Five days from when this essay airs, something nearly unimaginable will happen. Either we will see the end of a couple of years in which the name “Trump” has popped up seemingly every few minutes. Or we will begin at least four years in which the name “Trump” will be even more part of our consciousness than it already is.
We’re talking about Donald Trump and the US presidential election, of course.
As always, a slew of opinion polls try to capture the state of this endless campaign. Hillary Clinton has been consistently ahead—though who knows what havoc her email imbroglio will wreak. In any case, each poll warns of its “margin of error”.
Clinton’s lead has generally stayed within those margins, or just beyond them. So it’s possible that on 8 November, Trump will defy the polls and actually win.
Possible, but not probable. That’s the case that Nate Silver, of the famous FiveThirtyEight journal, has been making for months now. As I write this, FiveThirtyEight suggests there is a 86.3% chance that Clinton will win, compared with a 13.7% chance that Trump does.
Seems overwhelmingly as if Clinton will win this thing, right? Indeed, though even that can stand a closer look.
How did FiveThirtyEight come to this conclusion? That is, if a poll says Clinton has a four-point lead, what translates that to the 86.3% figure?
We know that the four-point lead reflects the opinion today of a small sample of voters. It’s not meant to suggest that Clinton will certainly win, and that too by four points. That, after all, is the caution of the margin of error. So yes, what does it mean to extrapolate from four points to a pretty high chance—86.3%—that she will win?
Think of an analogy here. I toss a coin once, it comes up tails, and I ask you what the chance of tails is the next time I toss. Would you assume that just because it came up tails once, it will do so every time, or even most of the time? I don’t think so. You’ve not seen anything to challenge your assumption that—like with every coin—there’s a 50% chance of it landing tails, 50% heads. So that’s how you’ll answer my question.
But let’s say I’ve been tossing the coin all day—hundreds and thousands of times. You’ve noticed that the coin shows tails about 75% of the time.
You naturally conclude that something is a little fishy about the coin. Asked, after watching me for several hours, what the chance of tails is on my next toss, you’ll likely say “75%”.
What’s the difference between the two situations above? Only the additional knowledge about the coin that you get from watching me toss it all day.
It sounds trivial to say it, but it is what you learn from watching that allows you to change your answer from 50% to 75%.
This notion of additional knowledge is, as you might expect, crucial to any calculation of probability. (It’s the basis of Bayes’ law, fundamental to probability calculations).
For example, let’s say I ask you what the chance is that my friend Kanakadurga will have cancer. You’ll probably look up some health statistics, find that one in every 100 people in the world (say) eventually gets cancer, and tell me “1%”.
But what if I now inform you that Kanakadurga is 75 years old?
This additional knowledge sends you scurrying back to your statistics, where you learn that of people 75 or older, one in every 50 get cancer. So with that new information, you revise your estimate to “2%”.
Similarly, every bit of additional knowledge I give you about Kanakadurga—her health, her family history, her surroundings—will change that estimate. You might find still more reason to revise if I tell you that tests on women older than 75 produce false answers 10% of the time.
In much the same way, FiveThirtyEight relies not just on one poll that shows Clinton with a four-point lead over Trump. Instead, they know that several polls tell essentially the same story. Each poll that finds this gap increases the chance that Clinton will win.
Certainly there are some more intricate calculations that flesh out their predictive model, but this is essentially how FiveThirtyEight came up with their 86.3% estimate.
All routine stuff so far, really. But what’s particularly interesting is that other poll analysts have looked at the same data, done some different calculations, and concluded that Clinton has an even greater chance of winning than FiveThirtyEight’s 86.3%.
Last week The Huffington Post, for one example, put it at 97.3%.
What is the real difference, you may wonder, between 86.3% and 97.3%?
After all, if you’re a Clinton fan, you’d be mightily encouraged by either of those numbers. Both indicate pretty high odds that we’ll see her as the President of the US.
True, but the best way to give those numbers perspective is to ask what they say about Trump. According to The Huffington Post, his chance of winning is just 2.7%. According to FiveThirtyEight, his chance is 13.7%.
In other words, FiveThirtyEight thinks a Trump victory is five times as likely as The Huffington Post does.
So if you’re a Trump fan, there’s a good chance you’re a FiveThirtyEight fan too.
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter of Numbers explores the joy of mathematics, with occasional forays into other sciences.
Comments are welcome at firstname.lastname@example.org.Read Dilip’s Mint columns at www.livemint.com/dilipdsouza