blockchain is just a tamper resistant method of distributing batches of new transactions in a distributed database
most of them use Practical Byzantine Fault Tolerance, a random selection process by which a limited set of servers (replicas) are assigned to be the authoritative source for that period (block or epoch)
most of them defraud their users by saying that proof of stake is anything other than a way to cap the number of nodes that can be selected as authoritative sources for a block
pBFT is perfect for a consortium of individuals or organisations to participating keeping a database as a group, with the limitation that if more than 1/3 of the participants are trying to change the record that the integrity of the database is broken
bitcoin does the leader selection with a random selection that is decentralized, ie, you don't need to make any agreement or trust anyone, by using partial hash collision searches - the reason why there can be only one chain like this is because another chain with a smaller value (incentive) than the main one is able to be plundered by those mining on the main one
this goes back to the right to issue tokens - once the chain has no token issuance in the consensus you can do such a consensus without risk of a secondary chain plundering yours
or in other words, if you could make a fair distribution without including it in the consensus you could make a PoW monetary ledger, but that's the whole point of the reward - to create a random distribution that is what is the REAL proof of stake - ie, you slapped down your cash and sacrificed to buy miners and you are thus committed to a ROI or you are an idiot
i'm sure the rest of the scam is clear once you grasp all that