Low Probability Events

It's no secret that politicians, political pundits, and political reporters are innumerate and scientifically illiterate. It's a job requirement.  Can't let those nasty old facts get in the way.  Joe Scarborough's famous attack on Nate Silver is just one of the most notable examples before the actual election results started coming in and the real meltdowns started:

Nate Silver says this is a 73.6% chance that the president's going to win. Nobody in that campaign thinks they have a 73.6% — they think they have a 50.1% chance of winning.

.... Anybody that thinks that this race is anything but a tossup right now is such an ideologue [that] they should be kept away from typewriters, computers, laptops, and microphones for the next ten days, because they're jokes.

— Joe Scarborough, Morning Joe, 2012-10-29

So what's Joe doing here?  There's the obvious answer that everybody in the news media absolutely needs to see the election as a "horse race".  As long as it's a close race, they can keep everybody interested.  If everybody agrees that one side is going to win, folks lose interest.  The pundits, not having facts (which they can't recognize) or math (which they can't understand), fall back on "momentum" and "energy" and "excitement" and other things that can't really be quantified.  Journalists -- want to cause a panic?  Force a politician to put a number on something.  And follow up on it.

What I suspect he's doing (other than supporting his favorite candidate, of course) is making a very common error. He's assuming that, since there are only two possible outcomes, that each has a "probability" of 50%. After all, it has to be one or the other.  That's not how it works.

Let's use a gambling example.  (After all, probability theory was originally developed to calculate gambling odds.) Assume we have a roulette wheel, but instead of the standard layout we have 100 numbers that are either red or blue.  Let's say, so we have a number to think about, that there are 75 blue numbers and 25 red numbers.  Over a very large number of plays, red will come up 25% of the time and blue will come  up 75% of the time.  Basic probability.  We'd have no trouble saying that "blue has a 75% chance of winning."

However, we're going to introduce a problem — we're only going to play once.  Now, what's the probability of blue winning?  Well, nothing has changed — it's still 75%.  Let's change the question a bit:  Who is going to win, red or blue?  We can't say.  As long as there is at least one number for a color, it has a chance of winning.  It may be a small chance, but it's not zero.  If we have 99 blue numbers and one red number, we can't guarantee that blue will win.  After all, lightning does strike; somebody does win the lottery.

And of course, let's not forget the tinfoil hat explanation.  The fix was in; they had to make it look like Romney pulled off a not-completely-unexpected upset.