The Ethcore Parity wiki states that it supports 'Proof of Authority Chains'. What distributed byzantine consensus mechanism is used?
No actual consensus mechanism is used.
Some nodes/keys have the right to sign blocks (configured in the example json you see at https://github.com/ethcore/parity/wiki/Proof%20of%20Authority%20Chains ), others don't.
As the text says, this is only for demo/development purposes. An actual consensus mechanism will need to be plugged in later.