by **Flannel Jesus** » Fri Jul 29, 2022 2:16 pm

There's a mathematical relationship between "we disagree on the probability of this event" and "there's a bet we can make where we both have positive expected value."

What you've offered there is a bet that gives me positive expected value, and you've willingly accepted negative expected value. So, yes, I would agree to that bet, but you're making the bet DESPITE our agreement, despite what you think about the actual probabilities, not because of them.

Obviously if you're making irrational decisions on bets that will benefit me, I'm happy to take the bet.

The "disagreement" requirement is under the assumption that you're also behaving rationally, and you're also only interested in bets that you think have positive expected value.

So you're right, pedantically, that I don't strictly require disagreement - irrational bets on your part can override the mandate that we disagree.