If Eliezer wins, he gets 1 bit of epistemic credit. So e.g. if Eliezer and I used to get equal weight in a mixture of experts, now Eliezer should get 2x my weight. Conversely, if I win then I should get 1.1x his weight.
The second and third sentences do not follow from the first. I would update to more like 1.05x vs 1.005x (or ideally something more specific depending on more details than binary questions like “solved hardest” or “won gold,” eg among other nuances I’d update more if the bet resolved for Eliezer in 2022 vs 2025).
If you are asserting that observers should eg update from 1:1 to 2:1 toward Eliezer if he wins, that seems far too strong to me, particularly given that neither of you seems to have spent a great deal of effort on the IMO question, but I would be very interested to hear why you think we should update so much.
These numbers come from if each party were actually in a mixture of experts, or equivalently Kelly-betting their epistemic credit points on a prediction market. We might update less due to some combination of
other evidence we have about Paul and Eliezer is not independent with this
The bet is between Paul thinking for a few hours, and Eliezer thinking for a few hours. But what we really want to decide between is Paul’s model being right vs Eliezer’s model being right, and the bet is not perfect evidence of that.
Edit: now refers to footnote 2, see below.
The second and third sentences do not follow from the first. I would update to more like 1.05x vs 1.005x (or ideally something more specific depending on more details than binary questions like “solved hardest” or “won gold,” eg among other nuances I’d update more if the bet resolved for Eliezer in 2022 vs 2025).
If you are asserting that observers should eg update from 1:1 to 2:1 toward Eliezer if he wins, that seems far too strong to me, particularly given that neither of you seems to have spent a great deal of effort on the IMO question, but I would be very interested to hear why you think we should update so much.
These numbers come from if each party were actually in a mixture of experts, or equivalently Kelly-betting their epistemic credit points on a prediction market. We might update less due to some combination of
other evidence we have about Paul and Eliezer is not independent with this
The bet is between Paul thinking for a few hours, and Eliezer thinking for a few hours. But what we really want to decide between is Paul’s model being right vs Eliezer’s model being right, and the bet is not perfect evidence of that.
I don’t really think we have particularly careful views; it would be reasonable to not update very much.
ETA: I moved that text to a footnote since I basically agree that it’s unreasonable as a prescription.