Moreover, the leaders are lease-based in the author's proposal, so I believe that what he describes correctly solves consensus. However, his proposal doesn't really give much of a resilience improvement over the original Paxos, since the system, in the worst case, tolerates only 2 failures (leader + one more process), same as a 5-process Paxos. Nevertheless, an interesting idea, one that I don't think I've seen elsewhere.
Especially since a flaky switch isn't the only issue. Power loss could bring down even redundant backbone switches, but leave communication within the rack going. You could accidentally push a bad routing config and blackhole traffic to a bunch of hosts. You could send out a bad push that intermittently breaks connectivity to some hosts. And so on.
However, I see a clear issue with the proposed model.
Taking the authors 11 node set up. 9 nodes are required for leader election. 3 nodes are needed for proposals.
Assume that a network partition splits the nodes with 5 nodes on side A and 6 nodes on side B. Assume also that the leader is on side B (though it works without loss of generality for side A as well).
At this point, no leader re-election can occur, since no side has the 9 total nodes required for a re-election. It's obvious that if the leader dies (or died as part of the partition) that no leader can be re-elected.
With the partition in place:
1.) let 1 node in side A make the proposal "X=3"
2.) Let 2 other nodes in side A agree to the proposal that "X=3"
3.) Let 1 node in the side B make the proposal "X=0"
4.) Let 2 other nodes in side B agree to the proposal that "X=0"
5.) Let the partition heal
6.) The cluster is now split brain on whether "X=0" or "X=3". According to the rule provided, the leader must accept any successful proposal.
Note that this split brain does not even require a network partition. Assume no network partition, and nodes are labeled 0-10. The leader is currently node 10.
1.) Let node 1 propose that "X=4"
2.) Let node 2 propose that "X=5"
3.) Let nodes 3 and 9 agree to the proposal that "X=4"
4.) Let nodes 6 and 8 agree to the proposal that "X=5"
5.) Split brain occurs as the leader has to accept any successful proposal, which includes "X=4" from nodes 1, 3 and 9, and also "X=5" from nodes 2, 6 and 8.