No I don't think they will do it offchain. They will keep it onchain to maintain seamless interoperability while they attack.
I can see you are confused. Unfortunately I don't think you understand how Bitcoin works well enough for me to explain this attack to you. Maybe just let the experts debate me. I will try to reply to you, but seems you are really confused.
Great argument.
How about you explain how a central off chain system can be vulnerable to double spends. Explain to me like I'm a child, I don't care.
If the cartel records your spends offchain, then you can spend them again onchain to non-cartel merchants. The Bitcoin money supply would be in effect doubled, tripled, quadrupled, depending how many separate cartels do this.
But then how do the cartels spend this offchain money? Receivers of this money would only be able to trust it has value within the cartel members. So which copy of the money would be worth more? Depends which network has more value.
So it just adds chaos and risk to the cartel's outcome. It might be a way to destabilize Bitcoin, but it looks like customers and members of the cartel would revolt. So I don't think this would be attempted.
Also, if they are not doing it off chain as you say, how on earth they are able to withhold a transaction I send from my non-cartel wallet.
I already explained this to you upthread.
I didn't say they can withhold what you send from a non-cartel wallet.
I said they can withhold only transactions that their customers send on the cartel's wallet. The cartel will not permanently withhold these from the blockchain. They only withhold them from non-cartel miners. Once a cartel miner adds a block, then all these transactions get added to the Bitcoin blockchain.
The transaction you send from a non-cartel wallet client is affected because the cartel miners may refuse to include your transaction in the blocks they win. So depending on what percentage of the total network hashrate the cartel has, your transactions might be delayed. Eventually the cartel gains so much mass and has bankrupted the non-cartel miners, so then when you send from non-cartel client, your transaction never gets added to a block or very delayed.
I'm still waiting...
Sorry for the delay but yours was the most difficult to explain because you were confusing some of the issues. So I responded to yours last.