This algorithm will prevent cheating if one of the 3 nodes is bad, or no-2 nodes are in coordinated cheating.
If two out of 3 nodes are from the same cheater or same cheating organization, then you can't do anything with p2p decentralized trustless system. Use a centralized trust system instead.
Of course you can. Your consensus system can be designed around consensus, this is the very nature of Bitcoin - if 2 nodes cheat on the Bitcoin network, they get rejected as outliers.
You've literally described a system that
requires you to trust that there's not collusion between 2 parties, that is
not a trustless system, which is a twist of irony given that you called that other piece of junk out as not being trustless. There is no Byzantine fault tolerance with this system, which is the very problem Bitcoin solves. You're trying to solve this problem:
http://en.wikipedia.org/wiki/Two_Generals'_Problem - but the described system does not do so.
We are talking two complete different things. The 2 nodes cheat in bitcoin will get rejected, is because 2 as compared to 100000 of the network. It is not the 2 in the sense of a transaction involving 3 parties. You completely messed up the concepts.
The trustless system here, is to ensure the randomly selected parties will collaborate, and avoid cheating. The mini-escrow scheme by multisig tx accomplished perfectly this. The system does not require any inherent trusts there.
BTW, this has nothing to do at all with the two-generals' problem. All communications here are point-2-point and signed with each party's private key. The message is verified with sender's public key on arriving. So there's no message-tampering issue at all.
Yes this is right. The trustless system we talk here has nothing to do with two-generals problem. Communications have no problem, the problem is that how to prevent any node from doing bad things (i.e. steal coins).