Nothing at stake problem
Blockchain is based upon incentivizing actors to behave correctly. More profitable to behave than misbehave
When presented with divergent chains, a PoS block creator has no incentive to only build their block on one of them. Longest chain rule means that the "accepted" one could potentially switch at any time
In fact, they're incentivized to build on any and all divergent chains. Creating a block carries a reward. If their chosen chain is beat out by another version, they lose their reward
Key points
Blockchain is based on incentives: In Blockchain, there is no central authority that enforces ethical behavior. Instead, the system is designed to make it more profitable to do good things than to not do them.
Block rewards: Miners or validators in the Blockchain ecosystem are rewarded for their efforts in creating blocks. It is more profitable to create legitimate blocks than fraudulent ones.
The nothing at stake problem: In a proof of stake system, block creators may be presented with two different versions of the Blockchain. Without protection against the nothing at stake problem, they are incentivized to build on both chains to ensure they don't lose their block rewards.
Misaligned incentives: The nothing at stake problem can lead to misaligned incentives. For example, if someone is performing a long-range attack, they may convince others to build on their malicious chain to avoid losing rewards on the legitimate chain.
Protecting against the nothing at stake problem: Proof of stake systems can be designed to protect against the nothing at stake problem by implementing mechanisms to penalize those who engage in such behavior.
Default behavior: By default, proof of stake systems have the issue of incentivizing participants to back every chain to ensure they receive their rewards.
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