"Finality" is just a fancy way of saying that non-blockchain entities have their own definition of when they consider a transaction irreversible. For example, if Alice sends to bittrex, then bittrex will consider the transaction irreversible after two confirmations, and credit her balance.
If the secret miners (attackers) don't get two blocks before the public miners get two blocks, then bittrex will credit Alice's balance and she will circumvent @dan's attempt at "censorship".
This is the part that @dan ignored when he made his faulty claims about being able to censor with 51% of the hashes.
Ah now it makes sense, I had been speculating that this was the meaning of it.
I have been going through your little quarrel :P. And I think both you and @dan are right depending on the situation. If we take your Bittrex example, Alice's transaction will be censored whenever she has no prior knowledge of the attack of Dan, because as you say her coin will be destroyed. If she knows dan is after her she can trade her coins or move her coins to another exchange. But in the case when her coins doesn't get destroyed when there is a fork (like btc vs bcc), she is in fact never censored.
It all comes down to the finality, if people accept both Alice's chain and @dan's chain. I am not sure how EOS works, but applying the PoW logic to the system and your probability function, it would indeed be impossible to censor Alice over a long period of time based if miners accept both Alice's and Dan's chain, in which case there will be 2 EOS coins. But as I understand the goal is to only have 1 EOS network. In which case censoring is successful on the new accepted chain, but total censoring will never happen because there exists a chain where Alice accounts still exists.
Your probability function is also very relevent in that Dan is not able to immediately censor Alice on a PoW chain as with 49% of the mining power she will still be able to put through messages for a while.
Well this is my two cents on this subject and please correct me if I am wrong. My reasoning followed logical conlusions from my current understanding of PoW :P
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