The main difference between Polygon's PoS system and that of others is that Polygon is not a Layer 1 platform, and it depends on Ethereum as a Layer-1 settlement layer. Therefore, all staking mechanics also need to be in sync with the Ethereum chain smart contracts.
Proposers for a checkpoint are initially selected via Tendermint’s weighted round-robin algorithm. A further custom check is implemented based on checkpoint submission success. This allows the Polygon system to decouple with Tendermint proposer selection and provides it with abilities like selecting a proposer only when the checkpoint transaction on the Ethereum mainnet succeeds or submitting a checkpoint transaction for previously blocks belonging to failed previous checkpoints.
Successfully submitting a checkpoint on Tendermint is a 2-phase commit process; a proposer, selected via the above-mentioned algorithm, sends a checkpoint with his address in the proposer field and all other proposers validate that before adding it in their state.
The next proposer then sends an acknowledgment transaction to prove that the previous checkpoint transaction has succeeded in the Ethereum mainnet. Every Validator set change will be relayed by the Validators node on Heimdall which is embedded onto the validator node. This allows Heimdall to remain in sync with the Polygon contract state on the Ethereum mainchain at all times.
The Polygon contract deployed on the mainchain is considered to be the ultimate source of truth, and therefore all validation is done via querying the mainchain contract.