Approval Elimination Runoff

Approval Elimination Runoff (AER) or Approval AV is an IRV variant under which one eliminates the least-approved candidate until there is a majority favorite.

It is similar to DMC except that DMC finishes once there is a Condorcet winner, not a majority favorite. AER can potentially eliminate the Condorcet winner.

Approval is usually envisioned as being implied by ranking the candidate.

Example
Suppose that the voters rank (and thus approve) their top two choices and leave the bottom two unranked.

As there is no majority favorite, the least approved candidate is eliminated, which is Knoxville (32%).

Then, there is still no majority favorite, so Memphis is eliminated (with 42% approval).

This results in Nashville being majority favorite, so Nashville is elected over the other finalist, Chattanooga.

Now instead, suppose that all voters rank their top three choices and leave the last choice unapproved. Then Memphis is the first candidate eliminated, and Nashville then has a majority of first preferences.

In comparison, in either of these scenarios, IRV eliminates first Chattanooga and then Nashville, electing Knoxville.