 (1974), Besley and Robin Burgess son, Josh Fischman, Edward Glaeser, , (2002), Besley and Prat (2002), Djankov et al. (2003), Simon Johnson, Emir Kamenica, Lawrence Katz, David David Stromberg (2001), and Alexander Dyck and Luigi Laibson, Dominique Olie Lauga, Emily Oster, Richard Pos- Zingales (2002) all advance this view of competition in the ner, Jesse Shapiro, Jeremy Stein, , and media as delivering greater accuracy. three anonymous referees for comments. This paper is a 2 H. L. Mencken (1920), Walter Lippmann (1922), substantially revised version of an earlier paper entitled Samuel Hayakawa (1940), Michael Jensen (1979), Doris “Media Bias.” Graber (1984), James Hamilton (2003), and the standard 1031 1032 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005

In this view, news provision can be analyzed in their beliefs is standard in the communications the same way as entertainment broadcasting.3 literature (Graber, 1984; Severin and Tankard, In this paper, we examine these two concep- 1992). Basic research in psychology strongly tions of what the consumers want and what the supports it. Research on memory suggests that media deliver, and evaluate media accuracy un- people tend to remember information consistent der different scenarios. We show, in particular, with their beliefs better than information incon- that these two conceptions have radically dif- sistent with their beliefs (Frederic Bartlett, ferent implications for the accuracy of news in 1932). Research on information processing the competitive media, and more specifically on shows people find data inconsistent with their the question of which news issues will be re- beliefs to be less credible and update less as a ported more accurately. result (Charles Lord et al., 1979; John Zaller, Our model of rational readers seeking infor- 1992; and Joel Schrag, 1999). mation shows that, indeed, consistent with According to Graber (1984, p. 130), “stories economists’ priors, media reporting is unbiased. about economic failures in third world countries We compare this to a specific behavioral model were processed more readily than stories about (of which the rational consumers are a special economic successes.” People seek information case), which relies on two assumptions, one that confirms their beliefs (Josh Klayman, about reader preferences and one about the tech- 1995). When people categorize, they tend to nology of delivering news.4 We assume that ignore category-inconsistent information unless readers hold biased beliefs, which might come it is large enough to induce category change from their general knowledge and , (Susan Fiske, 1995; Mullainathan, 2002). Sev- from previous news, from prejudices and ste- erin and Tankard (1992) see the demand for reotypes, or from the views of politicians or cognitive consistency as crucially shaping political parties they trust. With respect to pref- which news people listen to, and which they erences, we assume that readers prefer to hear ignore. or read news that is more consistent with their Our second assumption is that newspapers beliefs. Such biased readers might believe, for can slant the presentation of the news to cater to example, that corporate executives are cheats the preferences of their audiences. The term and crooks, and these readers prefer news about “slanting” was introduced by Hayakawa (1940), their indictments to news about their accom- and defined as “the process of selecting details plishments. They might think that China is up to that are favorable or unfavorable to the subject no good with respect to the , and being described.” Slanting is easily illustrated in appreciate stories about Chinese spies. Some a simple example. Suppose that the Bureau of readers might like President and Labor Statistics (BLS) releases data that show prefer to read about partisan Republicans per- the rate of unemployment rising from 6.1 per- secuting the hard-working president; others cent to 6.3 percent. What are the different ways might dislike Clinton and look for stories ex- a paper can report this number? One is a single plaining, in salacious detail, the impeachability sentence report that simply presents the above of his offenses. fact. But there are alternatives. Consider just The idea that people appreciate, find credible, two. enjoy, and remember stories consistent with (a) Headline: Recession Fears Grow. New data suggest the economy is slipping into a re- communications textbook (Werner Severin and James cession. The BLS reports that the number of Tankard, Jr., 1992) all advance this view of news. unemployed grew by 200,000 in the last 3 Entertainment broadcasting is analyzed by Peter quarter, reaching 6.3 percent. John Kenneth Steiner (1952), and Bruce Owen (1977), Ronald Goettler and Ron Shachar (2001), and Esther Gal-Or Galbraith, the distinguished Harvard econ- and Anthony Dukes (2003). Jean Gabszewicz et al. (2001) omist, sees this as an ominous sign of the take the approach closest to ours by conceptualizing news failure of the administration’s policies. “Not provision in a Hotelling framework. They examine how since Herbert Hoover has a president ig- advertisers have an impact on content, whereas we focus on media accuracy. nored economic realities so blatantly. This 4 For concreteness, we talk about newspapers, although news is only the beginning of more to our argument applies equally well to television and radio. come,” he said. (Accompanying picture: a VOL. 95 NO. 4 MULLAINATHAN AND SHLEIFER: THE MARKET FOR NEWS 1033

long line for unemployment benefits in De- chic costs of reading papers whose reporting troit, Michigan.) does not cater to their beliefs. We ask whether (b) Headline: Turnaround in Sight. Is the econ- competition by itself eliminates or reduces the omy poised for an imminent turnaround? slanting of news, as economists often argue. We Data from the BLS suggest that it might be. show that the answer for biased readers is Newly released figures show unemploy- clearly no. Competition generally reduces ment inching up just 0.2 percent last quar- prices, but does not reduce, and ter. Abbie Joseph Cohen, the chief stock might even exaggerate, media bias. market strategist at Goldman Sachs, sees Second, we study heterogeneity of reader be- the news as highly encouraging. “This is a liefs. What effect does such heterogeneity have good time to increase exposure to stocks,” on the nature of slanting and the overall accu- she says, “both because of the strong un- racy in media? What is the impact of competi- derlying fundamentals and because the soft- tion on media accuracy when reader beliefs are ness in the labor market bodes well for heterogeneous, as in the case of beliefs about corporate profitability.” (Accompanying President Clinton? To answer this question, it is picture: smiling Abbie Joseph Cohen.) crucial to distinguish between an average reader, who reads one source of news, and a Each of these stories could easily have been hypothetical conscientious reader, who reads written by a major U.S. newspaper. In fact, multiple sources. In general, competition with stories like these, in light of public disclosure of heterogeneous readers increases the slanting by identical facts, are written every day. Neither individual media sources. But with heteroge- story says anything false, yet they give radically neous readers, the biases of individual media different impressions. Each cites an authority, sources tend to offset each other, so the beliefs without acknowledging that a comparably re- of the conscientious reader become more accu- spectable authority might have exactly the op- rate than they are with homogeneous readers. posite interpretation of the news. Each omits Our central finding is that reader heterogeneity some aspect of the data: the first by neglecting plays a more important role for accuracy in to mention the starting point of the unemploy- media than does competition. ment rate, the second by ignoring unemploy- At a broader level, this paper contributes ment levels. Each uses a headline, and a picture, to one of the central issues in economics, to persuade readers who do not focus on the namely whether the presence of rational, details. Each, in other words, slants the news by profit-maximizing firms eliminates any effect of not telling the whole truth, but the articles are irrational participants on market “efficiency.” In slanted in opposite directions.5 the context of financial markets, Milton Fried- Our model of the market for news combines man (1953) argued long ago that it does, and the assumption of readers preferring stories con- that rational arbitrageurs keep financial markets sistent with their beliefs with the assumption efficient. Subsequent research, however, has that newspapers can slant stories toward specific proved him wrong, both theoretically and em- beliefs. We examine two crucial aspects of this pirically (Shleifer, 2000; Markus Brunnermeier environment. First, we consider two alternative and Stefan Nagel, 2004). One finding of this assumptions about the nature of competition: research is that, in some situations, such as stock monopoly versus duopoly. Our model of media market bubbles, it might pay profit-maximizing competition is analogous to a Hotelling model firms to pump up the tulips rather than eliminate of product placement (, 1988, ch. 7). irrationality (Brad DeLong et al., 1990). Subse- Newspapers locate themselves in the product quent research has considered the interaction space through their reporting strategies (i.e., between biased individuals and rational en- how they slant). Readers’ beliefs determine trepreneurs in other contexts, such as the their “transportation” costs, since they face psy- incitement of hatred (Glaeser, 2005), political competition (Kevin Murphy and Shleifer, 2004), and product design (Xavier Gabaix and 5 Persuasion can also work through outright fabrication of news, as was done routinely by the Communist press, and Laibson, 2004). Here we ask a closely related occasionally even in Western newspapers (e.g., Jason question for the market for news: does compe- Blair’s reporting for .) tition among profit-maximizing news providers 1034 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005 eliminate media bias? We find that the answer, reader optimistic about the economy experi- in both financial and political markets, is no. ences disutility when reading stories that sug- Powerful forces motivate news providers to slant gest a recession. At the same time, even biased and increase bias rather than clear up confusion. readers dislike blatant and extreme slanting, at The crucial determinant of accuracy is not com- least in the long run. Holding constant the con- petition, per se, but consumer heterogeneity. sistency with beliefs, they prefer less slanted news.6 So, if he reads the newspaper, the overall I. Model Setup utility of a biased reader is:

2 2 Readers are interested in some underlying (2) Ub ϭ u៮ Ϫ ␹s Ϫ ␾͑n Ϫ b͒ Ϫ P variable t, such as the state of the economy, ϭ ␾ Ͼ which is distributed N(0, vt). Let p 1/vt denote where 0 calibrates his preference for hear- the precision. Readers hold a belief about t that ing confirming news. may be biased; beliefs are distributed N(b, vt). Thus, readers are potentially biased about the B. Newspaper Strategy expected value of t, but have the correct variance. Before seeing the data d, a newspaper an- Newspapers are in the business of reporting nounces its slanting strategy s(d) and the price P news about t. They receive some data d ϭ t ϩ it charges. Potential readers buy the paper if the ␧, where ␧ ϳ N(0, v␧). In the example from the price P is lower than the expected utility asso- introduction, these data might be an unemploy- ciated with reading the paper, Ed[U(s(d))]. To ment rate release. We assume that the papers form expected utility, expectations are taken then report the data with a slant s, so the re- over d and are assumed to be the true expecta- ϭ ϩ ϳ ported news is n d s. For most of the paper, tions (d N(t, vd)) rather than the biased ones. the exact technology of slanting is not impor- This approach crudely captures the idea that this tant, but in Section V we study a specific one. is a long-run game. Readers get a general sense of how much pleasure the paper provides them A. Reader Utility and make their purchasing decisions accord- ingly. It then makes more sense to think of Suppose readers are rational and unbiased. expected utility using the empirical distribu- All they want is information. They dislike slant- tions. Practically, in the model both assump- ing because it is costly both in effort and the tions about expectations produce the same time it takes to read slanted news and figure out results. the “truth.” In the BLS example, the report of Once readers decide whether to buy the pa- the first newspaper does not tell the reader how per, the paper observes its signal d and reports much the unemployment rate changed, while n ϭ d ϩ s(d). Readers read the news and that of the second newspaper does not contain receive their utility. Timing of the full game is the unemployment rate. To get a full picture, the as follows: reader needs more information. We assume that a rational reader’s utility is decreasing in the (a) The newspaper announces a strategy s(d) amount of slanting. So, if he reads a newspaper, for how to report the news. When there are his utility is: two papers, both announce strategies simultaneously. (b) Price P is announced. When there are two (1) U ϭ u៮ Ϫ ␹s2 Ϫ P r papers, both announce prices simultaneously, after the other paper has revealed its strategy. where P is the paper’s price. If he does not read the newspaper, he receives utility 0. Biased readers, on the other hand, get disutil- 6 This assumption is immaterial to our results. All we ity from reading news inconsistent with their require is that newspapers face some quadratic cost of slanting. This cost could just as easily arise on the supply beliefs. We model consistency as the distance side, with firms facing a technological or private reputa- between the news and the reader’s beliefs, b, tional cost of slanting, and the results would be the same. measured as (n Ϫ b)2. In the BLS example, a The necessary feature is that firms cannot slant freely. VOL. 95 NO. 4 MULLAINATHAN AND SHLEIFER: THE MARKET FOR NEWS 1035

(c) Individuals decide whether to buy the paper transportation costs. Firms’ choice of a slanting based on average utility associated with its rule resembles their choice of location. In this strategy s(d) and price P. context, our utility function implies quadratic (d) Newspaper receives data d and reports news transportation costs and our distribution of d ϩ s(d). If there are two papers, they reader beliefs in the heterogeneous case corre- ϩ receive the same data d and report d sj(d) sponds to a uniform distribution of consumers. where j ϭ 1, 2. Consequently, many of our proofs resemble the (e) If individuals buy the paper, they read the proofs for the Hotelling models in this case news and receive utility. (Claude d’Aspremont et al., 1979).7

C. Cases Considered D. Defining Bias

We consider two different distributions of We are interested in the extent of newspaper reader beliefs: homogeneous and heteroge- bias in the market. We measure this by the neous. Homogeneity means that all readers hold average bias of the newspapers in the market, the same beliefs b with precision p. For exam- weighted by their market share. In the homoge- ple, all or nearly all readers in the United States neous case, where there is only one kind of might believe that the Russians are corrupt or reader, we simply define bias as that the French are anti-American. Heterogene- ϭ ͓͑ Ϫ ͒2͔ ity means that there is a distribution of reader (3) ARBhom Ed n d beliefs. Such heterogeneity could come from political ideology. For example, opinions about where n is the news read by these readers. So U.S. presidents often divide along party lines. bias is defined as the average amount by which We assume that heterogeneous beliefs are dis- the news read deviates from the data for the tributed uniformly between b1 and b2 where average reader. Ͻ Ͼ b1 b2 and b2 0. Readers in this uniform In the heterogeneous case, let ni be the news distribution are indexed by i ʦ [1, 2] so that read by reader i ʦ [1, 2]. Bias is then defined as: reader i holds belief bi. All readers hold their beliefs with precision p. We denote by b៮ the average of b and b . We also denote reader i’s (4) ARB ϭ ͵ E ͓͑n Ϫ d͒2͔. 1 2 het d i utility function as u (d)oru (d), depending on i bi i context. The homogeneous and heterogeneous cases are designed to capture two different types This measures the average bias that readers of issues: ones on which there is consensus in encounter. the population and ones where there is substan- tial disagreement. II. Rational Readers We also examine two cases of industry struc- ture. In the first case, there is a single monop- When readers are rational, newspapers face olistic newspaper. In the second, there are two only a disincentive to slant. The following prop- ϭ newspapers, indexed by j 1, 2, each seeing osition summarizes the outcomes for different the same data d. For a monopolist, s*hom and s*het cases. denote the optimal slanting strategy for the ho- mogeneous and heterogeneous case. Similarly, PROPOSITION 1: Suppose readers are ratio- P*hom and P*het denote optimal price in these nal. Then, whether readers are homogeneous or cases. For duopolists, s*j,hom and s*j,het denote the optimal strategy of paper j ϭ 1, 2 in the homo- geneous and heterogeneous cases, respectively. 7 As with all Hotelling models, the assumptions on trans- Similarly, P*j,hom and P*j,het denote each duop- portation costs matter. With linear transportation costs, an olist’s optimal price in these two cases. equilibrium does not exist. But while the results depend on This formalism of industry structure is simi- nonlinear transportation costs, they are not specific to the quadratic. Other convex functions produce similar results lar in spirit to a Hotelling model. Readers’ be- (Nicholas Economides, 1986). See Steffen Brenner (2001) liefs resemble consumers’ preferred locations. for a survey. Similarly, as with all Hotelling models, the Their dislike of inconsistent news resembles assumption of Bertrand competition is key to our results. 1036 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005

heterogeneous, the monopolist does not slant ␹␾ * ϭ ៮ Ϫ ͓ 2 ϩ ͔ and charges the same price: (10) P hom u ␹ ϩ ␾ b vd ϭ ϭ (5) s*hom s*het 0 ៮ Ͼ ␹␾ ␹ ϩ ␾ 2 ϩ if u [ /( )][b vd]. If not, there exists no slanting strategy that results in the news and being read. ϭ ϭ ៮ (6) P*hom P*het u. Because the monopolist can capture all sur- plus through the price he charges, to maximize In the duopolist case as well, papers do not profits he merely maximizes expected utility. slant and once again charge the same price: The news he reports is:

s* ϭ s* ϭ ␾ ␹ (7) j,hom j.het 0 ϭ ϩ (11) n ␹ ϩ ␾ b ␹ ϩ ␾ d. and The reported news is a convex combination of ϭ ϭ (8) P*j,hom P*j.het 0 bias and data, with weights given by utility parameters. In this case, we say the monopolist for all j on the equilibrium path. The only effect “slants toward b.” Since this linear slanting of competition is to lower prices. strategy will reappear throughout the paper, we define: PROOF: ␾ See Appendix for all proofs. ͑ ͒ ϵ ͑ Ϫ ͒ (12) sB d ␹ ϩ ␾ B d . Proposition 1 illustrates the normal logic of economists’ thinking about the media. When With this notation, the proposition above can be ϭ readers seek accuracy in news, newspapers pass rewritten as s*hom(d) sb(d). The monopolist on, without slant, the information they receive. chooses this linear form because expected util- Since perfect quality is achieved even without ity functions are separable in the value of d. The competition, the effect of competition is to re- monopolist maximizes utility for every given duce the price that readers pay. With both mo- value of d, which leads him to slant toward a nopoly and duopoly, consumers get what they biased reader’s beliefs.9 want and there is no media bias.8 In the rest of The following corollary derives comparative the paper, we focus on the case of biased statics for the magnitude of slanting. readers. COROLLARY 1: In the homogeneous reader III. Homogeneous Biased Readers case, slanting increases with the reader prefer- ence for hearing confirmatory news and de- The following proposition summarizes the mo- clines with the cost of slanting: nopolist’s behavior with homogeneous readers. Ѩ͉s* ͑d͉͒ hom Ͼ PROPOSITION 2: A monopolist facing a ho- (13) Ѩ␾ 0 mogeneous audience chooses: Ѩ͉ ͑ ͉͒ s*hom d ␾ (14) Ͻ 0. * ͑ ͒ ϭ ͑ Ϫ ͒ Ѩ␹ (9) s hom d ␹ ϩ ␾ b d

9 Even when b ϭ 0, there is slanting. This is because even a reader who has zero bias ex ante does not want to 8 As is clear from the proof of the proposition, this result change his mind ex post. Consequently, the monopolist generalizes trivially to J Ͼ 2 newspapers. slants news toward the reader’s bias, 0. VOL. 95 NO. 4 MULLAINATHAN AND SHLEIFER: THE MARKET FOR NEWS 1037

Proposition 2 suggests a theory of spin. Sup- With a homogeneous audience, competition is pose that a politician, or some other figure of Bertrand-like: it simply drives prices down to authority, has a first mover advantage, i.e., can zero.10 Each duopolist’s slant is exactly equal to choose which data d gets presented to the media the monopolist’s slant, and they split the readers first. The papers slant the data toward reader between them. The following corollary summa- beliefs, but by Proposition 2, d will have sig- rizes the impact of competition on bias in the nificant influence on what papers report as com- homogeneous case.11 pared to their getting data from an unbiased source. For example, by preemptively disclos- COROLLARY 2: For a homogeneous audi- ing that a Chinese spy has been found in Los ence, both monopoly and duopoly produce the Alamos, a politician can focus the discussion on same amount of average reader bias: the risk to U.S. security from Chinese espio- ͑ ͒ ϭ ͑ ͒ nage, rather than on the administrative incom- (18) ARBmon vd ARBduo vd . petence in the Department of Energy. This effect becomes even more powerful in a more Propositions 2 and 3 are the first critical re- general model of sequential reporting. In this sults of the paper. They show that when readers case, the initial spin may shape reader priors, have homogeneous biases, competition does not which future papers face and consequently slant eliminate them—it only leads to price reduc- news toward. The initial spin would then be tions. Both monopolists and duopolists cater to reinforced even by ideologically neutral papers. reader prejudices. These propositions basically ៮ Ͼ ␹␾ ␹ ϩ ␾ 2 ϩ The condition u [ /( )][b vd] say that one cannot expect accuracy—even in guarantees that this reader’s reservation utility u៮ the competitive media—on issues where the is high enough that he prefers reading the opti- readers share beliefs. One example of such uni- mally biased news to no news. From now on, formity might be foreign affairs, where there we assume that this condition holds. may be a great deal of commonality of views toward a particular foreign country, such as ASSUMPTION 1: Reader utility from news is Russia, China, or France. Another example is high enough that readers prefer the equilibrium law enforcement, where most readers might news to no news: sympathize with efforts by the government to prosecute members of a disliked group (e.g., the ␹␾ Arabs or the rich). ៮ Ͼ ͓ 2 ϩ ͔ (15) u ␹ ϩ ␾ b vd . IV. Heterogeneous Biased Readers With this assumption in place, we now turn to competition. How does competition between What happens when readers differ in their two newspapers affect the results above? beliefs? Newspapers must now decide which one of the heterogeneous reader groups is its PROPOSITION 3: Suppose duopolists face a target audience. homogeneous audience. Then there is an equi- librium in which duopolists choose on the equi- PROPOSITION 4: Suppose a monopolist faces librium path: a heterogeneous audience with b៮ ϭ 0. There exists a Cm, which depends on the parameters of ␾ the model, that determines the monopolist’s (16) s* ͑d͒ ϭ ͑b Ϫ d͒ Ϫ Ͻ j,hom ␹ ϩ ␾ strategy. If b2 b1 Cm, the monopolist max- imizes profits by choosing: and prices

10 ϭ For this same reason, and as is clear from the proof of (17) P*j,hom 0 the proposition, this result holds for any number of news- papers J Ն 2. 11 The stated equilibrium for the duopolists is not unique for both j ϭ 1, 2. Readers are indifferent be- because any strategy profile that differs on a set of measure tween the two papers. zero would also be an equilibrium. 1038 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005

␾ ␾ that firm 1 slants toward the left and firm 2 * ϭ ៮͑ ͒ ϭ ͑៮ Ϫ ͒ ϭ Ϫ (19) s het sb d ␹ ϩ ␾ b d ␹ ϩ ␾ d slants toward the right. All readers read the newspaper. ␾␹ (20) P* ϭ u៮ Ϫ v Ϫ ␾2b2. Each duopolist positions himself as far away het ␹ ϩ ␾ d 2 from the other as possible. The reported news in this case equals Ϫ Ͼ If b2 b1 Cm the monopolist chooses not to cover the market, i.e., not all readers read the ␾ 3 ␹ (25) n ϭ d ϩ s* ͑d͒ ϭ b ϩ d . paper. j j,het ␹ ϩ ␾ 2 j ␹ ϩ ␾ j According to Proposition 4, the monopolist cov- The reported news is a weighted average of the 3 ers the market if the dispersion of reader beliefs actual data d and ⁄2 bj, where bj is the endpoint is small enough. If beliefs are too far apart, of the reader bias distribution. So duopolists are 3 readers on either extreme will not read the slanting news toward ⁄2 bj, points that are more paper.12 extreme than the most extreme readers in the Duopolists, in contrast, respond completely population. differently to heterogeneity. For tractability, we This is analogous to the standard Hotelling now consider only the situation where duop- result with uniform distributions and quadratic olists choose linear strategies. transportation costs (Tirole, 1988; d’Aspremont et al., 1979). As in the standard Hotelling PROPOSITION 5: Suppose duopolists choose model, the monopolist caters to both audiences ϭ ␾ ␹ ϩ linear strategies of the form sB(d) [ /( unless they are too far apart, while duopolists ␾)](B Ϫ d) and that b៮ ϭ 0. Then there exists a maximally differentiate. But in the standard Ho- constant telling model, firms are constrained to choose within the preference distribution. In our model, 4 ␾ ϩ ␹ ␹ they can choose positions outside the distribu- (21) C ϭ ͱ ͫ u៮ Ϫ v ͬ tion of reader bias, and in equilibrium choose d 33 ␾2 ␾ d very extreme positions.13 Ͻ To see why this occurs, consider a simple such that if b2 Cd duopolists choose: ␾ ϭ ␹ ϭ ϭ ϭϪ case where 1, 1, b2 1 and b1 1. With these parameters, suppose the firms locate ␾ 3 Յ 14 (22) s* ͑d͒ ϭ ͩ b Ϫ d ͪ at z1 z2. Equilibrium prices then equal (see 1,het ␹ ϩ ␾ 2 1 1 the proof of Proposition 5):

␾ 3 z៮ (23) s* ͑d͒ ϭ ͩ b Ϫ d ͪ (26) P*͑z , z ͒ ϭ ⌬zͩ1 ϩ ͪ 2,het ␹ ϩ ␾ 2 2 2 1 1 2 3

6␾2 z៮ (24) P* ϭ b2 (27) P*͑z , z ͒ ϭ ⌬zͩ1 Ϫ ͪ j,het ␹ ϩ ␾ 2 2 1 2 3

⌬ ϭ Ϫ ៮ ϭ ϩ where we assume, without loss of generality, where z z2 z1 and z (z1 z2)/2. The more differentiated the duopolists (the greater is

12 ៮ ϭ Ϫ Ͼ If b 0, but b2 b1 Cm, the monopolist would use the same slanting strategy as in Proposition 4, but would 13 ៮ ϭ Ͼ charge a high enough price that not all people read the If b 0 but b2 Cd, the duopolists differentiate less paper. The case where b៮ 0 is more complicated. The than stated in Proposition 5. The participation constraint of monopolist would not slant toward b៮ anymore. Instead, he the reader with bias 0 begins to bind and the duopolists ៮ would slant toward a point between b and 0. This is because locate closer together than in the proposition. If b2 is suffi- readers closer to the origin enjoy higher overall surplus ciently large, the duopolists would even end up inside the ͉ ͉ Ͻ ͉ ͉ from reading the paper (see Lemma (A1)). Consequently, distribution of reader beliefs so that zj bj . the monopolist would prefer a distribution of readers closer 14 Recall that “located at z” means the paper biases ϭ ␾ ␹ ϩ ␾ Ϫ to the origin so as to be able to charge higher prices. according to the rule sz(d) [ /( )](z d). VOL. 95 NO. 4 MULLAINATHAN AND SHLEIFER: THE MARKET FOR NEWS 1039

⌬z), the higher the prices they can charge. Dif- sources can be even more extreme than their ferentiation softens price competition because most biased readers. One cannot, therefore, in- the temptation to undercut each other diminishes fer reader beliefs directly from media bias. as the firms move farther away from the mar- Another point is worth noting: ginal consumer (who is located between them). ͓͉͑ ͑ ͉͔͒͒ Ն ͓͉͑ ͑ ͉͔͒͒ Now consider firm 1’s choice of where to (30) E s*j,het d E s*het d . locate. When biasing toward z1, firm 1 captures Ϫ ϭ ៮ all readers between 1 and x*(z1, z2) z/3. Duopolists always slant more than the monop- ϩ ៮ Hence its profits equal P*1(1 z/3). Differenti- olist when readers are heterogeneous. In this ating with respect to z1 gives the first-order sense, competition tends to polarize the news. condition The following corollary summarizes the impact of competition on bias. Ѩ Ѩ P*1 x* (28) ͑x*͑z , z ͒͒ ϩ P*ͩ ͪ ϭ 0 Ϫ Ͻ Ѩz 1 2 1 Ѩz COROLLARY 3: Suppose b1 b2 Cm. In 1 1 the heterogeneous reader case, competition in- Ѩ ៮ creases the bias of the average reader: P*1 z 1 (29) ͩ1 ϩ ͪ ϩ P*ͩ ͪ ϭ 0. z 3 1 3 1 ͑ ͒ Ͻ ͑ ͒ (31) ARBmon,het vd ARBduo,het vd .

Increasing z1 (that is, moving closer to the ori- gin) has two effects on profits. The first is a Corollary 3 shows that, with heterogeneous price effect; there is a change in profits because readers, competition by itself polarizes reader- changing position affects the equilibrium prices. ship and, if anything, raises the average reader The second is a market share effect; there is a bias. Entry of a left-wing newspaper or a TV change in profits because moving closer to the station into a local market previously dominated origin raises market share. by a moderate or slightly right-wing monopolist Papers slant toward positions well beyond the might cause this monopolist to shift his report- extreme consumers because the price effect ing to the right. dominates the market share effect until firms are Corollary 3 might shed light on the growing very far apart. Focusing on the symmetric case controversy in the United States about media ៮ ϭ Ѩ Ѩ ϭ⌬ Ϫ with z 0, the price effect is P*1/ z1 z/6 bias. Several recent books have angrily attacked 1. The price effect is negative as long as ⌬z Ͻ media outlets for having a left-wing bias (e.g., 6, in other words, until the difference in firm Goldberg, 2002; Coulter, 2003). Several equally locations is three times as high as the difference angry books have responded that other media Ϫ ϭ in most extreme readers (3(b2 b1) 6). The outlets have an even stronger right-wing bias ϭ market share effect, on the other hand, is P*1/3 (Alterman, 2003; Franken, 2003). We suspect ⌬z/6. These two effects offset each other to that there is a grain of truth in all these books, produce an optimum when ⌬z/6 Ϫ 1 ϩ⌬z/6 ϭ and that the growing partisanship of alternative 0or⌬z ϭ 3. At the symmetric equilibrium, the media sources is a response to the growth in ⌬ ϭϪ ϭ ϭ optimum is reached at z 2z1 3orz1 competition, and market segmentation, in the Ϫ 3⁄2 . The distance between the newspapers media. Changes in media technology have led Ϫ ϭ (z2 z1 3) is greater than the distance to significant entry, especially in television. If Ϫ ϭ between the most extreme readers (b2 b1 2). these media sources divide the market along In short, when choosing how to slant, ideological lines, we expect them to become duopolists maximally differentiate them- more biased than they were in the regime of selves.15 Practically, this means that news moderate competition. This is perhaps what the various commentators are recognizing. Corollary 3 may also have implications for 15 This analysis also illustrates why Proposition 5 is the effects of entry of new media outlets on the about competition, per se, and not about variety alone. A nature of reporting. In a provocative recent monopolist who could start two newspapers does not need to differentiate to increase . He would differ- study, Gentzkow and Shapiro (2004) examine entiate simply to cater to reader tastes, but would not go the responses to a Gallup poll by residents of beyond the most extreme readers as duopolists would. nine Muslim countries about such topics as the 1040 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005

United States, terrorism, responsibility for 9/11, A. Technology of Slanting and so on. The authors document a striking pattern of factually inaccurate beliefs, but also Following Hayakawa (1940), we assume that suggest that the media have a strong effect on newspapers slant by selectively omitting spe- these beliefs. In particular, those who watch cific bits of news, i.e., not reporting the whole al-Jazeera (Arab television) are much more truth.17 To formalize this idea, suppose that, likely to hold factually false beliefs (as well as rather than simply receiving a composite d ϭ anti-American ones) than those watching t ϩ ␧, the newspaper receives a sequence of CNN.16 In concluding their paper, Gentzkow positive and negative “bits” or facts. In the and Shapiro appear to endorse recent proposals example from the introduction, these facts could favoring an expansion of Western news in the be the unemployment rate, the unemployment Arab world, because such news is likely to rate in the past, expert opinions, other relevant moderate opinions and beliefs. economic indicators, and so on. These bits or Our model suggests that caution is appropri- facts are modeled as a length L string f consist- ate. The people who watch or listen to Western ing of positive (ϩ1), negative (Ϫ1), or nonex- news are already sympathetic to its perspective istent (A) pieces of news. At each position, the and might already watch CNN, so they are probability of each of these values is a function unlikely to be strongly affected. Additional en- of d, so now instead of simply seeing the com- try might cause al-Jazeera and similar networks posite d, the paper sees all the bits of facts that to further differentiate their product by advanc- constitute it. The probability that the piece of ing yet more extreme views. The effect might news in position i, denoted fi, is positive, neg- be to radicalize, rather than moderate, their ative, or nonexistent is given by the distribution audience. function:

V. Reader Heterogeneity and Accuracy in ϩ1 ϭ qg͑d͒ Media ͑ ͒ ϭ Ϫ ϭ ͑ Ϫ ͑ ͒͒ (32) Pr fi ͭ 1 q 1 g d A ϭ ͑1 Ϫ q͒ Our results so far focus on how an average -reader in the population is affected. We can also where g٪ is a continuous and increasing func look at the impact of reporting on a conscien- tion that is bounded between 0 and 1, and 0 Ͻ tious reader, a hypothetical reader who reads all q Յ 1. With probability 1 Ϫ q, there is no news the news available but is too small to affect at position i. If there is news, it is positive with what is reported. The interesting insights arise probability g(d) and negative otherwise. Condi- in the duopoly case where the hypothetical con- tional on d, these probabilities are iid across scientious reader reads both papers. Since both different bits on a string. With multiple papers, papers are reporting on the same event, the we assume that they all see the same string f. conscientious reader might in principle be able A newspaper that does not slant at all would to use the two to undo the slanting. To under- simply report the string f without alteration. A stand this process we need a precise model of reader who sees the string f can draw inferences slanting. from the number of ϩ1’s and Ϫ1’s, which we define as Nϩ(f ) and NϪ(f ), respectively. By the Law of Large Numbers:

Nϩ ͑f͒ (33) ϭ g͑d͒ ϩ ␩ 3 g͑d͒ NϪ ͑f͒ ϩ Nϩ ͑f͒

16 These results are not unique to the Muslim world. where ␩ is a noise term that converges to zero as Steven Kull et al. (2003) document significant confusion the length of the string L 3 ϱ. Consequently, among large percentages of U.S. respondents on such ques- for large L, the information the reader receives tions as Saddam Hussein’s culpability in 9/11 and the dis- covery of weapons of mass destruction in Iraq. The study also finds that those who get their news from are less well informed about these issues than those who get 17 Importantly, newspapers do not slant by simply man- their news from PBS and NPR. ufacturing evidence. VOL. 95 NO. 4 MULLAINATHAN AND SHLEIFER: THE MARKET FOR NEWS 1041 is well approximated by the case in which he which paper 1 omits. By cross-checking, the Ϫ1 simply observes d since g [Nϩ(f )/(NϪ(f ) ϩ conscientious reader gets all the facts, as if she Nϩ(f ))] 3 d. were able to read an unslanted newspaper. De- :In this formalism, a newspaper slants the fine xc٪ to be the cross-checking function signal by selectively omitting positive or nega- ͕ ͖ Ͼ Ͼ tive bits of information. To slant upward, for min s1 , s2 if s1 0, s2 0 example, a newspaper drops negative bits. In- ͑ ͒ ϭ ͕ ͖ Ͻ Ͻ (35) xc s1 , s2 ͭmax s1 , s2 if s1 0, s2 0 stead of reporting ϩ1, Ϫ1, Ϫ1, A, ϩ1, Ϫ1, ... it 0 otherwise. reports ϩ1, A, A, A, ϩ1, Ϫ1 ... , for example. A paper that wishes to slant upward by s Ͼ 0 This function summarizes how the conscien- produces a string fЈ by dropping enough nega- tious reader can cross-check the two papers.18 tive bits to guarantee Define nc to be the news the conscientious reader is effectively exposed to: Nϩ ͑fЈ͒ (34) gϪ1ͩ ͪ Ϸ d ϩ s. NϪ ͑fЈ͒ ϩ Nϩ ͑fЈ͒ n ϭ ͭ if one newspaper (36) nc ϩ ͑ ͒ d xc s1 , s2 if two newspapers. Likewise, a paper that wishes to slant negatively by s Ͻ 0 simply drops enough positive bits. As We then define conscientious reader bias anal- L 3 ϱ, the paper can choose to drop bits to ogously to the average reader bias: approximate better and better any given slant s. For simplicity, assume that newspapers omit 2 (37) CRB ϭ Ed ͓͑nc Ϫ d͒ ͔. facts in fixed ways. To slant positively, a paper omits the lowest indexed negative bits until it This definition of conscientious reader bias is approximates the desired fraction. To slant neg- independent of heterogeneity of reader beliefs. atively, a paper omits the lowest indexed posi- However, CRB does depend on the equilibrium tive bits until it reaches the desired fraction. news reporting, which in turn may depend on This assumption is simply one way of formal- the heterogeneity of reader beliefs. izing the idea that two papers wishing to slant in As the discussion on cross-checking sug- a particular direction do so similarly. gests, reader heterogeneity can help the consci- entious reader quite a bit. To formalize this, let B. Cross-Checking us compare the case of homogeneous readers with bias b to the case of heterogeneous readers By cross-checking the facts in the two news- with beliefs distributed uniformly on [b Ϫ ␦, papers, a conscientious reader may be able to b ϩ ␦]. The following corollary summarizes our reduce the effect of slanting. Suppose each pa- principal finding: per receives string f, which can be thought of as implying data d ϭ t ϩ ␧, and paper j reports COROLLARY 4: The interaction of reader string fj. There are now several cases. If the heterogeneity and duopoly lowers conscientious implied slants for both papers are positive and reader bias. When readers are heterogeneous, Ͼ Ͼ s1 s2 0, then every fact that paper 1 reports, conscientious reader bias is lower under paper 2 also reports. Moreover, because paper 2 duopoly than monopoly: is slanting less, it reports some facts that paper Ͻ 1 does not. Consequently, a conscientious (38) CRBhet,duo CRBhet,mon. reader would interpret the news as if she had Ͼ Ͼ read only paper 2. The case where 0 s2 s1 is similar. On the other hand, if the two papers Ͼ are on opposite sides of the issue so that s1 18 The extreme cross-checking depends on the two pa- Ͼ 0 s2, paper 1 omits some negative details to pers slanting stories using the same rule. It is necessary for slant upward and paper 2 omits some positive our results only that the papers use similar rules. Suppose details to slant downward. The conscientious that when one paper omits a fact, it appears in a oppositely slanted paper only with probability z. In this case, the reader, however, can cross-check both papers. cross-checking function becomes (1 Ϫ z)s ϩ (1 Ϫ z)s ϩ Paper 1 reports the positive facts, which paper 2 1 2 zxc(s1, s2). Thus, the qualitative statements we make are omits, and paper 2 reports the negative facts, preserved. 1042 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005

Under duopoly, conscientious reader bias is Perhaps the clearest illustration of this corol- lower under heterogeneity than homogeneity: lary is the coverage of the Monica Lewinsky affair during the Clinton presidency. The left- Ͻ (39) CRBhet,duo CRBhom,duo. wing press presented an enormous amount of information designed to expiate the president’s Corollary 4 is the final result of our paper and its sins, while the right-wing press dug out as many bottom line. It points to the absolutely central details pointing to his culpability. In the end, role that heterogeneity of reader beliefs plays in however, as Posner (1999) remarks in his book, assuring accuracy in media. We have shown much of the truth has come out and a conscien- that when readers are homogeneous, competi- tious reader could get a fairly complete picture tion results in lower prices, but not in accurate of reality. news reporting. When readers are heteroge- neous, the news received by the average reader VI. Conclusion might become even more biased as competitive media outlets segment the market. Such market We have examined the roles of two forces in segmentation, however, benefits a conscientious promoting accuracy in media: competition and reader, who can then aggregate the news from reader diversity. We have found that competi- different sources to synthesize a more accurate tion by itself is not a powerful force toward picture of reality. When newspapers are at dif- accuracy. Competition forces newspapers to ca- ferent sides of the political spectrum, the con- ter to the prejudices of their readers, and greater scientious reader gets all the facts. While competition typically results in more aggressive individual news sources slant even more when catering to such prejudices as competitors strive faced with a heterogeneous public, the aggre- to divide the market. On the other hand, we gate picture becomes more clear. In this respect, found that reader diversity is a powerful force reader heterogeneity is the crucial antidote to toward accuracy, as long as accuracy is inter- media bias. preted as some aggregate measure of revelation This analysis indicates which issues are more of information to a reader who takes in all the likely to receive accurate media coverage, at news. Greater partisanship and bias of individ- least for the conscientious reader. Almost ual media outlets may result in a more accurate surely, the most likely domain of reader heter- picture being presented to a conscientious reader. ogeneity is domestic politics, where readers Reader heterogeneity comes in part from have diverse beliefs and media coverage is cor- underlying political competition, whereby po- respondingly diverse. Such dispersion of reader litical parties, movements, and individual en- beliefs could come from their self-interested trepreneurs attempt to generate support by economic and social preferences, what used to presenting their points of view. If they can be called “class differences.” But, as Glaeser generate enough interest, media outlets will try (2005) argues, such differences are reinforced to cater to the very same audiences that the by political entrepreneurs, who have an incen- political entrepreneurs attract, and diversity in tive to create particular beliefs that would bring media coverage will arise endogenously. In them support, especially if these beliefs distin- contrast, when potential audiences share similar guish them from the incumbent. Newspapers beliefs, and when there is no advantage from would then follow these entrepreneurs in mir- political entry, such as the coverage of foreign roring and reinforcing the beliefs of their sup- countries or crime, we do not expect to see porters. In fact, in many countries today, and in diversity of media reports or accuracy in media. the United States 100 years ago, newspapers Political competition is only one source of were affiliated with political parties (Hamilton, underlying reader diversity. We can also imag- 2003). Reader diversity, and newspaper diver- ine entrepreneurs starting newspapers on their sity, are partly a reflection of underlying polit- own and, as long as they have deep enough ical competition. In other areas of competition, pockets, creating enough demand for unortho- such as sports, we likewise expect local papers dox views to broaden the range of opinions (and to support local teams, thereby creating diver- slants) that are being covered. Ideological di- sity of reporting across cities reflecting the di- versity of entrepreneurs themselves may be the versity of reader beliefs. source of diversity of media coverage. VOL. 95 NO. 4 MULLAINATHAN AND SHLEIFER: THE MARKET FOR NEWS 1043

We have studied competitive persuasion in the suasion is more general, and that attempts to dif- market for news. Our principal finding is that, ferentiate competitively by moving toward when competitors can create or reinforce differ- extreme positions will arise in both political (Mur- ences of opinion, they will do so in order to divide phy and Shleifer, 2004) and product (Gabaix and the market and reap higher profits. There will be Laibson, 2004) markets. In these and other do- no convergence in reporting to the median reader mains, the influence of audience heterogeneity (as in a Downsian median voter framework). We and competition on the content of persuasive mes- believe that this consequence of competitive per- sages remains to be fully explored.

APPENDIX A: LEMMAS

LEMMA A1: Define

␾ ͑ ͒ ϭ ͑ Ϫ ͒ (A1) sB d ␹ ϩ ␾ B d

to be the strategy where a newspaper biases around point B. The reader’s expected utility (gross of price) of reading such a newspaper is:

␹␾ ␾2 ͓ ͑ ͑ ͔͒͒ ϭ ៮ Ϫ ͓ ϩ 2͔ Ϫ ͓ Ϫ ͔2 (A2) Ed U sB d u ␹ ϩ ␾ vd b ␹ ϩ ␾ B b .

Consequently when B ϭ 0:

␹␾ ͓ ͑ ͑ ͔͒͒ ϭ ៮ Ϫ Ϫ ␾ 2 (A3) Ed U s0 d u ␹ ϩ ␾ vd b .

And when B ϭ b:

␹␾ ͓ ͑ ͑ ͔͒͒ ϭ ៮ Ϫ ͑ ϩ 2͒ (A4) Ed U sb d u ␹ ϩ ␾ vd b .

PROOF: Expected utility for sB(d) is:

␾ 2 ␾ 2 ៮ Ϫ ␹ ͑ Ϫ ͒ Ϫ ␾ ϩ ͑ Ϫ ͒ Ϫ (A5) u ͵ ͩ␹ ϩ ␾ B d ͪ ͵ ͩd ␹ ϩ ␾ B d bͪ . d d

The first integral is:

␾ 2 Ϫ␹ͩ ͪ ͓ 2 ϩ ͔ (A6) ␹ ϩ ␾ B vd

ϭ 2 ϭ because E[d] 0 and E[d ] vd. The second integral is:

␹ 2 ␾ 2 ␾ Ϫ␾ͫͩ ͪ ϩ ͩ ͪ 2 ϩ 2 Ϫ ͬ (A7) ␹ ϩ ␾ vd ␹ ϩ ␾ B b 2 ␹ ϩ ␾ Bb

ϭ 2 ϭ again because E[d] 0 and E[d ] vd. Collecting terms produces 1044 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005

␾␹ ␾2 ␾2 ៮ Ϫ Ϫ ␾ 2 Ϫ 2 ϩ ϭ (A8) u ␹ ϩ ␾ vd b ␹ ϩ ␾ B 2 ␹ ϩ ␾ Bb

␾␹ ␾␹ ␾2 ␾2 ៮ Ϫ ͓ ϩ 2͔ Ϫ ␾ 2 ϩ 2 Ϫ 2 ϩ ϭ (A9) u ␹ ϩ ␾ vd b b ␹ ϩ ␾ b ␹ ϩ ␾ B 2 ␹ ϩ ␾ Bb

␾␹ ␾2 ␾2 ␾2 ៮ Ϫ ͓ ϩ 2͔ Ϫ 2 Ϫ 2 ϩ ϭ (A10) u ␹ ϩ ␾ vd b ␹ ϩ ␾ b ␹ ϩ ␾ B 2 ␹ ϩ ␾ Bb

␾␹ ␾2 ៮ Ϫ ͓ ϩ 2͔ Ϫ ͓ 2 ϩ 2 Ϫ ͔ (A11) u ␹ ϩ ␾ vd b ␹ ϩ ␾ b B 2Bb

and hence the result. Յ Ն Ն LEMMA A2: Let x1 x2 be the biases of two readers. For any 1 c 0, the strategy ␾ ͑ ͒ ϭ ͑ ៮ Ϫ ͒ (A12) sx៮ d ␹ ϩ ␾ x d

ϩ Ϫ ៮ ϭ maximizes weighted average reader utility cEdux (s(d)) (1 c) Edux (s(d)), where x ϩ Ϫ 1 2 cx1 (1 c) x2. Յ Յ ϭ ␾ ␹ ϩ ␾ Ϫ Moreover, for some x1 z x2, the strategy sz(d) [ /( )](z d) maximizes min{Eu (s(d)), Eu (s(d))}. x1 x2 PROOF: Consider total utility cE u (s(d)) ϩ (1 Ϫ c)E u (s(d)), which equals d x1 d x2

(A13) ͵ ͓u៮ Ϫ ␹s͑d͒2 Ϫ c␾͑d ϩ s͑d͒ Ϫ x ͒2 ϩ ͑1 Ϫ c͒␾͑d ϩ s͑d͒ Ϫ x ͒2͔. 1 2 d

Since the right-hand side shows no interdependency in d, maximizing this integral is equivalent to maximizing for every single d, the term

៮ Ϫ ␹ ͑ ͒2 Ϫ ␾͑ ϩ ͑ ͒ Ϫ ͒2 ϩ ͑ Ϫ ͒␾͑ ϩ ͑ ͒ Ϫ ͒2 (A14) u s d c d s d x1 1 c d s d x2 .

Taking derivatives with respect to s then produces the first-order condition

(A15) Ϫ2␹s Ϫ 2␾͑d ϩ s Ϫ x៮͒ ϭ 0,

which implies that the optimal slanting is: ␾ ͑៮ Ϫ ͒ (A16) ␹ ϩ ␾ x d .

For the second part, let s(d) be a candidate slanting strategy that maximizes min{Eu (s(d)), x1 Eux (s(d))}. Define u1 and u2 to be the expected utilities for s(d). Note that sx and sx maximize reader 2 1 2 ៮ ϭ ϩ Ϫ 1 and reader 2 utilities, respectively. Consequently, there must be a c such that for x cx1 (1 c)x2 the strategy sx៮ yields the same ratio of reader 1 and 2 utilities as the candidate strategy does: Ն ϭ u1/u2. But by the first part of the Lemma, Eui(sx៮(d)) ui for i 1, 2. Otherwise, the candidate strategy s(d) would yield higher weighted average utility. But this shows sx៮ maximizes the min and ϭ hence s sx៮. VOL. 95 NO. 4 MULLAINATHAN AND SHLEIFER: THE MARKET FOR NEWS 1045

APPENDIX B: PROOFS OF PROPOSITIONS

PROOF OF PROPOSITION 1: Consider the monopolist’s maximization problem. Reader utility is

2 (B1) Ur ϭ max͕u៮ Ϫ ␹s Ϫ P,0͖.

Since readers only dislike slanting, a newspaper gets no benefit from slanting and only pays costs. The optimal strategy for both the homogeneous and heterogeneous case is therefore s*(d) ϭ 0. Since the reader’s gross utility in this case is u៮, the monopolist can extract all surplus and charge P, so that the reader’s net utility is 0. Consider now the duopoly case. Begin with the homogeneous reader case and proceed by backward induction. Consider the price setting stage. Define Vj to be the utility the reader associates with reading newspaper j. There are two cases here: equal and unequal utilities. For the case of Ͼ unequal utilities, suppose without loss of generality that V1 V2. The price equilibrium is for paper Ϫ ϭ 1 to charge V1 V2 and capture the full market. If V1 V2, then both papers charge zero. In the strategy-setting stage, holding constant the other’s strategy, both papers’ profit functions are increasing in the reader utility from the strategies they choose. Consequently, it is a weakly dominant strategy for each paper to maximize reader utility. From the monopoly case, we know these strategies are s(d) ϭ 0. It is an equilibrium, therefore, to have both prices and slanting equal to zero. In the heterogeneous reader case, the logic remains the same because reader utility functions are the same as in the homogeneous case, since utility is independent of beliefs for rational readers. The homogeneous and heterogeneous cases produce the same incentives for the firm.

PROOF OF PROPOSITION 2: Since the monopolist can extract all surplus, he maximizes expected utility,

(B2) max u៮ Ϫ ␹ ͵ ͑s*͑d͒͒2 Ϫ ␾ ͵ ͑d ϩ s*͑d͒ Ϫ b͒2. s*͑d͒ d d

There are no interdependencies in this utility maximization across d’s. Because the maximand is separable in d, choosing the optimal s*(d) is equivalent to choosing the optimal s* for each d or

2 2 (B3) s*͑d͒ ϭ argmaxsu៮ Ϫ ␹s Ϫ ␾͑d ϩ s Ϫ b͒ .

For a given d, differentiating with respect to s produces the first-order condition

(B4) ␹s ϩ ␾͑d ϩ s Ϫ b͒ ϭ 0,

which implies ␾ * ͑ ͒ ϭ ͑ Ϫ ͒ (B5) s hom d ␹ ϩ ␾ b d .

Prices then are equal to the expected utility under this strategy. From Lemma (A1), we know the expected utility and hence price is ␹␾ * ϭ ៮ Ϫ ͓ 2 ϩ ͔ (B6) P hom u ␹ ϩ ␾ b vd . 1046 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005

PROOF OF PROPOSITION 3: We proceed by backward induction. Consider the price-setting stage. Let Vj be the reader’s utility associated with reading paper j. There are two cases here: equal and unequal utilities. For the case Ͼ of unequal utilities, suppose without loss of generality that V1 V2. The price equilibrium is for Ϫ ϭ paper 1 to charge V1 V2 and capture the full market. If V1 V2, then both papers charge zero. In the stage where the slanting strategy is set, maximizing reader utility is, as before, a weakly dominant strategy. Holding constant the other firm’s strategy, each firm’s profit is increasing in the reader utility associated with its strategy. We know from Proposition 2 that the utility-maximizing strategy is to slant [␾/(␹ ϩ ␾)](b Ϫ d). Therefore, it is an equilibrium for duopolists to choose this strategy. Since this means both papers provide equal utility, prices equal zero. This shows that this is an equilibrium. Moreover, this logic directly implies that the only equilibrium involves both papers choosing a slanting strategy that maximizes utility and prices equal to zero on the equilibrium path.19

PROOF OF PROPOSITION 4: We proceed in three steps:

(1) First, we show that a linear strategy is an optimal one. (2) Second, we show that of the linear strategies, the strategy with zero bias produces maximum profit. (3) Third, we compute the prices the monopolists would charge.

Step 1: Linearity of monopolist’s strategy. The first step is to show that the linear strategy of the type ϭ ␾ ␹ ϩ ␾ Ϫ sB(d) [ /( )](B d) is optimal. To show this, suppose s(d) and P form an optimal strategy ϭ ͉ Ϫ Ն for the monopolist. Let X {bi Eui(s(d)) P 0} be the biases of the readers who read the paper in this case.20 ʚ Since X [b1, b2] is non-empty, it must have a well-defined inf and sup. Let x1 and x2 be the inf and sup of this set and u1 and u2 be the utility of these readers. Lemma (A2) shows that a linear ϭ ␾ ␹ ϩ ␾ Ϫ ϭ ϩ Ϫ strategy of the form sz(d) [ /( )](z d), where z cx1 (1 c)x2, maximizes min{u1, u2}. So, sz yields the maximum payoffs for x1 and x2. But by Lemma (A1), all readers with bias between x1 and x2 have even greater utility from this strategy. Define the price Pz to be min{u1, u2}. Since x1 and x2 are the inf and sup of the set X, by the formula in Lemma (A1), it is easy to see that the strategy sz, with price Pz, satisfies the participation constraint of all readers in X. Let us now contrast the supposed optimum strategy (s, P) with this strategy (sz, Pz). By construction, sz has at least as large a market share as s since it spans all readers between the inf and sup of the set X. Moreover, since s satisfies the participation constraint of x1 and x2 we know that Յ it cannot yield higher gross utility for readers at x1 and x2 than sz does. Hence, we know that P Pz. Thus, the linear strategy sz(d) yields at least as much profit as the supposed optimum. This shows that we can work with a linear strategy as an optimum.

Step 2: Optimal bias is zero. The second step is to show that a monopolist would choose a linear ϭ strategy of sB(d) with B 0. To do this, we proceed by contradiction. Let (B, P) be a linear strategy B and price P set by a monopolist that we suppose is an optimum strategy. Lemma (A1) shows that for a reader with bias b receives utility

␹␾ ␾2 ៮ Ϫ ͓ ϩ 2͔ Ϫ ͓ Ϫ ͔2 Ϫ (B7) u ␹ ϩ ␾ vd b ␹ ϩ ␾ B b P.

19 Any slanting strategy that deviates on measure zero from the optimal one also forms an equilibrium since expected utility is the same. 20 This set must be non-empty since the strategy stated in the proposition earns positive profits and an empty readership would earn zero profits. VOL. 95 NO. 4 MULLAINATHAN AND SHLEIFER: THE MARKET FOR NEWS 1047

All readers for whom this term is positive will read the paper. Since this is a quadratic equation, we can define the indifferent readers from this equation. By the quadratic formula, the zeros of this ͌ 2 2 equation are at zϩ(P, B) ϭ (2B␾ ϩ Ϫ4␾␹B ϩ 4(K/␾)(␹ ϩ ␾) )/2(␹ ϩ ␾) and zϪ(P, B) ϭ ␾ Ϫ ͌Ϫ ␾␹ 2 ϩ ␾ ␹ ϩ ␾ 2 ␹ ϩ ␾ ៮ Ϫ ␾␹ ␾ ϩ ␹ Ϫ (2B 4 B 4(K/ )( ) /2( ), where K is defined to be u [ /( )]vd P. Of course, these zero points may lie outside the range of reader biases, so define bϩ(P) Џ ϭ max(zϪ(P, B), b1) and bϪ(P) min(zϩ(P, B), b2). By definition, therefore, all individuals within this interval have weakly positive utility and therefore will purchase the paper. With these definitions in hand, suppose now the monopolist chooses a B 0. We will consider three different cases: (a) the case where bϩ and bϪ are both interior (i.e., equal to zϩ and zϪ); (b) the case where they are both at the boundary (i.e., equal to b2 and b1); and (c) the case where one is at the boundary and the other is at the interior. First, consider the case where bϩ(B, P) ϭ zϩ(B, P) and bϪ(B, P) ϭ zϪ(B, P) so that the end points are defined by the quadratic equation and not by the boundaries of the reader bias distribution. The size of the interval in this case then equals

K Ϫ ␾␹ 2 ϩ ͑␹ ϩ ␾͒2 ͱ 4 B 4 ␾ ͑ ͒ Ϫ ͑ ͒ ϭ (B8) zϩ P zϪ P ␹ ϩ ␾ .

But, since the constant K does not depend on B, this is strictly decreasing in B2. Hence, a B 0 strategy cannot be optimal. If B Ͼ 0, reducing it and keeping prices the same would increase profits, and similarly for B Ͻ 0. ϭ Ͻ Second, consider the case where both endpoints are defined by the boundary so that bϩ b2 ϭ Ͼ zϩ and bϪ b1 zϪ. Let U1 be the gross utility of the reader at the left boundary (i.e., with bias b1) and U2 be the corresponding utility for the reader at the right boundary. Prices in this case are ϭ defined by P min{U1, U2}. A price smaller than this could be increased marginally without violating the participation constraint and raising profits. A price higher than this would violate the participation constraint of the boundary readers and would be inconsistent with the definition of the boundary. Yet this price implies a violation of optimality. Lemma (A2) shows that for some c, choosing B ϭ cb ϩ (1 Ϫ c)b would maximize min{U , U }. Moreover, by the symmetry of the 1 2 1 2 ៮ formula in Lemma (A1) it is clear that c ϭ 1⁄2 . So a strategy of B ϭ b ϭ 0 would still satisfy the participation constraint since it is maximizing the minimum utility. Moreover, by switching to this strategy, the monopolist could increase the price he could charge since min{U1, U2} rises. Profits also rise because he continues to cover the whole market. Hence, by switching to this strategy, the monopolist could raise profits and this contradicts B 0 as an optimal strategy. ϭ Ͼ ϭ Ͻ Third, consider the case where (without loss of generality) bϪ zϪ b1 but bϩ b2 zϩ.By definition of the roots zϪ and zϩ, the reader at b2 earns greater utility than the reader at zϪ who is indifferent between buying the paper and not. But in this case, consider a deviation that leaves prices fixed but changes strategies to BЈϭB Ϫ ␧. For small enough ␧ Ͼ 0, this continues to give strictly positive utility to the reader at b2 and hence he will continue to read. This will increase market share, however, because some readers with b Ͻ zϪ now earn positive utility from reading. Since this deviation increases market share without decreasing price, the original B could not be an optimum. As this includes all the cases, we have now shown that profits are maximized by a linear strategy ء with B ϭ 0. What should optimal prices look like? For B ϭ 0, the monopolists profits equal P ͌␾ ϭ ៮ Ϫ ␾␹ ␾ ϩ ␹ Ϫ m 2 K where K u [ /( )]vd P. Let P be the global maximum of this function. At Ϫ ϭ ͌␾ ៮ Ϫ ␹␾ ␹ ϩ ␾ Ϫ m Ϫ Ͻ this maximum bϩ bϪ 2 /[u ( /( )) P ]. Define this to be Cm.Soifb2 b1 Cm, the monopolist will cover the whole market. He can then set a price equal to the utility of the ៮ Ϫ ␹␾ ␾ ϩ ␹ Ϫ ␾2 2 boundary reader’s utility, which by Lemma (A1) equals u [ /( )]vd b2.

PROOF OF PROPOSITION 5: We proceed by backward induction in several steps: 1048 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005

(1) We calculate x(P1, P2, z1, z2), the bias of the reader who is indifferent between reading the two papers if paper j charges Pj and has bias zj (chosen in the first stage of the game and taken as given in this stage). This allows us to determine the market share of each firm for that location and price pair. R R (2) We then calculate P1(P2; z1, z2) and P2(P1; z1, z2), the best response functions for firms 1 and 2, respectively. These are the best price responses of each firm to the other’s price (given the biases zj which are chosen in the first stage and taken as given in the second stage). (3) Using these prices, we calculate the equilibrium prices P*1(z1, z2) and P*2(z1, z2) and market share x*(z1, z2) that result from the choice of bias in the first stage. (4) We then use these equilibrium prices to show that in the first stage, firms will want to Յ ϭ ϭ ϭϪ differentiate as long as z2 3b2. We show that at z2 3b2 and z1 3b1 3b2, the firms are indifferent between lowering and raising zj and thus in equilibrium. (5) Finally, we show that all participation constraints for the consumer are satisfied at the equilibrium.

Step 1: Calculating x(P1, P2; z1, z2). A reader with bias x receives utility:

␹␾ ␾2 ៮ Ϫ ͓ ϩ 2͔ Ϫ ͓ Ϫ ͔2 Ϫ (B9) u ␹ ϩ ␾ vd x ␹ ϩ ␾ zj x Pj from reading paper j (Lemma (A1)). If the reader with bias x is indifferent between these two papers, then the utilities from reading the two papers are equal:

(B10)

␹␾ ␾2 ␹␾ ␾2 ៮ Ϫ ͓ ϩ 2͔ Ϫ ͓ Ϫ ͔2 Ϫ ϭ ៮ Ϫ ͓ ϩ 2͔ Ϫ ͓ Ϫ ͔2 Ϫ u ␹ ϩ ␾ vd x ␹ ϩ ␾ z2 x P2 u ␹ ϩ ␾ vd x ␹ ϩ ␾ z1 x P1 .

This equality can in turn be simplified to

␾2 ͓͑ Ϫ ͒2 Ϫ ͑ Ϫ ͒2͔ ϭ Ϫ (B11) ␹ ϩ ␾ z1 x z2 x P2 P1

␾2 ͑ Ϫ ͓͒ Ϫ ͑ ϩ ͔͒ ϭ Ϫ (B12) ␹ ϩ ␾ z2 z1 2x z2 z1 P2 P1

2␾2 ⌬ ͓ Ϫ ៮͔ ϭ ⌬ (B13) ␹ ϩ ␾ z x z P

⌬P ␹ ϩ ␾ (B14) x͑P , P ; z , z ͒ ϭ z៮ ϩ 1 2 1 2 ⌬z 2␾2

៮ ϭ ϩ ⌬ ϭ Ϫ ⌬ ϭ Ϫ where z ( z1 z2)/2, P P2 P1, and z z2 z1.

R Step 2: Calculation price best response functions Pj (PϪj). Since the indifferent reader is located at x, firm profits are given by

P ⌸ ͑ ͒ ϭ 1 ͑ Ϫ ͒ (B15) 1 P1 , P2 ; z1 , z2 Ϫ x b1 b2 b1 VOL. 95 NO. 4 MULLAINATHAN AND SHLEIFER: THE MARKET FOR NEWS 1049

P ⌸ ͑ ͒ ϭ 1 ͑ Ϫ ͒ (B16) 2 P1 , P2 ; z1 , z2 Ϫ b2 x . b2 b1

The firm’s best price response can be derived by differentiating profits with respect to own price. For firm 1, this first-order condition is

1 Ѩ x ͫ Ϫ ϩ 1ͬ ϭ (B17) Ϫ x b1 P1 Ѩ 0 b2 b1 P1

Ѩ x Ϫ ϩ 1 ϭ (B18) x b1 P1 Ѩ 0 P1

⌬P ␹ ϩ ␾ ␹ ϩ ␾ (B19) z៮ ϩ Ϫ b ϩ P ͩϪ ͪ ϭ 0 ⌬z 2␾2 1 1 2␾2⌬z

␹ ϩ ␾ ␹ ϩ ␾ P2 (B20) z៮ ϩ Ϫ b ϭ P ⌬z 2␾2 1 1 ␾2⌬z

⌬ ␾2 z P2 (B21) ͑ z៮ Ϫ b ͒ ϩ ϭ P . 1 ␹ ϩ ␾ 2 1

So the best response function is

⌬ ␾2 P2 z (B22) PR͑P ; z , z ͒ ϭ ϩ ͑b ϩ z៮͒ 1 2 1 2 2 2 ␹ ϩ ␾

ϭϪ where we’ve used the fact that b2 b1 by assumption. Similarly, the best response function for firm 2 is

⌬ ␾2 P1 z (B23) PR͑P ; z , z ͒ ϭ ϩ ͑b Ϫ z៮͒ . 2 1 1 2 2 2 ␹ ϩ ␾

Step 3: Calculating equilibrium prices and market share. The Nash equilibrium of prices can be calculated from the best response functions by solving

ϭ R͑ R͑ ͒͒ (B24) P*1 P1 P2 P*1 ; z1 , z2

ϭ R͑ R͑ ͒͒ (B25) P*2 P2 P1 P*2 ; z1 , z2 .

The first equation can be calculated as follows:

ϭ R͑ R͑ ͒͒ (B26) P*1 P1 P2 P*1 ; z1 , z2

R͑ ͒ ⌬ ␾2 P2 P*1 ; z1 , z2 z (B27) P* ϭ ϩ ͑b ϩ z៮͒ 1 2 2 ␹ ϩ ␾

⌬ ␾2 ⌬ ␾2 1 P1 z z (B28) P* ϭ ͩ ϩ ͑b ϩ z៮͒ ͪ ϩ ͑b ϩ z៮͒ 1 2 2 2 ␹ ϩ ␾ 2 ␹ ϩ ␾ 1050 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005

␾2⌬ ៮ 3 z b2 z (B29) P* ϭ ͫ Ϫ ϩ z៮ ϩ b ͬ 4 1 ␹ ϩ ␾ 2 2 2

␾2⌬z 2z៮ (B30) P* ϭ ͫ2b ϩ ͬ. 1 ␹ ϩ ␾ 2 3

By a similar calculation

␾2⌬z 2z៮ (B31) P* ϭ ͫ2b Ϫ ͬ. 2 ␹ ϩ ␾ 2 3

Using these equilibrium prices, we can also calculate equilibrium market share as

␹ ϩ ␾ (B32) x*͑ z , z ͒ ϭ z៮ ϩ ⌬P 1 2 2␾2⌬z

4z៮ ␾2⌬z ␹ ϩ ␾ (B33) x*͑ z , z ͒ ϭ z៮ ϩ ͫϪ ͬ 1 2 3 ␹ ϩ ␾ 2␾2⌬z

2 (B34) x*͑ z , z ͒ ϭ z៮ Ϫ z៮ 1 2 3

z៮ (B35) x*͑ z , z ͒ ϭ . 1 2 3

Step 4: Differentiation in choosing bias (the first stage). These prices and market share allow us to backward induct and examine the firm’s decision in stage 1. Taking the other firm’s bias as given, they can be used to calculate each firm’s profits for each bias chosen. Specifically profits in stage 1 are

⌸ ͑ ͒ ϭ ͑ ͓͒ ͑ ͒ Ϫ ͔ (B36) 1 z1 , z2 P*1 z1 , z2 x* z1 , z2 b1

⌸ ͑ ͒ ϭ ͑ ͓͒ Ϫ ͑ ͔͒ (B37) 2 z1 , z2 P*2 z1 , z2 b2 x* z1 , z2 .

The first-order condition for this problem is instructive. Focusing on firm 1, we can write profits as

z៮ (B38) P*͑ z , z ͒ͫ Ϫ b ͬ. 1 1 2 3 1

Differentiating with respect to z1 gives

Ѩ⌸ P*͑ z , z ͒ ѨP*͑ z , z ͒ z៮ 1 ϭ 1 1 2 ϩ 1 1 2 ͫ Ϫ ͬ (B39) Ѩ Ѩ b1 z1 6 z1 3

Ѩ⌸ z៮ 2␾2⌬z z៮ 2␾2 ⌬z z៮ 1 ϭ ͩ ϩ ͪ ϩ ͩ ϩ ͪ ͫ Ϫ Ϫ ͬ (B40) Ѩ b2 ͑␹ ϩ ␾͒ b2 ␹ ϩ ␾ b2 . z1 3 6 3 6 3 VOL. 95 NO. 4 MULLAINATHAN AND SHLEIFER: THE MARKET FOR NEWS 1051

Now we are interested in the sign of this derivative. Define sign( x) to be the function that equals ϩ1ifx Ͼ 0 and Ϫ1ifx Ͻ 0. We can then write

Ѩ⌸ z៮ z៮ Ϫ Ϫ ៮͔ͪ ⌬͓ ء ͪ ϭ ͩͩ ϩ ͪ⌬ ϩ ͩ ϩ 1ͪ ͩ (B41) sign Ѩ sign b2 z b2 z 6b2 2z z1 3 3

Ѩ⌸ z៮ ϩ ⌬ Ϫ Ϫ ៮͒ͪ ⌬͑ ء ͬ ϭ ͩͫ ϩ 1ͪ ͩ (B42) sign Ѩ sign b2 z z 6b2 2z . z1 3 ϭϪ ៮ ϭ Now suppose that we are in a symmetric case where z1 z2 so that z 0. In this case, Ѩ⌸ 1 ͒͒ z Ϫ 6b⌬2͑ ء B43) signͩ ͯ ͪ ϭ sign͑b) Ѩ 2 2 z1 z៮ ϭ 0

Ѩ⌸ 1 (B44) signͩ ͯ ͪ ϭ sign͑2⌬z Ϫ 6b ͒) Ѩ 2 z1 z៮ ϭ 0

Ѩ⌸ 1 (B45) signͩ ͯ ͪ ϭ sign͑Ϫ4z Ϫ 6b ͒). Ѩ 1 2 z1 z៮ ϭ 0

Ѩ⌸ Ѩ ͉ Ͻ Ϫ Ͻ Ϫ Ͻ 3 So ( 1/ z1) z៮ ϭ 0 0 if and only if 2z1 3b2. In other words, if z1 ⁄2 b2, firm 1 always Ϫ Ͼ 3 has an incentive to further lower z1.If z1 ⁄2 b2, firm 1 has an incentive to raise z1. A similar Ѩ⌸ Ѩ ͉ Ͼ Ͻ 3 ϭ derivation shows that ( 2/ z2) z៮ ϭ 0 0 only if z2 ⁄2 b2. This, therefore, shows that at z*2 3 ϭϪ3 ⁄2 b2 and z*1 ⁄2 b2, the firms are at a Nash equilibrium for the first stage game. Substitution ␾2 ␹ ϩ ␾ 2 shows that for this choice of z*j , prices must be equal to [ /( )]6b2.

Step 5: Boundary conditions. Finally, we must verify that in equilibrium, the participation con- straints of the consumer are satisfied. It suffices to show that the consumer located at zero receives non-zero utility from buying either paper. That is, we must show (by Lemma (1)) that:

␹␾ ␾2 9 ␾2 (B46) u៮ Ϫ v Ϫ b2 Ϫ 6 b2 Ͼ 0 ␾ ϩ ␹ d ␹ ϩ ␾ 4 2 ␹ ϩ ␾ 2 where the first three terms are the gross utility of reading the paper and the last term is the price. This is equivalent to:

33 ␾2 ␾␹ (B47) b2 Ͻ u៮ Ϫ v , 4 2 ␹ ϩ ␾ ␹ ϩ ␾ d which is equivalent to

4 ␾ ϩ ␹ ␹ (B48) b Ͻ ͱ ͫ u៮ Ϫ v ͬ, 2 33 ␾2 ␾ d which is what was assumed in the statement of the proposition. 1052 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005

PROOF OF COROLLARY 4: Ͻ Consider the first comparison: CRBhet,duo CRBhet,mon. From Propositions 5 and 4, we know that duopolists report more diverse news than the monopolist when readers are heterogeneous. But from the functional form of xc( ⅐ , ⅐ ), we know that this diversity allows the conscientious reader to cross-check and thus produces less bias for her overall. Ͻ Consider the second comparison CRBhet,duo CRBhom,duo. By Propositions 5 and 3, we know that reporting in the heterogeneous case is more diverse. So, once again, the increased diversity means lower conscientious reader bias.

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