Probability Theory 101

Gregg Easterbrook:

 

Gingrich is a wild card. He probably would end up a flaming wreckage in electoral terms, but there’s a chance he could become seen as the man unafraid to bring sweeping change to an ossified Washington, D.C. There’s perhaps a 90 percent likelihood Obama would wipe the floor with Gingrich, versus a 10 percent likelihood Gingrich would stage an historic upset.

 

This is the dumbest thing I’ve seen since . . . ummm, I dunno, how bout this? It actually gets worse because Easterbrook then invokes game theory. What next? Catastrophe theory? Intelligent design?

P.S. Maybe I should explain for readers without an education in probability theory. Let’s suppose “wipe the floor” means that Obama gets 55%+ of the two-party vote, and let’s suppose that “an historic upset” means that Obama gets less than 50% of the vote. Now try to draw a forecast distribution that has 90% of its probability above 0.55 and 10% of it’s probability below 0.50. It’s a pretty weird-looking distribution, huh?

I will publicly offer Easterbrook a bet, conditional on Gingrich getting the nomination, that Obama receives between 50% and 55% of the two-party vote. My bet is based on Easterbrook’s implicit odds of infinity to 1. To keep it simple, I’ll set up the bet as follows: if Gingrich gets the nomination and Obama receives between 50% and 55% of the vote, Easterbrook gives me $1000. If Gingrich gets the nomination and Obama receives more than 55% or less than 50% of the vote, I give Easterbrook $0. That sounds fair to me!

A good classroom example, maybe? In statistics, political science, or journalism. (In the latter, it could be part of the ever-popular class on “How to get paid for writing about something you know nothing about.”)

P.P.S. To clarify (for the first commenter below and perhaps others) why I wasted my time writing about this: Political reporting is important, and I have every reason to believe it affects how people think about politics. A bit of innumeracy in reporting is perhaps unavoidable—-after all, Easterbrook is a journalist, not a scientist—-but I still like to do my part and point out the gross innumeracies I happen to come across. Also, Easterbrook is an interesting target because he’s a political centrist (I guess I’d characterize him as slightly center-left in the U.S. political spectrum), so it’s harder to imagine his errors arising from simple bias.

P.P.P.S. And, no, I don’t think that Easterbrook was simply stating in a dramatic way that he thinks that Obama would have a 90% chance of beating Gingrich. For one thing, the terms “flaming wreckage in electoral terms” and “wipe the floor” suggest a non-close election. For another, Easterbrook explicitly makes a variance argument, writing, “In an Obama-Gingrich race, practically anything could happen.” Finally, Easterbrook writes, “If I am Barack Obama, I want to run against Mitt Romney,” thus implying that Obama’s chance of winning against Romney is morethan 90%. That’s a 9:1 bet that I’d take. But Easterbrook doesn’t have to bet me on this one—-he can go straight to Intrade, which currently has Romney with a 33% chance of being elected president in 2012, unconditional on the results of the Republican nomination. (Earlier, Easterbrook implies that running against Gingrich would “maximize [Obama’s] chance of a huge victory,” while running against Romney would “minimize his chance of a stinging defeat.” Put the numbers together and you get that Easterbrook thinks that Obama’s chance of beating Romney is greater than his chance of beating Gingrich, thus more than 90%.)

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