Weighted by credence means you’re scored on Probability*Prediction, which isn’t a fair rule. If I sincerely believe its 60:40 between two options, and I write that down, I expect 36+16=52 payout, but if I write 100:0 I expect 60+0=60 payout, putting more credence on higher probability outcomes gets me more money even in excess of my true beliefs.
Weighted by credence means you’re scored on Probability*Prediction, which isn’t a fair rule.
If I sincerely believe its 60:40 between two options, and I write that down, I expect 36+16=52 payout, but if I write 100:0 I expect 60+0=60 payout, putting more credence on higher probability outcomes gets me more money even in excess of my true beliefs.