# 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

Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities, and that everyone wants to live as near the capital as possible.

The candidates for the capital are:

• Memphis, the state's largest city, with 42% of the voters, but located far from the other cities
• Nashville, with 26% of the voters, near the center of Tennessee
• Knoxville, with 17% of the voters
• Chattanooga, with 15% of the voters

The preferences of the voters would be divided like this:

42% of voters
(close to Memphis)
26% of voters
(close to Nashville)
15% of voters
(close to Chattanooga)
17% of voters
(close to Knoxville)
1. Memphis
2. Nashville
3. Chattanooga
4. Knoxville
1. Nashville
2. Chattanooga
3. Knoxville
4. Memphis
1. Chattanooga
2. Knoxville
3. Nashville
4. Memphis
1. Knoxville
2. Chattanooga
3. Nashville
4. Memphis

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.