What is the nothing-at-stake problem in proof-of-stake?

The nothing-at-stake problem is a vulnerability in proof-of-stake (PoS) systems where validators can cheaply sign competing chain forks at the same time. In PoS, validators confirm transactions by locking up cryptocurrency rather than doing computational work. Because endorsing an alternative version of history costs them almost nothing, validators have little incentive to commit to one chain — they can hedge their bets by voting for multiple conflicting histories simultaneously. This matters for beginners because it means PoS networks must layer on extra rules just to discourage this behavior, while proof-of-work prevents it by making any competing fork expensive in real energy.