On Polling: Approval and Probability – or – Now I Understand How Trump Bankrupted His Own Casinos

On Polling: Approval and Probability – or – Now I Understand How Trump Bankrupted His Own Casinos

Sunday morning, Donald Trump tweeted something that may have been accidentally revealing about why he doesn’t believe that he is as unpopular as he is, and why his fans don’t either. Trump tweeted that in an ABC/WaPo poll he had “almost 40% [favorability],” that this wasn’t bad, and that the same poll was inaccurate during the election. There are three basic problems with the statement in this tweet, which I should remind you is, according to the White House, an official statement from the president. These problems are: a) Trump has only a 36% approval rating, b) Approval ratings are not predictions about the future, but are snapshots in time, and c) Predictions are based on probability, which is by how much something is likely to happen.

Let’s start with the first and second points, Trump’s “almost 40% at this time.” For starters, he is sort of correct in that 36 does round up to 40. However, it isn’t 40, and that’s an important distinction to make when counting the approval rating of the President of the United States. Ignoring the more humorous talking point that 36 rounds up to 40, and 40 is almost 50, and 50 rounds up to 100; there is a significant difference between 36 and 40. 36% is just over a third of the country. This is really only about the amount of support that Trump ever really had during the primaries. This suggests that his base hasn’t really grown since he took office. On the contrary, his support appears to have shrunk dramatically since the election.

During the election, Trump was running against Hillary Clinton, who is a rather divisive figure in her own right. It has been speculated that a great deal of Trump’s voters in the general election never really supported him that much, but would never vote for Clinton, a Democrat, or both. Indeed, Clinton lost the support of many Obama voters, and some of them did vote for Trump, but it remains unclear if that was because they genuinely liked him, or they just really didn’t like her. Clinton also lost support of many progressive liberals who opted to either vote for Jill Stein or just not vote at all. Trump not only famously lost the popular vote by the largest margin in history, but in total vote share of eligible voters, it would appear that he even lost support of Republicans and more conservative voters.

As a percentage of vote share, he won a smaller percentage than Mitt Romney. In the final tally of votes, Trump won about 46% of the vote, to Clinton’s 48% (Incidentally, if the election was decided on a popular vote, neither of the candidates would have had a majority, which is one reason why switching to such a measure would almost surely require either only two parties, or a runoff voting system, which would, at least for the foreseeable future further entrench the two major parties). If we interpret the percentage of the vote share as indicative of his support, Trump has lost 10% of the voters since taking office. This isn’t entirely unusual in the long run. In fact, most presidents lose popular support the longer they are in office. What is unusual however, is that Trump had no honeymoon period. Most presidents do take office with over 50% approval and enjoy somewhere around that number for a few months, and in some cases a few years. Trump is different in that he is the first president since the Truman administration, when tracking began, to take office with less than 50% approval. If the trends hold true, and there is no reason to believe that they won’t, Trump’s approval rating will likely continue to slide. Yes, approval ratings rise and fall, but with the exceptions of Ronald Reagan and Bill Clinton, no president since World War II has left office with a higher approval rating than when he came in.

To put this into perspective, Nixon had a higher approval rating after the Watergate story first broke than Trump did when he took office. Carter had an approval rating when he left office that was only 2 percentage points lower than where Trump is today, 170 days into his term. Simply put, “almost” 40% is bad for any president, it’s especially bad “at this time.” Most of this, too, is Trump’s fault. He ran a divisive campaign. He has insulted his critics. He has labelled the press as the “enemy of the people.” He has neither signed nor seriously pursued any major legislation. He has spent roughly 30% of his time in office (52 days out of 170) on vacation at his own properties to his financial benefit. He has behaved poorly on the world stage. He continues to show that he is not up to the job. And, perhaps most damning, he has suggested that Constitutional checks and balances should be removed and attacked private citizens. Further, he has shown no actual interest in doing his job, learning about his job, or any attempts to get better or take it seriously. In a nutshell, he has been disliked by nearly two-thirds of the country since he announced he was running, and remains there, largely due to his own actions.

Now to where the second and third point overlap. Approval ratings are snapshots in time and they do not necessarily predict the future, though they can be used to do just that. For instance, if we know that someone is disliked by two-thirds of the country, it’s probably not likely that that person would a presidential election. However, just because on day X of an election cycle a candidate is unpopular, it does not mean that they will not win an election. That candidate might have a low probability of winning, but it is still possible that they will win. Probability of a future event is not the same thing as a current public opinion about a particular individual.

Trump has, since the primaries, spent much of his time trying to undermine the faith that people have in opinion polling. He’s done a good job of it, too; at least in so far as the people that like him believe him, and refuse to believe that other people do not. However, he has deliberately confused, and caused confusion, about the differences between an opinion poll and a probability based on statistics. I say that Trump has deliberately confused these points because I am going to take him at his word that he is “like a smart person.”

Popularity and probability are not the same thing, and never have been. This is somewhat similar to the point that correlation does not equal causation. Just because two things happen at similar times does not mean that they are related. For instance, the number of films that Nicolas Cage stars in in any given year is highly correlated with the number of people that will die in a drowning in that same year. The more films starring Nicolas Cage, the more people die from drowning. It would, of course, be ridiculous to assert that these are somehow related, that Nicolas Cage movies cause people to drown by the hundreds. Nonetheless, they are correlated.

Similarly, it cannot be accepted as a given that an unpopular candidate will not win an election. There are many factors to consider. First and foremost is voter turnout. If a candidate is incredibly unpopular, it is likely that a large share of the voters will not vote, thinking that the result is inevitable, and then they are surprised. This gets even murkier when one considers how presidential elections are decided in the United States. California might have 100% turnout, but if middle America does as well, and half the voters stay home in Ohio and Michigan, the candidate who is less popular is likely to win. See: Donald Trump, 2016.

Further, probability is determined by how likely an outcome is expected to happen. If you flip a coin, for instance, you have a 50/50 shot of getting heads or tails. That is, you have the same 50% probability of getting heads as you do tails. It does not mean that you will always get heads, or that you will always get tails, or that each flip of the coin will be heads and then tails, in succession. There are only two outcomes, and there is only one way to reach the outcome. It is one or the other. Consider the weather. If the weatherman says that there is a 30% chance of rain, it does not mean that you will get no rain, or that you will only get rain 30% of the day, or that it is guaranteed to rain. What it means is that when given all the factors, and taking them all into consideration, that you have a chance of rain that is greater than no rain, and less than total rain. It might rain. You should pack an umbrella. But, it probably won’t and if you don’t, you might be ok, but there is still a chance.

As far as the 2016 election is concerned, Trump was not given favorable odds. It was not however, a guarantee that he would not win. Consider a game of chance at a gambler’s table. If you have an 80% chance of failure, there is a high likelihood that you will not win the game. It does not mean that you will never win the game, but that chances are you will lose. This type of thing is how casinos make their money. They generally operate games of chance so that the likelihood that the House loses is low – around 20%. Most of the time, the House will win and you will lose. However, if you keep playing, you might win. This is the same assumption that gamblers make. The same is true of lottery tickets.

With the weather and the gambling examples, your odds aren’t 50/50. Yes, it is true that it will either rain or it won’t, or that you will win or lose, but that’s not what that means. It means that you have specific chances of winning. In a roll of 100 lottery tickets, you might have 10% odds. That means that of all those 100 lottery tickets, only 10 of them are winners. In a weather scenario, 70% of the time that they ran the models they found that there was no rain event. In an election however, there is only one time that the event occurs. If someone has a 30% chance of winning the election, then 3 out of 10 times the models were ran, that person won. But we don’t get 10 elections, we get 1. Yes, Trump won, but that doesn’t mean that the probability was wrong. In fact, it doesn’t even mean what he, and his supporters often say: That the polls were wrong, or made up, or whatever else.

Trump was never given a 0% chance of winning. Indeed, as election day drew closer, his odds of winning were raised. At one point, several outlets calculated that he had about a 30% chance of winning. These are even better than Vegas odds.

The point of all this is that just because he had a low chance of winning, it does not now, nor did it ever mean that he wouldn’t win. It just meant that it wasn’t that likely. But just as it is not likely that you will win the jackpot on the first pull of a lever at a slot machine, it does happen. And Trump did win. This also has nothing to do with how popular he is or is not, currently, among the voters of the country. While it is true that he has around a third of the country that will seemingly support him no matter what, it does not mean that everyone supports him. Likewise, it does not mean that the fact that nearly two-thirds, and counting, of the country does not support him is fake news.

You might like Trump, and maybe all your friends do too. But that does not mean that everyone does. Conversely, you may despise Trump and so do all of your friends. That does not mean that everyone does. This is what is called a confirmation bias. The assumption that because I do, and so does everyone I know, therefore everyone does, and I will only listen to those who agree. Trump, and many of his supporters, appear to be stuck in this loop. Maybe it’s because they don’t understand the biases they deal with. Maybe it’s because they don’t understand the mathematical workings in opinion polling and how probability is figured. Maybe it’s because they don’t want to know. But, just because Trump thinks highly of himself does not mean that nearly two-thirds of the country does as well.

And, if this is how Trump understands probability, well that explains why he was able to bankrupt a series of casinos; an industry where people literally give you money on the assumption that they won’t get it, or anything else, in return.

Image Credit: Gallup Presidential Approval Center

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