One-fifth of Americans what?

As you probably know, there’s a (US presidential) election soon.   And there are a whole bunch of people who are predicting the probability that each candidate will win.  But as Nathan Collins has pointed out at Pacific Standardone-fifth of Americans can’t understand election predictions.

My first reaction, upon seeing this, was to think that one-fifth of Americans don’t understand what “one-fifth” means.  (I had just recently come across the old idea that Americans didn’t want a third-pound burger because they thought it was smaller than a quarter-pound burger, so I was primed to think this.)  But of course that’s too meta.

What this really is saying is that people mistake a result from one of these models like “Clinton has a 65% chance of winning the election” for “Clinton will get 65% of the vote”.   I don’t know if there’s direct evidence for this, but:

  • people have trouble interpreting, say, weather forecasts which give a probability of rain.
  • I actually made this mistake a few nights ago when listening to the FiveThirtyEight elections podcast.  For a brief moment I heard “Clinton has a 65 percent chance of winning according to our model”, thought it meant that Clinton had 65 percent of the vote, was happy, then realized that that was inconsistent with the way I’ve been feeling about the election and went back to remembering that Clinton was just a two-to-one favorite.

And if I can make that mistake, surely people who don’t have training in probability can. These examples are actually more similar than you might think: a 30% chance of rain means that there’s a 30% chance that somewhere in the forecast area there will be at least some cutoff amount of rain. Both are the case that some random variable (the difference between the two candidate’s vote percentage, the maximum amount of rain over an area) ends up over some cutoff. And complicated random variables such as these are surely hard to reason about.

Also, probabilities are used as rhetorical devices, not just pure numbers.  On Morning Joe just before the 2012 election, Joe Scarborough said:

Nate Silver says this is a 73.6 percent chance that the president is going to win? Nobody in that campaign thinks they have a 73 percent chance — they think they have a 50.1 percent chance of winning. And you talk to the Romney people, it’s the same thing […] Both sides understand that it is close, and it could go either way. And anybody that thinks that this race is anything but a tossup right now is such an ideologue, they should be kept away from typewriters, computers, laptops and microphones for the next 10 days, because they’re jokes.

What I think Scarborough intended to says here is that everyone in both campaigns acted as if they had a 50.1 percent chance of winning, i. e. they were the favorites to win but by a tiny margin. If you think someone is just on your tail that keeps you motivated. But at that time Obama did have a slight lead in the polls, and therefore was more likely to win the election. (Modulo polling errors, electoral college math…)

Oh, and go vote. But really you didn’t need me to tell you that.

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