MaidSafe’s blog about their new PARSEC consensus system, agrees with my assessment of Hashgraph:

Most significantly, the Hashgraph consensus is closed source, restricting its use significantly. It is also unusable for our purposes as it requires a fixed set of known nodes.

[…]

Anyone who has looked a little further into the Hashgraph algorithm will see that it has only been shown to work so far on a network in which the nodes are identified and do not change — in other words, a permissioned network.

They also claim that in addition to ⅓ liveness threshold, that a sufficiently sophisticated adversary with less than that threshold could stall the progression of finality:

Furthermore, a network using the Hashgraph consensus is only proven to reach agreement if it is guaranteed that there is no sophisticated adversary on the Network.

However this alleged sophisticated attack that reduces liveness could be rectified in theory with a “common coin” algorithm that introduces randomness into the consensus process so that the sophisticated attacker is foiled. But such “common coin” algorithms are a trusted multiparty cryptographic scheme of which the key setup (analogous in some respects to Zerocash’s key setup ceremony) is impractical for a system where nodes are churning in and out of the validators set rapidly. Thus the claim that Hashgraph can’t handle such churn and it’s node set being less changeable if it employed such a “common coin” algorithm.

The quote above could be considered incorrect by associating churn with permissionless. A consensus round is required (for both PARSEC and Hashgraph) to add or remove validators from the set for validators. Thus for both systems exceeding the liveness threshold of the elder set of validators can lead to a stuck chain that doesn’t confirm any more transactions. However I think the point the above quote is making is that without churn then since Hashgraph has a less adaptable validator set, then it is more prone to problems of an entrenched validator set. Well I would mostly disagree with that assessment been always (i.e. generally) true because as whether the liveness threshold is exceeded depends on other factors too, not just whether the validator is not changing (much). IOW I think MaidSafe’s PARSEC is also permissioned in some sense. The devil is in the details of the holistic game theory of the system in which the consensus algorithm is deployed.