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gwern comments on The Yudkowsky Ambition Scale - Less Wrong
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I've been musing about the same sort of proof-of-work algorithm, but I haven't come up with a good actual system yet - there's no obvious way to decentralizedly get a guaranteed-hard new useful problem.
Interesting! I was actually inspired by some of your IRC comments.
I am thinking the problems would be produced by peers and assigned to one another using a provably random assignment scheme. When assigned a problem, each peer has the option to ignore or attempt to solve. If they choose ignore they are assigned another one. Each time this happens to a problem is treated by the network as evidence that the problem is a hard one. If someone solves a scored-as-hard problem, they get a better chance of winning the block. (This would be accomplished by appending the solution as a nonce in a bitcoin-like arrangement and setting the minimum difficulty based on the hardness ranking.)
Hm. It never occurred to me that provable randomness might be useful... As stated, I don't think your scheme works because of Sybil attacks: