The birthday problem and voter fraud

I was traveling at the end of last week, which means I had some time to listen to podcasts while in transit. This American Life is always a hit for me, though sometimes I can’t listen to it in public because the stories can be too sad, and then I get all teary eyed in airports…

This past week’s was both fun and informative though. I’m talking about Episode 630: Things I Mean to Know. This post is about a specific segment of this episode: Fraud Complex. You can listen to it here, and here is the description:


We’ve all heard reports that voter fraud isn’t real. But how do we know that’s true? David Kestenbaum went on a quest to find out if someone had actually put in the work—and run the numbers—to know for certain. (17 minutes)
Source: TAL – Episode 630: Things I Mean to Know – Act One – Fraud Complex

The segment discusses a specific type of voter fraud, double voting. David Kestenbaum interviews Sharad Goel (Stanford University) for the piece, and they discuss this paper of his. Specifically, there is a discussion of the birthday problem in there. If you’re not familiar with the birthday problem, see here. Basically, it concerns the probability that, in a set of randomly chosen people, some pair of them will have the same birthday. The episode walks through applying the same logic used to solve this problem to calculate probability of having people with the same name and birthdate on voter records. However it turns out the simple calculation assuming uniform distribution of births over the year does a poor job at estimating this probability because of reasons like people born in certain times of the year to be more likely to be named a certain way (e.g. June for babies born in June, Autumn for babies born in fall, etc.). I won’t tell the whole story, because the producers of the show do a much better job at telling it.

If you’re teaching probability, or discussing the birthday problem in any way in your class, I highly recommend you have your students listen to this segment. It’s a wonderful application, and I think interesting applications tend to be hard to come by in probability theory courses.