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Elo comments on Open Thread August 31 - September 6 - Less Wrong Discussion
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My version of making this work would be choosing to only share limited information.
i.e. estimates of 33% heads. or estimates of >10% heads and >80% tails. Where they don't sum to 100%, and will be harder to work out the "unknown space" in the middle. Limiting the prediction set to partial information. Also playing with multiple people should make it more complicated. Also an optional number of coin flips (optional to the person flipping coins and unknown to others within parameters)