Your post is very well written, and I agree that the MMEU rule is wrong. That said...
Colloquial bets are offered by skeevy con artists who probably know something you don’t. Bayesian bets, on the other hand, are offered by nature.
The distinction seems a bit unclear, because skeevy con artists are also part of nature, and nature certainly knows something you don’t ;-)
Sometime ago I came up with a thought experiment that might make it clearer. Imagine that I flip a coin, look at the result, but don’t tell it to you. Then it’s rational for you to say that your probability of heads is 50%, but it’s not rational for you to make a standing offer to accept either side of the bet, because then I would just take your money. So I suppose “Bayesian bets” are bets whose outcome is independent from which side of the bet is offered to you, while “colloquial bets” are everything else. I’m not sure if most real-life bets are “Bayesian” or “colloquial”.
Your post is very well written, and I agree that the MMEU rule is wrong. That said...
The distinction seems a bit unclear, because skeevy con artists are also part of nature, and nature certainly knows something you don’t ;-)
Sometime ago I came up with a thought experiment that might make it clearer. Imagine that I flip a coin, look at the result, but don’t tell it to you. Then it’s rational for you to say that your probability of heads is 50%, but it’s not rational for you to make a standing offer to accept either side of the bet, because then I would just take your money. So I suppose “Bayesian bets” are bets whose outcome is independent from which side of the bet is offered to you, while “colloquial bets” are everything else. I’m not sure if most real-life bets are “Bayesian” or “colloquial”.