2 examples of multiparty games of choosing random numbers:
1)
You and I each write either "1" or "0" onto a piece of paper, and simultaneously reveal to each other.
If the sum is even, I win. If the sum is odd, you win.
This simple 2-person game randomly generates 1 bit. It can be extended to arbitrary numbers of people by replacing addition with XOR.
2)
N people each vote either "0" or "1". They reveal votes simultaneous. The minority participants are rewarded. The median of the votes is the next random bit.
Yeah, these work great out of consensus systems. Please consider that you're working on a consensus system though.
"Simultaneous" has no meaning. There are no means of instant communication, there is latency. There also is no proof of time without a consensus system.
So what is the proof that I committed my 0 or 1 value before they revealed? Well you could trust a central authority to maintain that timestamping, or you could even use Bitcoin for your timestamping. In fact, your PoS system could probably work if it piggy backed on Bitcoin completely.
If that's too abstract for you, consider that I say I'm ready to commit, everyone sends me their commits, I construct a block with all their commits and a ton of other possible commits and then once I have created a seed that allows me to win and control the network permenantly.
After reflecting more on the difficulties of a random number generator on a consensus system, we decided to use round robin method to choose the next leader from the validators.
If the sum is even, I win. If the sum is odd, you win.
This simple 2-person game randomly generates 1 bit. It can be extended to arbitrary numbers of people by replacing addition with XOR.
2) N people each vote either "0" or "1". They reveal votes simultaneous. The minority participants are rewarded. The median of the votes is the next random bit.
I prefer (1) over (2).