In addition to what the others said: if you try to cheat in a proof-of-stake system, your stake is forfeited. Which is kinda the whole point: if someone wants t

In addition to what the others said: if you try to cheat in a proof-of-stake system, your stake is forfeited. Which is kinda the whole point: if someone wants to make a double spent / revert a transaction and gets caught, his stake is destroyed and all the people helping him to try to do his double-spent have their stake destroyed to. The one issue is "long range attacks": where someone creates a fake chain and then tries to substitute it for the real-chain. In a PoW model you need more PoW than the real chain to mount your attack: that's how PoW chains are protected. In a PoS model not so much. But Vitalik Buterin (the Ethereum creator) and a few others are pretty sure they've got a working proof-of-stake system. Time will tell: expensive experiment ongoing!