this post was submitted on 17 May 2024
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It doesn't have to be addition. It could be a hash function, etc.
The last person would still decide the outcome. They could keep choosing values for whatever function until it produces their desired result and then post that.
What you would want instead is for everyone to post a (salted) hash, and after the hashes are posted, reveal what the original numbers were and then publicly add them. Everyone could verify everyone else's numbers against those hashes.
Could you do it in 2 phases? First, everyone selects a random partner and exchanges their random number. Each pair then has a result that is locked in. Then everyone submits their result to be summed up as already suggested (Pos/neg = heads/tails).
If there are an uneven number of players, then one player makes a three-some.
If the function is known by all parties then the last person to send still has control