Who Believes Fake News? A Bayesian Perspective, and a Lesson from Thanksgiving Dinner

November 30, 2016

Thanksgiving is supposed to be a minefield, but I've always enjoyed discussing the world with friends and family gathered around the holiday table. This year was no exception. One of my friends--let's call him Dan--is a keen observer of human behavior. We were talking about fake news and why so many people believe it. Dan said that the problem was not that such people were idiots, but that so much of the news media was reputable for so long. For those raised on Walter Cronkite, it's hard to believe that something that looks like news is actually baloney.

Let's try to understand this by adopting a Bayesian perspective. (For more along these lines, see my work with Konstantin Sonin on "Government Control of the Media" and my review article with Sonin and Milan Svolik on "Formal Models of Nondemocratic Politics.") Suppose a state of the world (think the color of the sky) can take two values, blue or green. Citizens do not directly observe the state but instead receive a signal--"blue" or "green"--generated by a news outlet (interpreted liberally: YouTube, etc.). The news outlet always sends the signal "green" when the state is green, but with probability B it also sends the signal "green" when the state is in fact blue. The parameter B measures the \emph{bias} of the news outlet.

Consider a citizen with prior belief that the state is green with probability P. By Bayes' rule, this citizen's posterior belief that the state is green, conditional on having observed the signal "green," is P / [P + (1 – P)*B]. (If she receives the signal "blue," she knows that the state is blue.)

The posterior belief is increasing in the prior P. Thus, holding media bias B constant, the citizens who are most likely to believe that the state is green when in fact it is blue--that is, most likely to believe fake news--are those who were already inclined to believe that the state is green. Put differently, we may find it infuriating that so many of our fellow citizens believe fake news, but those who do may not be the swing voters who decide elections.

But let's push on this a little harder. Look around, and you realize that citizens have very different understandings of the bias of media outlets. We could model this properly, but for our purposes it's sufficient to note that the posterior belief is decreasing in the (perceived) bias B of the news outlet. Thus, citizens who are more inclined to think that the news outlet is unbiased are more inclined to believe fake news.

And here's the point of the conversation with my friend Dan: Many of our fellow citizens have never learned to distinguish between a legitimate and an illegitimate news outlet. Back in the day, the only time you would see a video report was on the ABC, NBC, or CBS evening news. Now your friend sends you a link to a YouTube video that is as polished as anything the networks ever broadcast. It looks like news, and many treat it as such.

From a Bayesian perspective, this is the danger of fake news--that those who believe some crazy story are not the cranks who were already inclined to believe it, but the well-intentioned folks who can't tell the Denver Post (a real news outlet) from a fake news site like the Denver Guardian.

I've always felt like one of my most important functions as an undergraduate instructor is to help my students become better newspaper readers. I now understand that there is an even more fundamental mission: to help my students understand what a newspaper is.