PBFT is Practical Byzantine Fault Tolerance (cited here for example) which “chooses a leader in round-robin fashion.” Note PBFT suffers from the leader being faulty or being DoS attacked, and it can be stalled indefinitely.

Sorry the very late reply. I have extensively edited the original blog and added Part 2 and Part 3. Also I wrote a comment on this page which links of to extensive discussion over at bitcointalk.org.