Urban Dynamics Blog

# The mathematical ignorance of the mainstream media

By Matt Johnson

Since Donald J. Trump clinched the presidential nomination early Wednesday morning on November 9th, several mainstream publications and writers have been claiming that pollsters and forecasters got this election wrong. Politico, Fox News Insider, and USA Today, just to name a few media sources, have attempted to claim this in their articles. USA Today claimed the following

Donald Trump’s victory dealt a devastating blow to the credibility of the nation’s leading pollsters, calling into question their mathematical models, assumptions and survey methods.

In most of the articles that were read by this author, the prevailing hypothesis was the accusation that the sample drawn from the population was not sufficient for predicting the final outcome of the 2016 presidential election. That is, the samples of participants polled did not reflect the final outcome. Thus, the pollsters were wrong. But they weren’t wrong.

The most likely explanation for why the polls appeared to have been wrong is because many in the mainstream media did not understand probability, i.e., mathematical statistics.

As Scott Adams argues in his book God’s Debris: A Thought Experiment, probability is a force of nature. And this argument is prescient and correct. The natural world, which the social world belongs to, is indeed probabilistic. And so the question to ask is, “What is probability?”

The best way to understand probability is not by its definition, but rather by its process.

If you were to flip a coin, you would have a 50 percent chance of getting heads or a 50 percent chance of getting tails. If you were to flip a coin again, you would have a 50 percent chance of getting heads or a 50 percent chance of getting tails. And finally, if you were to flip a coin a third time, you would once again have a 50 percent chance of getting heads or a 50 percent chance of getting tails. In other words, no matter how many times you toss a coin, you have a 50 percent chance of getting heads or 50 percent chance of getting heads.

This is the most simplistic example of a probabilistic system and explanation of probability.

Now scale this up to a pair of die, where each die has six sides. This example illustrates how probability can become very complex, very quickly. It becomes quite difficult, for example, to predict one two and one five when tossing two die. This is because a pair of die are a much more complex system than flipping a coin. And so what would be the odds of predicting two ones or two sixes?

There is a three percent chance that a roll will produce two ones or two sixes. What’s very interesting about this fact is that Donald J. Trump’s odds of winning were better than rolling two ones or two sixes, although two die are a much more simplistic system than that of predicting a presidential election. And so there are two important revelations from this reality of probability.

First, it was never the case that Donald J. Trump would not become the president of the United States. It was assumed he wouldn’t become president because many of the purveyors in the mainstream just didn’t understand how the polls worked. And second, the polls never suggested such an outcome, nor were they wrong. They suggested he probably wouldn’t win.

Some polls that were conducted by NBC/WSJ, ABC News, Fox News, and others measured who the participants would vote for on that very day. In no way did those polls predict what would happen on November 8th. That assumption was perpetuated by those, a good number of pundits in the mainstream media, who didn’t understand basic probability. In other words, they didn’t, at the very least, understand the coin flip experiment. Again, journalists are the purveyors of information so understanding basic probability is important, especially during a presidential election; and it is reasonable for the public to expect some sort of mathematical and scientific competency from journalists and pundits.

Other polls conducted were Nate Silver’s 538 and Princeton. In both cases, their polls were much more sophisticated. And in both cases, their polls were continuous projections based on mathematical statistics. And although 538 and Princeton were scientifically rigorous, at no point did they convey or pretend to convey a Clinton win with a 100 percent certainty. Rather, they conveyed she would more than likely win. And this was the case up until the night of the election. But as the conditions (the information in the system) changed during the evening of the election, their projections changed.

And so what happened? How did the pollsters get it so wrong?

To be frank, they didn’t get it wrong. As mentioned before, the first set of polls measured the current state of voters. But of course a poll is only as good as the methodological process – how the poll is conducted – and those who are able to understand and explain them. And the second set of polls forecasted the most likely outcome based on current information.

At no point was there a 100 percent chance of Clinton becoming president. 538 at times computed an 80 to 90 percent chance of her winning. But 80 never equaled 100, and it still doesn’t. What probably happened was the purveyors of information became convinced that she would win because the polls and projections so heavily favored her.

So then isn’t it 100 percent? No!

Just because a person flips a coin and it lands on heads one hundred times in a row doesn’t mean it will land heads on the hundred-and-first flip. And that’s the disturbing but yet beautiful and fascinating nature of probability. Heads one hundred times in a row, although extremely unlikely, can create overconfidence and an illusion of absolute certainty. This explanation best explains why the polls appeared to be so wrong. And this is the point.

We will never hear many in the mainstream media say they are ignorant of science or mathematics. That wouldn’t fit the media narrative. Besides, that would take some remnant of integrity and honesty to perform such an act, and acknowledgement of their own mathematical ignorance. And this is why statements like that of USA Today are so concerning. Their very statements perpetuate inaccurate information to the public.

Instead of asking questions like “What is a mathematical model? What is an assumption? And what survey methods did the pollsters and forecasters use?” and then forwarding that information to the readers, many mainstream outlets went straight to “Donald Trump won; the polls said Hillary Clinton would win. Therefore the polls were wrong.”

That’s the mathematical ignorance of the mainstream media.

Matt Johnson is a writer for The Systems Scientist, and a mathematical scientist. You can connect with him directly in the comments section, and follow him on Twitter or on Facebook