t he newspaper. This prejudice could be shaped by basic beliefs about how the world operates. For example, in the Wen Ho Lee case readers may have st arted wit h the presumpt ion that the Chinese are likely to be spy ing on the U.S. Alternat ively, this signal may it self be the result of ot her newspaper stories or rumors the person has heard. In short, r is summary of the reader's prior conv ictions and prejudices before he reads the newspaper. The signal r is a noisy est imate of the trut h, so t+er here er is distributed normally N(O, a2). The reader uses this signal to update his beliefs The newspaper may also receive a signal. Good newspapers receive a signal for sure d bad news denoted n and equals the truth plus some noise: n =t+en, where en is normally distributed wit h variance on. Though we make n uni-dimensional for simplicity, one can think of n as really a bundle of facts In the second period, t he newspaper decides what to report. A bad newspaper has no news to report. A good newspaper, in contrast, has news n which it may modify reporting. Let s denote this modificat ion, so the paper reports v =n +s We are t hinking of a newspaper receiving a lot of fact s about a particular issue, all potentially point ing in somew hat different direct ions, and needing to distill them int a memorable story. We think of the modificat ion s not as invention or fabricat ion of new facts, but rather as a way to emphasize some facts, and de-emphasize ot hers, so the readers extract from the story a sy nt, hesized bot tom line Manipulation of informat ion can take a variety of forms. In some countries, news papers just make up facts to corroborate t heir stories, but we do not believe that this phenomenon is import ant in the U.S. Rat her, we are modeling the sit uation where a newspaper biases stories in more subt le ways. Reports can ignore or omit information inconsistent with t he message of t he story, build up"informat ion sources that corrob orate the story, ignore or undermine information sources that contradict the message. We form ally study this second case when we r multiple new
the newspaper. This prejudice could be shaped by basic beliefs about how the world operates. For example, in the Wen Ho Lee case readers may have started with the presumption that the Chinese are likely to be spying on the U.S. Alternatively, this signal may itself be the result of other newspaper stories or rumors the person has heard.5 In short, r is summary of the reader's prior convictions and prejudices before he reads the newspaper. The signal r is a noisy estimate of the truth, so r = t + er where er is distributed normally N(0; 2 r ). The reader uses this signal to update his beliefs. The newspaper may also receive a signal. Good newspapers receive a signal for sure and bad newspapers receive no signal. The signal they receive is denoted n and equals the truth plus some noise: n = t + en, where en is normally distributed with variance 2n. Though we make n uni-dimensional for simplicity, one can think of n as really a bundle of facts. In the second period, the newspaper decides what to report. A bad newspaper has no news to report. A good newspaper, in contrast, has news n which it may modify before reporting. Let s denote this modi cation, so the paper reports = n + s. We are thinking of a newspaper receiving a lot of facts about a particular issue, all potentially pointing in somewhat di erent directions, and needing to distill them into a memorable story. We think of the modi cation s not as invention or fabrication of new facts, but rather as a way to emphasize some facts, and de-emphasize others, so the readers extract from the story a synthesized bottom line. Manipulation of information can take a variety of forms. In some countries, newspapers just make up facts to corroborate their stories, but we do not believe that this phenomenon is important in the U.S. Rather, we are modeling the situation where a newspaper biases stories in more subtle ways. Reports can ignore or omit information inconsistent with the message of the story, \build up" information sources that corroborate the story, ignore or undermine information sources that contradict the message, 5We formally study this second case when we consider multiple newspapers. 5
colorful but misleading language and images that support the story. These types of informat ion manipulat ion need not involve inaccuracies, but at the same time address"t he narrat ive imperat ive Modificat ion is cost ly to the newspaper. First, it requires cost ly story-telling and research necessary to bolster t he t heme of the report. Second, and far more import ant ly, bot h the newspapers and the reporters that work for them care about accuracy, and excessive modificat ion of the news raises the risk of being wrong. Let c(n-v)denote the cost of modify ing the news We assume that c(0)=0 and that sign(c(x))=sign(x)>0 (x)=0, limr-1 c(x)=l and limx-0 c(x)=0. These assumpt ions mean that manipulat ion, in either direct ion, is costly to the newspaper In the third period, the e reader rea the story. He then combines what he reads ith his priors to form an assessment of t. Define this belief to be t. After beliefs are formed, the reader may forget the story or not. If he remembers the story, he presumes the newspaper is good. If he does not he presumes the paper is bad 2,1 Re ader p sy chology The model turns on how we assume readers form beliefs and remember infor mat ion. At one extreme, we might suppose people form Bayesian beliefs and have perfect recall In this case, after reading the news v, the individual updates and forms beliefs t=r+k1(-r) where ki is a const ant that equals aton But t his bayesian framework does not allow us to t hink about the media's desire t tell a story. To understand readers demand for "stories", we consider a model where readers t hink in coarse categories rat her that in precise fine-tuned priors (Mullainat ha 2002). Coarse categories capt ure the idea t hat readers carry away general impressions of the sit uat ion rat her than tracking all the det ails. In our simple case of a one- dimensional signal, the coarse categories may be somet hing like "goodand"bad Clinton is eit her a persecuted mo dern man or a villain. Wen Ho Lee is a spy or a victim. In more complicated sit uat ions wit h more dimensions, the categories would be
or use colorful but misleading language and images that support the story. These types of information manipulation need not involve inaccuracies, but at the same time address \the narrative imperative". Modi cation is costly to the newspaper. First, it requires costly story-telling and research necessary to bolster the theme of the report. Second, and far more importantly, both the newspapers and the reporters that work for them care about accuracy, and excessive modi cation of the news raises the risk of being wrong. Let c(n) denote the cost of modifying the news We assume that c(0) = 0 and that sign(c 0(x)) = sign(x) > 0 and c 00(x) = 0, limx!1 c(x) = 1 and limx!0 c(x) = 0. These assumptions mean that manipulation, in either direction, is costly to the newspaper. In the third period, the reader reads the story. He then combines what he reads with his priors to form an assessment of t. De ne this belief to be t^. After beliefs are formed, the reader may forget the story or not. If he remembers the story, he presumes the newspaper is good. If he does not he presumes the paper is bad. 2.1 Reader Psychology The model turns on how we assume readers form beliefs and remember information. At one extreme, we might suppose people form Bayesian beliefs and have perfect recall. In this case, after reading the news , the individual updates and forms beliefs: t^= r + k1( r) where k1 is a constant that equals 2n 2 r+2n . But this Bayesian framework does not allow us to think about the media's desire to tell a story. To understand reader's demand for \stories", we consider a model where readers think in coarse categories rather that in precise ne-tuned priors (Mullainathan 2002). Coarse categories capture the idea that readers carry away general impressions of the situation rather than tracking all the details. In our simple case of a onedimensional signal, the coarse categories may be something like \good" and \bad". Clinton is either a persecuted modern man or a villain. Wen Ho Lee is a spy or a victim. In more complicated situations with more dimensions, the categories would be 6
more nuanced. But the "goodand"bad"in our simple one-dimensional case capt the important feat ure of categoric at ion: readers have coarse rat her than fine-t beliefs.Specifically, define t, and t to be the posit ive and negat ive categories and assume these are sy mmetric in that t=-t6 Denote the categorical thinker'sbeliefs to. We assume that he believes in the category closest to what the Bayesian would believe. In this context. that means that he believes t when the Bayesian would have believed a posit ive tand he chooses t if the Bayesian would have expected a negative t if t> (1) t if te=I For example, suppose the reader has several pieces of ev nce mt which sugg Wen Ho Lee is a spy but some of which suggest the government scape-goated him A categorical t hinker walks away having placed Wen Ho Lee in the spy category, essent ially collapsing his informat ion into this simply summary a key feature of story telling is that stories need to be memorable. To capture this idea, we assume that readers forget some of the stories they read. Specificall re assume t hat the reader selectively forget s information that is inconsistent wit h his category. This select ive recall is an extension of t he reader holding coarse beliefs. He recalls dat a t hat just ify these coarse beliefs. In the above example, once the categorical t hinker places Wen Ho Lee in the spy category, he is less likely to remember stories which suggest t hat the government scapegoated him. Formally, we assume that recall probabilities are a funct ion of consistency wit h t he reader's category after he reads the story. So a story is more likely to be remembered if sign)=signt). specifically inconsistent stories have probability f of being remembered and consistent stories have lowing more categories does not change the "It is worth noting that not every category or story-line is equally likely. The background for any particul ar news item deter hich st ories fit. The t to elucidate exactly how any story is spun, but to underst and how the narr ative imperative inter acts with competition Several psy chology experiments suggest that category consistent information is more likely to be remem bered than category inconsistent inform ation. This is discussed in greater detail in Mullainathan(2002) POne might wonder whether extreme in cosistent stories would al so be remembered. In this set-up, they uld be if they are big h to change the readers category. In this case, they bec me consistent with the new category. If they. simplified, summary world-view of the reader: ader's mind, then they are discarded re inconsistent but not enough to cha since they dont fit
more nuanced. But the \good" and \bad" in our simple one-dimensional case captures the important feature of categorization: readers have coarse rather than ne-tuned beliefs. Speci cally, de ne t+ and t to be the positive and negative categories and assume these are symmetric in that t+ = t.6 Denote the categorical thinker's beliefs to be t^ c. We assume that he believes in the category closest to what the Bayesian would believe. In this context, that means that he believes t+ when the Bayesian would have believed a positive t and he chooses t if the Bayesian would have expected a negative t. Formally: t^ c = 8 >< >: t+ if t >^ 0 t if t <^ = 0 (1) For example, suppose the reader has several pieces of evidence most of which suggest Wen Ho Lee is a spy but some of which suggest the government scape-goated him. A categorical thinker walks away having placed Wen Ho Lee in the spy category, essentially collapsing his information into this simply summary.7 A key feature of story telling is that stories need to be memorable. To capture this idea, we assume that readers forget some of the stories they read. Speci cally, we assume that the reader selectively forgets information that is inconsistent with his category.8 This selective recall is an extension of the reader holding coarse beliefs. He recalls data that justify these coarse beliefs. In the above example, once the categorical thinker places Wen Ho Lee in the spy category, he is less likely to remember stories which suggest that the government scape-goated him.9 Formally, we assume that recall probabilities are a function of consistency with the reader's category after he reads the story. So a story is more likely to be remembered if sign() = sign(t^ c). Speci cally, inconsistent stories have probability f of being remembered and consistent stories have 6Allowing more categories does not change the results. 7 It is worth noting that not every category or story-line is equally likely. The background for any particular news item determines which stories t. The purpose of our model is not to elucidate exactly how any one story is spun, but to understand how the narrative imperative interacts with competition. 8Several psychology experiments suggest that category consistent information is more likely to be remembered than category inconsistent information. This is discussed in greater detail in Mullainathan (2002). 9One might wonder whether extreme incosistent stories would also be remembered. In this set-up, they would be if they are big enough to change the reader's category. In this case, they become consistent with the new category. If they are inconsistent but not enough to change the reader's mind, then they are discarded since they don't t the simpli ed, summary world-view of the reader. 7
probability 1 of being remembered. Denote this probability of recall as p v, tc In this paper, we examine w hat these two different assumpt ions about reader psy. chology imply for media bias. We consider bot h Bayesian and categorical readers not because we think readers are one or the other type. Instead this split allows us t make clear w hich results are driven by reader psy chology and which are driven by the truct ure of competit ion it self 2.2 Newspaper payoffs A newspapers payoff depends on several factors. First, it depends on whet her the newspaper is perceived to be good, since presumably good newspapers sell better. The paper receives a payoff T if it is t hought to be good and zero ot herwise, where T t he capit alized value of the increment al profits from being remembered. Second, the newspaper may have an ideology T which is either 0, +l or-1. A newspaper wit h an ideology of +l prefers to report posit ive stories whereas a newspaper with an I prefers to report negat ive stories. We assume the newspaper recev ies an benefit equal to BTv. In this sense B measures the int ensity of t he newspaper's ideology We furt her assume that readers form inferences ignoring the newspaper's ideolog o When readers are Bayesian, there is no confusion of good or bad newspapers since stories are remembered. A good newspaper no mat ter w hat it reports has its story remembered and is recognized as good. And by assumption a bad newspaper can never appear good. a good newspaper therefore receives a payoff of BTv-c(n-v) and a bad newspaper receives a payoff of When readers are categorical, however, good newspapers can be confused with bad ones. If a good newspaper's story is forgotten, t hought of bad one This assumption is merely to simplify the calcul ations. At the opposite extreme, readers would know and recognize these ideologies and would de- bi as stories before incorporating them into beliefs. Media biases would have no effect on beliefs at all. Our assumption is a simple version of the more realistic case where readers partly but not fully recognize the bias
probability 1 of being remembered. Denote this probability of recall as (; t^ c). In this paper, we examine what these two di erent assumptions about reader psychology imply for media bias. We consider both Bayesian and categorical readers not because we think readers are one or the other type. Instead this split allows us to make clear which results are driven by reader psychology and which are driven by the structure of competition itself. 2.2 Newspaper Payo s A newspaper's payo depends on several factors. First, it depends on whether the newspaper is perceived to be good, since presumably good newspapers sell better. The paper receives a payo if it is thought to be good and zero otherwise, where is the capitalized value of the incremental pro ts from being remembered. Second, the newspaper may have an ideology which is either 0, +1 or 1. A newspaper with an ideology of +1 prefers to report positive stories whereas a newspaper with an ideology of 1 prefers to report negative stories. We assume the newspaper recevies an ideological bene t equal to . In this sense measures the intensity of the newspaper's ideology. We further assume that readers form inferences ignoring the newspaper's ideology.10 When readers are Bayesian, there is no confusion of good or bad newspapers since all stories are remembered. A good newspaper no matter what it reports has its story remembered and is recognized as good. And by assumption a bad newspaper can never appear good. A good newspaper therefore receives a payo of: + c(n ) and a bad newspaper receives a payo of: c(n ) When readers are categorical, however, good newspapers can be confused with bad ones. If a good newspaper's story is forgotten, it is thought of as a bad one. 10This assumption is merely to simplify the calculations. At the opposite extreme, readers would know and recognize these ideologies and would de-bias stories before incorporating them into beliefs. Media biases would have no e ect on beliefs at all. Our assumption is a simple version of the more realistic case where readers partly but not fully recognize the bias. 8