Quote from: alkan on November 30, 2016, 07:52:15 PM

Quote from: iamnotback on November 27, 2016, 10:52:50 PM

By that definition, proof-of-work is also not objective, because you don't know which hidden chains are the longest chain. You are trusting that the sources who send you chains are omniscient.

That's a fair point if you look at objectivity in a strict sense. However, practically, it does make a difference if you only need one honest and omniscient (or at least up-to-date w.r.t. the longest block chain) node to get the latest state of the network. If you can connect to an unbounded number of nodes, you can asymptotically achieve objectivity since the probability that one of them will send you the longest chain will approximate 1 provided that at least one out of all nodes is honest and up-to-date.

That doesn't help if the longest chain is not yet published, which is a plausible issue for short and medium range attacks and especially if your blockchain is not "the one chain that rules them all". And in theory this can also be the case for a long-range attack if a quantum computer becomes reality and is able to rewrite the entire chain in a fraction of a second.¹⁸

¹⁸ Serguei Popov. The tangle. §4.3 Resistance to quantum computations, p. 24, Apr 3, 2016.

Quote from: alkan on November 30, 2016, 07:52:15 PM

Whereas with subjectivity, different nodes might come to different conclusions if some of the nodes are malicious.

Since we are mostly convinced that long-range attacks on PoW are not likely unless a quantum computer arrives, I argue that TaPoS with significant burned transaction fees is equivalently objective and does not depend on the honesty of any node. A long range chain with millions of transactions referencing the hashes of blocks is objective per my prior comment on this topic. The current stake holders are not going to accept a long-range attack which double-spends their stake back to a former stake holder's private key. The decentralized objectivity is in the community's unwillingness to build on that attacker's chain.

The weak subjectivity seems more applicable to nothing-at-stake (i.e. without TaPoS) and where propagation makes a difference in terms of which transactions are confirmed and there is nothing other than centralized checkpoints to resolve ambiguity. TaPoS is decentralized checkpointing.

Quote from: alkan on November 30, 2016, 07:52:15 PM

Quote from: iamnotback on November 27, 2016, 10:52:50 PM

Vitalik's entire premise was undecidable and irrelevant.

Vitaliks definition is too narrow and thus irrelevant.

Even if we are talking about "asymptotic" objectivity, its impact on security (and partition tolerance) of a decentralized network seems questionable to me. You cannot download and use the network client without trusting anyone (expect if you are the creator of the network) because you can never be sure if it's the right client or just a malicious copycat that is perhaps using a different protocol.

The objectivity of PoW is that the longest chain of hashrate difficulty wins. The objectivity of TaPoS with burned transaction fees is that the most burned transaction fees wins.

In both cases, the attacker can burn less PoW or fees than he double-spends, and thus attack. But for PoW, I argued that for the "the one chain that rules them all", the mining farms are not going to rent out 51% of the systemic hashrate for short-term attacks. I would however not make the same argument for minority PoW blockchains (especially those without an ASIC) such as Monero. And I would not make that argument for burned fees for the short-term because it can be plausibly more liquid to attack and short, then to sell xx% of the stake. However for the long-term and assuming minting of new money supply tapers asymptotically towards 0, the burned fees will asymptotically approach 100% of the stake (and the current stake holders can not build on an attacker's chain which reverts their stake) so it becomes more and more implausible the longer-range the attempted attack (note this does require that stake being infinitely divisible or practically so). Thus nodes that recently come online (for both Monero and my design) would need to wait a while for the network to stabilize in absence of either node reputation and/or a more objective finality to the consensus. I resolve this in my design with a two-factor, fail-safe combination of the two (optional node reputation and optional deterministic finality) with a fallback to the need to wait a while otherwise.

I discuss this in my whitepaper:

Quote from: @AnonyMint's whitepaper

Analogous to the finality of the longest chain rule in PoW, the proposed probabilistic finality is deterministically ambiguous because [redacted] nodes can stand up or down at will; thus there is no unambiguous deterministic finality of the consistency of the [redacted] provided by the weighted majority of [redacted] nodes. It is not sufficient to define the longest [redacted] to be the one that has the most burned transaction fees with a rule to revert the conflicting transaction(s) in the shorter [redacted] when two or more [redacted] are merged via [redacted], because this would enable an attacker with control over the majority of stake which has been transacted over the period to launch a (somewhat far-fetched) long-range double-spend attack wherein the double-spent theft exceeded the burned transaction fees.

Thus, instead when the [redacted] node ...

Bottom line is I can't imagine any real-time instant microtransactions system functioning without some reliance on community oversight. A key facet in my design is that the oversight should be objectively driven and decentralized. The inertial statistical objectivity of the nodes that are online carries over to those who recently come online, i.e. nodes which recently come online aren't trusting any of the nodes but rather trusting that at least one of them is honest. Which is essentially what you wrote, "you can asymptotically achieve objectivity since the probability that one of them will send you the longest chain will approximate 1 provided that at least one out of all nodes is honest and up-to-date". In other words, the Linus law so modified to our context, that "given objectivity and enough eyeballs, all malevolence is shallow and eventually orphaned". That even defeats a Sybil attack.

Concluding that PoW is more objective is to say that the winner-take-all power vacuum with one victor securing the chain, is more reputable than the decentralized community. In other words, the subjectivity pops out in other facets. Sure the longest chain is (probabilistically) objective if it is not hidden, but that doesn't mean the system is behaving objectively in a Nash equilibrium and without malevolence. So I agree with you as quoted:

Quote from: alkan on November 30, 2016, 07:52:15 PM

Vitaliks definition is too narrow and thus irrelevant.

Vitalik's blog is useful as starting point for discussion.

I am not insinuating that Vitalik doesn't make valuable and interesting insights. He is overachieving for his age, and he has contributed to the prior art which we build on. And in hindsight we can state things which we didn't know at the time he wrote that. He has I assume learned a lot since then as well. And he was arguing that he learned to love subjectivity. Yeah because there is no such thing as absolute objectivity in our universe.