>Why does everyone repeat that Byzantine consensus requires maximum 33% of participants to be dishonest?

Not 33% of participants, 33% of the hash power, could just be one participant with a pile of GPUs or ASICS or "JINN" chips lol. That's the claim made by the IOTA author, anyway.

Right now it wouldn't surprise me if someone could amass 90+% of IOTA hash power anyway.

>If messages cannot be forged

Tbh this is not even a given with IOTA.

Okay but it was more of a general question. I see Hashgraph and others always saying that they need 33% of participants to be honest. But with unforgeable message signatures that limitation doesn't apply.

Virtual Voting in hashgraph requires a 2/3 agreement.

Of course PoW provides some protection against sybil attacks, but the reality is that with enough hashpower the network can be overtaken. (Hence why HashGraph is a closed network.)

What does POW have to do with Hashgraph? It doesn't use POW.

oops right, I mixed up IOTA with HashGraph.

Proof of work isn't about forging transactions, it is about ordering them.

If all you needed was a way to order transactions you would not need proof of work at all. Here for example is the PTN:

https://intercoin.org/technical.pdf

First, a paper written three weeks ago of an unproven currency is a bit of stretch.

Second, I didn't say it was necessary to order transactions, I said that is what it is used for, which is correct. You are replying to a point that I didn't make.

You said proof of work is ABOUT ordering transactions. I was trying to say that it's not. It's used for other things: namely as a way to determine the next miner, like leader election in consensus protocols. It also adds a lot of computation on top of the transactions to show that the miner is heavily invested in the ecosystem and thus serves as an economic incentive. It has almost NOTHING to do with ordering transactions. Transactions are ordered by the blockchain, and everyone has to verify them anyway.

You do realize that the miners' purpose is to order transactions right?

Pretty sure it's not. Go ahead and prove it with a link.