The proof in the case where nodes can be malevolent is easy to visualize with 3 colored marbles as voters: red, white, and blue. Given 3 jars representing ballot boxes for 3 elections, two marbles can be placed in each jar without any marble voting more than twice, i.e. no voter has cheated yet the result is ambiguous. Declaring any of the jars as the first epoch, results in two quorum choices (forks) for which jar is the next epoch. One jar has red and white, the next red and blue, and the last white and blue. This is why the proof requires that the excess of the quorum be less than ¹/₃ (aka “-¹/₃”). So by adding a green marble, the ambiguity is resolved because the green marble can only be placed in two of the three jars― again presuming no voter cheated to vote more than twice. Thus the +²/₃ instead of ¹/₂+ is required for quorums in the presence of possible malevolence given an  asynchronous network, because the ordering of the quorums can’t be proven.

Note if any 3 of the 4 marbles are colluding, i.e. ²/₃ or more (aka “+²/₃”) of the voters are malevolent, they can vote for as many conflicting quorums (forks) as they wish and it will be ambiguous which of the 4 marbles is cheating, because given 3 sets of 3 jars, a different one of the 3 cheaters can vote in each set. And the honest marble has to vote on the fork which the quorum is extending, because otherwise not voting is indistinguishable from unresponsive. It can’t be irrefutably proven that the 3 malevolent marbles were cheating because they can each claim that other one became unresponsive; thus voting for more than two quorums became necessary. And the honest marble voted more than twice also. Propagation order and responsiveness can’t be proven nor disproven in an asynchronous network.

They didn't turn against Bitcoin, Bitcoin turned against them.  

...and by "giving up" the OP means he will continue to post FUD well into the future!

Yeah, what a strange world. Bitcoin should be the universal micro payment money that everybody should use,

now only the richest nation in the world can afford the fees and really use it.

Thx BScore


 

I hope segwit gets activated eventually. Only morons are actively blocking it.

Banks in developed countries already know about bitcoin, but it's a fiat competitor - so it won't be adopted by them.
Blockchain on the other hand it gaining entrance into the banking industry.

Finally, after this blockchain hype we see right now, attracting so many thinkers , projects and budgets, many of the intelligent will finally debunk the real power of bitcoin itself.

If this is because of its feature to be a mostly uncorrelated investment class, a money transfer system or together with Rootstock on top some smart contract / dapp enabling super asset, who knows?

I say it will.