Proving the negative is notoriously hard (often impossible), and yet that's exactly what you're asking of me.
No, friend, game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." Mathematical models are the very essence of being open to proof,
see here.
So, on one hand, you dont need to provide any proof that non-mining nodes (or nodes) are irrelevant to Bitcoins security. On the other hand, you suggest that mathematical models make such proof possible. Then,
instead of providing any evidence of your argument, you link to an encyclopedia article about Mathematical proof. Really compelling.
Several times now youve dishonestly used the concept of proof to back contradictory claims. Its simply a red herring you use to disguise the fact that you have no valid argument, never mind providing evidence for it.
And are you really suggesting that humans are now able to mathematically prove what intelligent rational decision-makers will do in given situations? Last I heard, our understanding of causal effects in macroeconomics is virtually nil.
Lol, that's where the root of your problem lies -- you think that "there's no such thing as proof in game theory and economics," so it's OK to ask me for proof when logic fails you.
Excellent strawman. I merely asked you to provide evidence for your baseless opinions, while pointing out the epistemic limits of proof in the context of human actions. The latter was for your benefit. The lone phrase you quoted out of context (from two posts ago) was clarified in my last post:
I'm asking that you provide a modicum of evidence, logic, for a statement you made -- i.e. more than just a mere repeated opinion.
Youve only managed a couple fallacious retorts, so youre not in a position to say when logic has failed anyone. If my logic has indeed failed, simply refute my arguments on a logical basis. Ive summarized them below. Youve even suggested that you can indeed
prove your case on the basis of mathematical models, which I am excited to see:
Every node must receive and process every transaction in every block. That distributes blockchain data to all nodes who enforce the rules, rather than a system where nodes trust a central source. [i.e. decentralization as a solution for the security faults of trust]
The more nodes that exist that are enforcing the same rules, the more likely the longest valid blockchain data that you receive from them is accurate.
If there are only mining nodes, the userbase, by definition, trusts miners. Hence why the existence of non-mining nodes secures bitcoin: by decentralizing hash power from validating nodes.
One of the primary determining factors in whether a Sybil attack is possible is how cheaply identities (nodes) can be generated. The more nodes there are, and the more decentralized said nodes are, the bigger the cost of mounting a Sybil attack, since attackers must set up more nodes in more distinct locations.
There have been past double-spend attacks by miners, so we know that rational miners will attack nodes if it is profitable to do so. That they have not used Sybil attacks specifically does not prove that it is not (and was not historically) possible to do so, but it certainly does not help your claim that non-mining nodes do nothing to secure the system. If they did nothing -- like padlocks on the lawn -- wouldn't that suggest it was cheap enough to attack them with Sybils?
Non-mining nodes obviously aren't impotent because we are talking about theoretical Sybil attacks, not historical ones.
In summation: Nodes enable a decentralized, trustless system to exist in the first place (securing users' funds from centralization failure). They are the system's defense against Sybil attacks (preventing double-spending and censorship attacks) from miners or other attackers. Further, nodes, by self-validating, also decrease the number and scope of attacks on users of the system by eliminating trust-based protocols.you simply have no clue about the shit you talk about.
I respect that you take a dishonest approach to debate; its nothing new.
But even if you could show this to be true (rather than being based on transparent fallacies), you still havent begun to make your case that nodes are irrelevant to Bitcoins security. You're merely attacking me as a person.