# Media Bias and the Ability to Uncover the Truth

## Media Bias

Those of you familiar with my Wartime Elections model know that I assume the actor, I call the Media (M), to be “unbiased”. Specifically, Nature send a noisy signal to M, and M sends that “unbiased” but potentially noisy signal to the Electorate (E) about the “true” state of the war.

You may already be thinking, “the Media is clearly biased, so that assumption is wrong”. I am not going to present a rant about why simplifying assumptions need only be useful, not necessarily true, in order to tell us something interesting about the way phenomena works (although I do believe this to be true).

Moreover, when we think about the democratic process, we often think that if citizens were better informed they would be better democratic citizens. And of course – whether it is true or not – journalists often claim that “the central purpose of journalism is to provide citizens with accurate and reliable information they need to function in a free society” (Project for Excellence in Journalism, 2007). Thus, my assumption of an unbiased, yet potentially inaccurate, Media is not far from what we think the world should look like based on normative evaluations. In fact, I find it interesting that such tragic possibilities (see here and here) are possible given the assumption of an unbiased Media.

## More Bias, Yet Closer to the Truth?

Nevertheless, I have just come across an interesting and revealing formal model of news consumption and media bias, by Xiang and Sarvary, which actually demonstrates that the ability to uncover the true state of the world is higher (what they call information efficiency) when the media is more biased! Yes, when competing media outlets are more biased “conscientiousness consumers”, who seek the truth, are actually better able to uncover reality – but they must pay a higher price for said media because they must purchase from multiple media outlets.

The authors assume that there is some true state of the word – $\theta$ – which is bound between 0 and 1 – this parameter can be whether the war is actually worth fighting or the true value of a new healthcare law. The true state of the world is not observable to the Media, rather they they have to collect data which is modeled as a series of random draws from a Bernoulli process. The draws make up a string (D) which consists of 0s or 1s; these represent negative or positive signals about the truth, respectively. Thus, assume the string $d=[1,0,0,1,1,1,0,0,1,1]$. The unbiased estimate of the truth is $\hat{\theta} =\frac{6}{6+4} = 0.6$. Thus, is the string $d$ contains $n_{1}$ of 1’s and $n_{0}$ of 0’s, the unbiased estimate of the truth is $\frac{n_{1}}{(n_{1}+n_{0})}$. The authors then assume that the Media can “slant” what they report by selectively omitting parts of the string and thus changing $\hat{\theta}$ or the estimated true state of the world. But slanting is costly for the Media because they have to collect more data (which are random draws) to be able to slant. Moreover, the Media cannot manufacture data; slanting is constrained by the truth and the cost of data collection.

In the authors’ model there are two types of consumers – “biased” and “conscientiousness”; the former uses mass media for entertainment purposes, while the later actually seeks the truth. Media outlets can report how biased their messages are in order to attract specific consumers ($m = \theta$ or $m = s$) – $\theta$ being as close as possible to the real state of the world and $s$ being some purported amount of slant.

Under monopolist media conditions the media simply caters to whichever consumer represents a larger portion of the population – biased or conscientiousness . Under a duopoly there exists an interesting equilibrium. When there exists a significant number of conscientiousness consumers and their disutility for biased media is high, media outlets will actually collect more data in order to present highly slanted views. The existence of a significant amount of conscientious consumers with a high disutility for bias forces them to buy both pieces of media and thus the media outlets are more willing to increase prices to capitalize on this consumer segment. In fact, these media sources also report news which is more biased than the average “biased” consumer desires.

What is even more interesting is that Xiang and Sarvary show that under these conditions information efficiency is also very high. Because biased consumers’ consumption preferences are heterogeneous the conscientiousness consumer knows that the truth will be on the the left of the message $m <s$ and on the right of messages $m> s$. Thus, when consuming both slanted news sources (which share the same random draws of information) the conscientiousness consumer can come closer to the “true state of the world”.

Thus, the punch line of the model is that a significant number of conscientiousness consumers can actually drive media to be more biased in a competitive setting, but these same consumers “may actually recover more information from multiple, increasingly biased news than from a single nonpartisan news provider” (Xiang and Sarvary 2007, p. 623).

## Interesting Implications

Xiang and Sarvary’s model has some interesting implications. The most provocative implication is that increasing media bias may actually make it easier (albeit more costly) for “truth-seeking” consumers to figure out the true state of the world. Moreover, this model rejects the notion that media bias is driven by consumer demand for bias; rather increased bias is a function of more truth-seeking consumers and competing media outlets ability to drive up price, knowing these consumers will purchase both types of media in order to maximize their utility for unbiased media.

This model would also imply that given a biased media environment (as so many scholars contend) those that want to find the truth can do so with more, not less, efficiency. Thus,  my “unbiased” media actor assumption may not be so problematic if we look at the ability of truth-seeking consumers to gather unbiased data in the context of the authors’ model.

We can also look at my assumption another way. Instead of Nature reporting a noisy signal to the Media who faithfully reports that signal with accuracy $\alpha \in [0.5,1]$, we can think of the Media as being predictably biased with the same parameter $\alpha \in [0.5,1]$. Either way the math is the same. Nevertheless, given the discussion in this blog post, the reality may very well be that “truth-seeking” consumers can use multiple media outlets to gather an unbiased signal from the “mass media” writ large.

## References

Xiang, Yi and Miklos Sarvary. (September-October, 2007). “News Consumption and Media Bias.” Marketing Science. Vol. 26, No. 5: pp. 611-628.