No, Bayes does not like Mayor Pete. (Pitfalls of using implied betting market odds to estimate electability.)

This one’s from 2019, but it’s worth reposting given recent interest in prediction markets. The story starts with a post from economist Greg Mankiw, who wrote: Who has the best chance of beating Donald Trump? A clue can be found using Bayes Theorem. Here is the logic. Let A be the event that a candidate wins the general election, and B be the event that a candidate wins his or her party’s nomination. Predictit gives us the betting market’s view of P(A) and P(B). It is a safe assumption that P(B|A) = 1, that is, a candidate can win only if nominated. We can then use Bayes theorem to compute P(A|B), the probability that the candidate will win the general election conditional on being nominated. So here are the results for P(A|B) as of now: Buttigieg 0.80 Biden 0.77 O’Rourke 0.67 Sanders 0.65 Booker 0.60 Yang 0.60 Harris 0.57 Warren 0.44 That is, the betting markets suggest that Mayor Pete would be the strongest candidate if nominated, with Joe Biden close behind. (Of course, these…