Note that I helped Dan Larimer invent TaPoS.¹
I've read Dan's paper and the thread
https://bitcointalksearch.org/topic/transactions-as-proof-of-stake-white-paper-354573, but I'm a bit confused as there seems to exist several versions or understanding of TaPoS. In principle (as explained in the great BitFury paper), TaPoS is nothing more than having a block reference in every transaction to prevent them from being included in multiple blocks/chain forks. On the other hand, Dan's paper is describing a consensus mechanism that is based on coin-days-destroyed, with no PoW involved at all. According to the conversion you had with him, he replaced PoW all together in favor of transaction fees to regulate block production. Vitalik in his blog is talking about yet another (simplified) model where transactions are chained together directly (without any blocks). Can you please enlighten me what TaPoS is actually all about?
Now, coming back to your new concept...
I argue in my white paper that TaPoS is as objective as proof-of-work.
Okay, but does it also provide objective consensus in the strict sense of the following definition (personally, I'm sharing Vitalik's opinion that weak subjectivity is sufficient)?
A consensus protocol is objective if a new node can independently arrive to the
same current state as the rest of the network based solely on protocol rules (e.g., a definition of the
genesis block) and messages propagated across the system (e.g., a set of all blocks).
Although I won't reveal my proposed improvement in detail now, I will reveal that the solution involves objective "eventual consistency". Satoshi's design suffers from fact that blocks compete with each other instead of being complementary (additive and subtractive in the notion of sets of events).
Again consensus systems are probabilistic. Just like with Bitcoin, the probability of an orphaned virtual partition declines over time. One difference from Bitcoin is there isn't the requirement of not more than one virtual partition (just one longest chain), yet convergence is probabilistically inevitable.
Based on your earlier statement, I would assume that by "Eventual consistency" you meant that the transactions would eventually become probabilistically consistent (as in Bitcoin), rather than (provably) immutable like in Swirlds (which in its current form cannot effectively deal with node churn and thus relies on PoW or PoS for Sybil defence).
"The hashgraph is provable. Once an event occurs, within a couple of minutes everyone in the community will know where it should be placed in history. More importantly, everyone will know that everyone else knows this. At that point, they can just incorporate the effects of the transaction, and then discard it." See
http://www.swirlds.com/downloads/Overview-of-Swirlds-Hashgraph.pdfBut you are critisizing Satoshi's PoW for ...
7. Orphans blocks. High transaction confirmation latency. Confirmation only probabilistic, never final. Burning must exceed double-spend value."
... which makes me think that your model does provide provable consensus.
A key design decision distills down to mitigating that Satoshi's design has aliasing error due to taking point samples on the continuous domain of partial orders.
Just because someone can Sybil attack the UTXO, doesn't necessarily follow they can Sybil attack the "inertia" which an interpretation (a chronological, partitioned structuring) of the UTXO. Someone could send a zillion transactions to their Sybil addresses (if they can recoup the TX fees by running their own full node), but if the rest of the inertia doesn't consume those UTXO, then it isn't inertia and it is a private, virtual "subnetwork" of the attacker.
I have mentioned the long-term inertia limits the rate of change in the near-term (a form of anti-aliasing) so that objective reality in the near-term moves into the long-term history before the rate of change could enable a double-spend by "replacing the 51% of delegated authority".
So, your strategy appears to make use of latent social information present in the graph determined by the past transactions (does that correspond to your notion of "inertia"?). This is a very interesting aspect indeed.
Social graphs and their mixing times are a well-known subject of anonymity literature by the way (though I'm sure you already know that):
http://www.cs.unibo.it/~babaoglu/courses/cas05-06/papers/sybildht.pdfhttps://www.princeton.edu/~pmittal/publications/pisces-ndss13.pdfhttps://www-users.cs.umn.edu/~hopper/sybil_asiaccs.pdfI'm not sure how that's related to the idea of Economic Clustering as discussed here:
https://nxtforum.org/news-and-announcements/economic-clustering/?PHPSESSID=mlinoglt5ii5d6mjeeka013l03https://bitcointalksearch.org/topic/pos-economic-clustering-622440