Its right in the message above. FBA is the result of researching how to make a bitcoin like system without PoW.
PoS however is based on the ideas of PoW, it just moves the flaws, its not a solution.
FBA was "invented/discovered" before PoS coins even existed.
Essentially FBA is a distributed voting solution. Instead of let the person who has solved the PoW write the Tx in a block, everyone just votes on Tx order. The threshold is rather arbitrary. Most systems use something around 80%. In practice every valid Tx has near 100% votes anyway because no one listens to dishonest nodes. But nodes can go offline or Tx propagation can be delayed so a Tx could have only reached part of the network and thus not reach 100%
Not a big deal even if a Tx has less than 80%. Nodes just re-vote for the Tx for the next round.
Double spend is solved by the ordering alone. If one Tx is first the second that moves the same funds somewhere else, breaks a fundamental Tx rule so nodes wont vote to include the second. Which one came first is irrelevant. Each node just votes for the one he got first and in a possible second round it votes for what the majority of other nodes said came first. So the distributes system can not reach a state where a Tx is stuck.
This is all very very very much simplified ofc but you can easily lookup systems and dig into details if you are interested. There are real "blocklchains" running with FBA since many many years so it without any doubt works. Although like I said in my original post it can allays be improved.
What you described doesn't even address the reason PoW exists. So, I’m sorry but it sounds like you are repeating something you heard without understanding the issues at hand. I suggest you read “There’s nothing cheaper than proof of work” by Paul Storzc
Enlighten us please? Suggesting to read a book of which the title already suggests some completely irrelevant content about "cost" or PoW surely does not convince me or anyone. I dont care about the energy/cost or the fact that bitcoins may speed up the destruction of this planet by a incredible tiny tiny fraction that has zero effect on my life. I couldn't care less, and it wasn't part of my argument at all.
People can have an argument about that, its fine but mine wasn't so you cant debunk it by telling me to read a book that seems 100% irrelevant.
PoW was simply used to solve the double spending problem in a decentral way. Which is exactly what FBA solutions do without it.
Solving the double spending in a decentral way is the key "invention" of bitcoin NOT PoW. PoW existed way way before, it was just used to create the solution to the problem it was not invested/discovered for bitcoin nor was it the key element.
People came up with different solutions solving the same double spending problem in a decentral way but without using PoW. Some solutions are objectively better regardless of energy consumption and other secondary properties. They are objectively better because they scale to high throughput, allow short block times, have a proper and path forward to improve these properties over time with very limited "risk" of causing forks for every proposed change.
FBA was "invented/discovered" before PoS coins even existed.
Essentially FBA is a distributed voting solution. Instead of let the person who has solved the PoW write the Tx in a block, everyone just votes on Tx order. The threshold is rather arbitrary. Most systems use something around 80%. In practice every valid Tx has near 100% votes anyway because no one listens to dishonest nodes. But nodes can go offline or Tx propagation can be delayed so a Tx could have only reached part of the network and thus not reach 100% Not a big deal even if a Tx has less than 80%. Nodes just re-vote for the Tx for the next round. Double spend is solved by the ordering alone. If one Tx is first the second that moves the same funds somewhere else, breaks a fundamental Tx rule so nodes wont vote to include the second. Which one came first is irrelevant. Each node just votes for the one he got first and in a possible second round it votes for what the majority of other nodes said came first. So the distributes system can not reach a state where a Tx is stuck.
This is all very very very much simplified ofc but you can easily lookup systems and dig into details if you are interested. There are real "blocklchains" running with FBA since many many years so it without any doubt works. Although like I said in my original post it can allays be improved.