"It assumes an anonymous protocol. The identity of the nodes does not matter." Nor would it matter in a protocol where each node is assigned a unique ID. All

"It assumes an anonymous protocol. The identity of the nodes does not matter." Nor would it matter in a protocol where each node is assigned a unique ID. All that matters is whether or not the nodes are malicious and whether malicious nodes can violate some security property of the protocol. "I had considered that to be the definition of a majority consensus." This is kind of like saying that a Merkle puzzles approach is the only key exchange system. "Lets just assume that some alternative protocol has a property where a an attack with the >50% computing power would be ignored." Why even bother with "computing power?" Let's make the adversary more powerful by allowing attacks that run in polynomial time, and furthermore allowing the attacker to coordinate parties of its choosing, and to adaptive corrupt more parties in the system. Security against such attackers is not at all unheard of: http://eprint.iacr.org/2012/441.pdf http://eprint.iacr.org/2012/441.pdf "Then it follows that it would also allow an attack with <50% computing power— unless "attack" could be detected as a function of network state," Yes, that is how secure multiparty computation is usually approached. That is why secure protocols in the malicious model (or some multiparty variant of it) often involve zero-knowledge proofs, commitment schemes, and so forth. "A _consensus_ ultimately depends on linear energy applied to an attack" Again, it sounds like you are arguing against the use of consensus systems. It sounds like you are saying Bitcoin cannot be secure (at least not as a digital cash system), at least not by any cryptographic security definition. To put it another way, would you want the person or group with the loudest voice to prevent you from spending your money, or to take money they gave you back against your will? It is one thing for a currency issuer to destroy an economy; it is another for anyone who spins their CPU to be able to cheat or engage in targeted attacks.