Similar to this existing question that was closed due to lack of detail, I want to figure out a way for $n$ players to agree on a randomly generated ordering of themselves where they only know their own position in the order.
For example, starting with a set of players consisting of Alice, Bob, and Charlie.
A random ordering might look like:
[Alice, Charlie, Bob]
Where Alice only knows $0$, Charlie only knows $1$, and Bob only knows $2$.
There is no restrictions on the type of calculations used, other than that there is no centralised source of truth, so it must be done on the consensus of the group.
Players can be considered semi-honest, in that they will cooperate with the algorithm, but will work backwards to figure out the positions of other players if it's possible.
I may I have found a potential solution in "Mental Poker", in that this is a subset of that problem where $n$ players have $n$ cards and each draw 1. If anyone can confirm or deny the viability of this please let me know.
