I was sent a copy of “Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present,” by George Szpiro. It’s an interesting book that I think a lot of people will like, going over a bunch of voting paradoxes in the context of historical stories. Some of the topics (Arrow’s theorem and its recent refinements) are more interesting than others (the always nauseatingly boring (to me) of the “Alabama paradox” and various rules about which states get one extra House seat; for some reason people are always writing about this topic about which I could care less). But you can pick and choose among the chapters, so unevenness isn’t really such a problem.

One thing that fascinates me about the topic of mathematics and representation is how many different ways there are to look at it.

In 2002, I published a paper in Chance called Voting, Fairness, and Political Representation (here’s a preprint version; it later appeared, slightly revised, as a chapter in our Quantitative Tour of the Social Sciences book), and what’s striking is that there’s zero overlap between my article and Szpiro’s book. And somebody else could probably write another article on the same topic with zero overlap with both of ours.

My article on voting and fairness grew out of a talk I gave in 2000 to the Lifelong Learners, a program at Columbia where retired people can come and hear university lectures. The audience was just great–much better than any college class I’ve taught. They asked lots of good questions and offered thoughtful comments. And . . . at one point I offhandedly used the old joke, “How much is a congressman worth? If you have to ask, you can’t afford one.” To which a lady in the audience stood up and said that her late husband had been a congressman for 20 years and had served with honor, and she didn’t appreciate that sort of remark. I felt really bad and I apologized. Then later in the talk, I offhandedly referred to some districts as so partisan that they’d vote for a dead guy if he was running on the Democratic ticket. . . . I couldn’t believe I said that, and I was afraid to look at the woman who’d spoken up earlier. I just hope she didn’t take that remark the wrong way. We’re so used to joking about the things we work on, day after day, that sometimes we don’t catch what we’re saying.