Randomized in this case means the selection order can't be known a priori when prospective SH peers chose their ID.
So the whole issue is based on the ability of SH to choose their IDs? Let their ID be their number in the SH sequence. So the very first SH has ID=1, the one who registers after him ID=2 and so on.
And who decides who was 1, 2, 3?
You keep pushing the problem to the same problem all over again. I already told you this, but you refuse to listen. See quote of myself below.
There is no possible solution. This is why only Proof-of-Work is viable for achieving consensus.
Even if that solution didn't work out, there is no proof of this statement.
The proof is that the only way you get the necessary entropy is by having every peer compete to be first. Everyone other form of entropy has a point of failure that there is no decision,
the consensus is required ad infinitum at every point where you design it away to another point.
For how many more posts are you going to waste time talking in circles like a dog chasing his tail? You can't design away the problem of needing consensus on the order but no one can make that decision (without opening a point of failure that can be gamed).
I hear an echo:
I skipped the rest because it was all based on this.
I tried explaining this to him, but he adamantly refused to accept it. There is no point in arguing with him.
Because it is wrong as explained above.