Earlier quoted context omitted.
I don't get it. Suppose a bad actor tries to double spend. They have to cryptographically sign both transactions, so the whole network will eventually receive knowledge of both transactions. Why can't the network simply wait for some duration of time before accepting a transaction, to verify that no double-spends propagate from elsewhere? If double spending is ever detected from a party, that party is dis-trusted by…
Well let's say we do things this way, and I double spend a transaction, sending one to Alice and one to Bob. Suppose Alice waits t seconds after receiving the transaction, and if she doesn't see any double spends in that time, she accepts that the coin is hers and she then sends me something in return. One second before Alice "confirms" my transaction, I can send out my transaction to Bob. Since my message takes time…
In Ethereum's PoS, by waiting a similar amount of time you actually get finality; at that point your transaction cannot be reverted without a third of total stake being destroyed.