There are two main ways to assign rewards to PoS consensus algorithm validators:
- Chain-based proof-of-stake algorithms that choose availability over consistency, and establish security in a way similar to proof-of-work algorithms.
- BFT-style proof-of-stake consensus algorithms that choose consistency over availability.
In chain-based proof-of-stake, the algorithm pseudo-randomly selects a validator during each time slot (e.g. every period of 10 seconds might be a time slot). It then assigns that validator the right to create a single block, and this block must point to some previous block (normally the block at the end of the previously longest chain), so over time most blocks converge into a single constantly growing chain.
Casper uses a hybrid model of chain-based and BFT consensus algorithm that prefers availability, but provides as much consistency as possible, and makes both on-chain applications and clients aware of the consistency guarantee’s strength at any given time.