Perhaps you're thinking of Byzantine Paxos (not regular Paxos)? I'll have to read up on that to determine its relevance to the double-spend problem. One concern

Perhaps you're thinking of Byzantine Paxos (not regular Paxos)? I'll have to read up on that to determine its relevance to the double-spend problem. One concern I'd have is how parliament membership is determined (e.g. what about Sybil attacks?).