Elon's Fermi problem

Elon Musk posted a table on X claiming that enormous numbers of social security payments are being made fraudulently, as much as 83%. That seemed...excessive. I teach my students Enrico Fermi's technique for getting quick estimates, good enough numbers to help direct you toward a more accurate solution. Also great for detecting bullshit. Let's see how it works for Elon's claim!

One way to estimate roughly the number of social security recipients is to say everyone in the US over 65 collects it.  (Not true, but Fermi's approach says look at the big effects.)  In 2023 that was 59.2 million people. The Social Security Administration says that the average annual payment is $24,000. So that means we should pay out 59,200,000 x $24,000 a year. That's about $1.4 trillion. What did Social Security pay out in 2023? Its total budget was...wait for it..about $1.4 trillion. Just what you'd expect. So, BS, Elon.

This may be the biggest fraud ever, but I don't think the payments are the problem.