Mina uses a Nakamoto-style, “longest fork” consensus which is great since this approach to consensus allows for maximum decentralization. At a high level, the tradeoff compared to alternative BFT consensus protocols is slower time to finality.
I came across this paper which claims to realize the best of both worlds and thought it was worth starting a topic here for discussion: TaiJi: Longest Chain Availability with BFT Fast Confirmation
The abstract claims:
We present a new construction which combines a longest chain protocol and a BFT protocol to get the best of both worlds.
While the paper is focused on PoW chains, a substrate project (Polkadot’s ecosystem) called Subspace is using a variation of TaiJi for their “Proof of (Storage) Capacity” consensus (their consensus whitepaper is here). I would assume TaiJi could theoretically be applied to PoS as a result.
Curious to hear what others think of this possibility and whether TaiJi is a legitimate innovation?
At a minimum, this topic may be useful for future reference as consensus becomes a higher-priority aspect of the protocol.
Cheers 
,
Brett