Is this a problem with commitment schemes?<p>I want a heads to come up. I add a couple of hacked members to the group, so there are 3 honest members, and lets say 3 coordinated dishonest members.<p>Everyone shares their commitment hash, and the dishonest members share their actual commitments amongst themselves. Once everyone has the commitment hashes, the 3 honest members broadcast their commitment. The three dishonest members now have everyone's commitments, but honest members only have other honest member commitments. Dishonest members compute the ultimate value - if it turns up heads, then they just share their commitments with everyone, and the final answer is heads.<p>If it turns up tails, then the dishonest members compute possible permutations of various dishonest members dropping out and never sending their commitments. So maybe if dishonest member 1 drops out, the resultant value from just the group of 5 would be heads. So dishonest member 2 and 3 share their commitments and dishonest member 1 goes offline.<p>So, this system will work when it is composed of only people you trust, but will not work when it may be composed of people you don't trust. And if you trust everyone in it, why go through this process in the first place? And if you decide that when someone drops out and doesn't share their commitment, you just have to rerun the algorithm, then you have just given a very easy way to give the dishonest people a way to spike your coin flipper, so that no one can ever get a value out of it, or the dishonest members can just keep dropping out until they encounter a round where the final value is determined to be heads.