Making Inferences from “Fake News” (a Bayesian Approach)

When it comes to understanding news on politically divisive topics I follow a simple rule:

Only trust biased news sources when they say the opposite of what you would expect, otherwise lean on your own intuition.

For example if CNN or Vox were to say something positive about Donald Trump you should give that information some merit. If they say something negative then consider it noise and instead lean on your own intuition (you can use the inverse logic on Fox News or Breitbart). This heuristic can actually be justified using Bayesian inference and the language of probability theory.

The most well-known biased news source is Fox News, so I will use them for the following example.

blog data

The first table above reflects what it means for a source to be biased: A high probability of support (or non-support) for a person or position, regardless of the data. The second table can be thought of as your own personal bias on a given issue. If you think you are perfectly unbiased on the topic then you would set the corresponding probabilities at 50/50.

Recall Bayes’ Rule:

P(A|B) = \frac{P(B|A) \times P(A)}{P(B)}

From this we can obtain the following results:blog data 2

This result exactly reflects my initial heuristic. i.e. We can place a high degree of certainty in an event if a biased source says the opposite of our expectations. Also note that if the source says exactly what we expect them to say (i.e. Fox tends to say good things about Trump), then the probability above comes pretty close to our own personal intuition. This means the source can mostly be ignored.

An interesting result emerges when we compare this analysis to an unbiased source. Consider the how we might perceive information from an unbiased source, like say, Reuters:

blog data 3

Our intuition tells us that assessing positive Trump news from Reuters is more reliable than pro-Trump sources. But what I find even more interesting is that Reuters is actually less reliable for assessing negative news about Trump than Fox News.

Lesson: Sometimes Fake News is actually the most reliable source of information!

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