I believe you can support all three types of consensus:
- Proof of Authority (i.e., just trusting some entity)
- Proof of Stake
- Proof of Work
However, the third option (Proof of Work) is somewhat problematic because the whole raison d’être of Plasma is that you can support the chain with a lot fewer computational resources than the full public chain, but POW isn’t really practical for small chains (since a big mining entity could arbitrarily switch its POW power to your chain and destroy the consensus)
Therefore, POA and POS seem like the only options that are really practical.