Thinking about this makes me think people should record not just their bets, but the probabilities. If I think the probability is 1% and you think it’s 99%, then one of us is going to make a fairly big update. If you think it’s 60% and I think it’s 50%, yeah, not so much. As a rough rule of thumb, anyway. (Obviously I could be super confident in a 1% estimate in a similar way to how you describe being super confident in a 40%.)
But OTOH I think in many cases, by the time the bet is resolved there will also be a lot of other relevant evidence which determines questions related to a bet. So the warranted update will actually be much larger than would be justified just the one piece of information. In other words, if two Bayesians have different world-models and make a bet about something much into the future, by the time the actual bet is resolved they’ll often have seen much more decisive evidence deciding between the two models (not necessarily in the same direction as the bet gets decided).
Thinking about this makes me think people should record not just their bets, but the probabilities. If I think the probability is 1% and you think it’s 99%, then one of us is going to make a fairly big update. If you think it’s 60% and I think it’s 50%, yeah, not so much. As a rough rule of thumb, anyway. (Obviously I could be super confident in a 1% estimate in a similar way to how you describe being super confident in a 40%.)
But OTOH I think in many cases, by the time the bet is resolved there will also be a lot of other relevant evidence which determines questions related to a bet. So the warranted update will actually be much larger than would be justified just the one piece of information. In other words, if two Bayesians have different world-models and make a bet about something much into the future, by the time the actual bet is resolved they’ll often have seen much more decisive evidence deciding between the two models (not necessarily in the same direction as the bet gets decided).
Still, yeah, I agree with your concern.