He makes several errors here. First, in spite of what many economists say, it is not irrational to vote:
Despite what is sometimes said, voting is not particularly irrational as compared to other other social and political activities. Voting has low cost and a very small chance of making a difference, but in that unlikely event, the difference can have huge repercussions nationally and globally; hence, the expected return from voting is arguably on the same order of magnitude as its cost (see Parfit, 1984, and Edlin, Gelman, and Kaplan, 2007).Second, Obama's intellect and eloquence are not particularly unusual even among Levitt's fellow professors. Levitt is a big-shot tenured professor at the U. of Chicago, while Obama was a lowly untenured lectured with no significant academic publications or accomplishments. His biggest such accomplishment is his autobiography, but I am persuaded by Jack Cashill that it was largely ghostwritten. (But see a contrasting view here and here.)
I don't know how anyone could think that Obama is an impressive speaker, unless he has not heard good public speakers. Just try attending a local public speaking competition, and you will see speakers that are so much better than Obama that it is not funny. They give smooth convincing entertaining speeches with no notes, and they Obama look like an amateur with his stilted reading of a Teleprompter script.
At least Levitt is willing to admit that he was wrong. I'll give him credit for that.