Comment by spiddy

Weirdly this reminds me of the Raft consensus protocol: two nodes cancel each other when failing consensus as you can't tell which is the valid one, three gives you better chances, if one fails you have the other two that can get consensus. Of course in the off chance you have two failures you cannot get consensus with the only living node. Adding another two nodes make you robust to two failures.

Now replace fail with lying and you have the exact same problem.