paxos - In Paxos, assume that acceptors do not change their vote, can it reach a livelock?

Question

So, I’m studying Paxos and the Professor made this question:

Assume that acceptors do not change their vote. In other words, if they vote for value v in round i, they will not send learn messages with value different from v in larger rounds. Show that Paxos does not work any more (it can reach a livelock).

I’ve reasoned about this for the entire day, but I’m not understanding how can the livelock arises and so my colleagues.

Does anyone have a clue?

Answer 1

Assume there were network failures such that every acceptor accepted a different value. Without the ability to change their value in future rounds, no progress could ever be made and you have a "livelock".