The claim is that, once a leader is elected (ie. Q1), is no longer necessary to attain a majority quorum for actually accepting writes (ie. Q2). A minority quorum can accept writes, provided the minority contains at least one node that participated in the leader election. By increasing the leader election quorum number to higher than N/2+1 (as to have a sufficient number of nodes that participated in the Q1 election), the cluster can then operate much faster because writes require only minority quorum. The drawback is that it no longer tolerates N/2-1 failures, as N/2-1 failures leaves too few electors to choose a new leader in Q1.
NB. the Paxos terminology uses terms like 'decide a value', but practically in clusters this is equivalent to 'accept writes' so I used that instead for easier comprehension.
I recently proposed this idea (informally) and had to retract it: https://bentrask.com/?q=hash://sha256/b40971e7b30324fdda15ce...
Disclaimer: totally not an expert.
In turn, you have a concrete model checked implementation you can talk about or use a basis for understanding where either their or your proposed idea either holds or fails.
Note that a model can specify the wrong correctness criterion in practice. So you may have a "proof" which works, yet the proposition proven is wrong.
In general, when working on distributed systems, we usually want some kind of formal criterion of correctness. The failure modes of such system are quite hard to get right, and hence retractions of claims are plenty. Sadly, we have too little literature on how to on-board people on model checkers such as TLA+, proof assistants such as Coq, Isabelle/HOL or NuPRL, and QuickCheck systems such as Haskell or Erlang QuickCheck, Clojure's core.spec (I believe), etc.
[0] https://www.amazon.ca/Specifying-Systems-Language-Hardware-E...