Steven Levitt says that he has a “good indicator” that Aaron Edlin, Noah Kaplan, Nate Silver, and I are “not so smart”

by Andrew Gelman on October 25, 2012 · 47 comments

in Campaigns and elections,Methodology

Here’s the transcript (link from here):

DUBNER: So Levitt, how can you in your life, when you wander around, tell the difference between a smart person and a not-so-smart person?

LEVITT: Well, one good indicator of a person who’s not so smart is if they vote in a presidential election because they think their vote might actually decide which candidate wins. . . . there has never been and there never will be a vote cast in a presidential election that could possibly be decisive.

In Illinois in 2012, sure, I don’t think there’s any chance that a single vote, or any thousand votes, could determine the presidential election. So I’m with Levitt regarding his particular vote in his state. In swing states (or for close non-presidential elections), though, it’s a different story Aaron, Nate, and I have estimated the probability of your vote being decisive in a swing state as being in the range 1 in a million to 1 in 10 million. Low, but not zero, and Aaron, Noah, and I argue that it can be make sense to vote because of the social benefits that a voter might feel arise from his or her preferred candidate winning.

I have no problem if Levitt wants to argue that it doesn’t matter who wins the election—-I disagree with him, given the evidence that the positions of the Democratic and Republicans in the U.S. are farther apart on economic issues than are left and right groupings in many other countries, but Levitt can make that argument if he wants to. And I have no problem if Levitt wants to say that, for a one in a million or one in ten million chance, he doesn’t think it’s worth it to vote. As Aaron, Noah, and I write, we think of such a vote as equivalent to the purchase of a lottery ticket which, if it wins, corresponds to a huge donation to a charity—-but I realize that not everyone will agree with this. But I don’t think Levitt is making sense when he writes that “there never will be a vote cast in a presidential election that could possibly be decisive.” A low probability is not a zero probability.

Levitt follows up:

And one thing we see for sure, and we saw it in the Gore versus Bush election is that if it’s even within thousands of votes it’s not the votes themselves that decide the election, because nobody can figure out how many votes were cast. It’s the courts that always decide, the judges that always decide. It’s virtually impossible that any vote you cast in a national election could ever actually be decisive.

This reflects a common misunderstanding and probability and uncertainty. At a purely technical level, it’s not true that litigation of elections means that a single vote can’t matter. Most elections are not litigated, and your vote can be the one that makes the election close enough to send it to the courts. Under any reasonable model, the probability that your vote determines the election is the same whether or not the courts are involved, and you can show this by adding up the probability of any vote margin being decisive. For a mathematical derivation, see page 674 of our article in the British Journal of Political Science.

This confuses a lot of people, so I can understand Levitt missing the point, but it’s important. Just cos you don’t know whether a particular vote was decisive, that doesn’t mean a single vote can’t be decisive. Or, to put it another way, when he says “virtually impossible,” I’d say “1 in a million to 1 in 10 million if you live in a swing state.” Levitt’s statement, “It’s the courts that always decide, the judges that always decide,” misses the point in that your vote can be the one that triggers the recount or that sends the case to the courts.

Levitt also says:

If anything I think you want to go in the other direction and find ways to let people who care a lot vote repeatedly. That’s really more in the spirit of trying to get to the right answer. That way you get the people who have the strongest convictions acting most aggressively to express those convictions.

I don’t know if this will make Levitt feel any better, but this is the system we currently have in the United States! We have lots and lots of elections, with relatively high turnout (60%) in presidential elections, lower for governors and congress, still lower for state legislators and local elections, etc. Indeed, people who care more about politics do get to vote “repeatedly,” while people who are more indifferent can vote never or only occasionally. I’d never thought of this as a feature of our electoral system but I suppose it is.

P.S. I would not conclude from the above discussion that Levitt is not so smart. Of course he’s very smart, he just happens to be misinformed on this issue. I applaud Levitt’s willingness to go out on a limb and say controversial things in a podcast, to get people thinking. I just wish he’d be a bit less sure of himself and not go around saying that he thinks that Aaron, Noah, Nate and I are not so smart.

P.P.S. I live in New York, so, like Levitt, I don’t think my vote has any chance of making a difference in the presidential election. But if I were voting in a swing state, that would be a different story.

P.P.P.S. Yes, this has come up before.

P.P.P.P.S. The linked podcast also includes some very reasonable comments by Bryan Caplan on the motivations of politicians trying to get the support of confused and ignorant voters.

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