Nothing-at-stake problem

The heart of the problem is the cost difference with proof of work. In proof of work, betting on two forks splits physical compute power, a real cost. In naive proof of stake, signing blocks on several branches costs no more: the stake is the same and only adds voting weight. Without a penalty, the dominant strategy would be to sign on every branch to maximize the reward whichever one wins, and consensus would never converge.

The solution, put simply, is slashing. The protocol defines cryptographically provable conditions that, if a validator commits them, confiscate part or all of its stake. Casper FFG, formalized by Vitalik Buterin and Virgil Griffith in 2017, reduces them to two rules: do not cast two distinct votes for the same target height (double vote) and do not cast a vote whose interval is contained within another of your votes (surround vote). Signing on two forks violates the first rule, so it stops being free.

Slashing turns a free bet into a costly one and is the piece that makes proof of stake secure at the incentive level. On Ethereum, Gasper (Casper FFG plus LMD-GHOST) applies slashing for double vote and surround vote from the Beacon Chain. Cosmos and Tendermint (CometBFT) penalize double signing. Cardano, with Ouroboros, addresses the same problem through private-lottery leader election and chain-selection rules, an approach distinct from punitive slashing.