Thank you. I have corrected the mistake.
The relationship between Lindy, Doomsday, and Copernicus is as follows:
This is brilliant!
I think we can actually do an explicit expected-utility and value-of-information calculation here:
Can I get the data please?
It just occurred to me that you don't actually need to convert the forecaster's odds to bits. You can just take the ceiling of the odds themselves:
Which is more useful for calibrating in the low-confidence range.
Additional note: BitBets is a proper scoring rule, but not strictly proper. If you round report odds which are rounded up to the next power of two you will achieve the same scores in expectation.
Thanks for the insightful comments.One other thought I've had in this area is "auctioning" predictions, so that whoever is willing to assign the most bits of confidence to their prediction (the highest "bitter") gets exclusive payoffs. I'm not sure what this would be useful for though. Maybe you award a contract for some really important task to whoever is most confident they will be able to fulfill the contract.
Let me know if you do. I'd be keen to help!