Approval-based primary election methods

This page lists three sets of rules
 * St, Louis method - this is the method adopted by the city of St. Louis for their non-partisan primaries.
 * "Maximum approval top-two" or "MATT" is an approval-based primary where voters use an approval voting ballot to select which candidates would be acceptable to advance to the general election. The maximum approval top-two method then selects no more than two candidates to advance to a general election.
 * "Majority approval filter" or "MAF" is an approval-based primary election method that advances all candidates who are approved by a majority of the electorate, as well as often selecting one or more opposition candidates.

History
In 2018, User:RobLa led discussions about "MATT" and "MAF" on the election-methods mailing list. They led to the creation of the "Maximum approval top-two" and the "Majority approval filter" pages here on electowiki.

Neither MATT nor MAF took the world by storm.
 * "Maximum approval top-two" or "MATT" is an approval-based primary where voters use an approval voting ballot to select which candidates would be acceptable to advance to the general election. The maximum approval top-two method then selects no more than two candidates to advance to a general election.
 * "Majority approval filter" or "MAF" is an approval-based primary election method that advances all candidates who are approved by a majority of the electorate, as well as often selecting one or more opposition candidates.

Meanwhile, the Center for Election Science helped the folks at STL Approves get off the ground in 2019. They were able to get St. Louis to switch to approval voting in the primary. This method is called the "St. Louis method" on this wiki page and is described below.

Rules
The rules for the various methods are described below, in order from simplest to most complicated:

St. Louis method
The St. Louis method is defined in a short paragraph on the 2020 ballot petition: "Notwithstanding any other provision of law to the contrary, in the primary election for the [offices in question], voters shall select as many candidates as they approve of for each office. The two candidates receiving the most votes for each office shall advance to the general election. The candidate for each office receiving the most votes in the general election shall be declared the winner."The ballot petition above passed with over 68% of the vote in the city of St. Louis in November 2020.

Maximum approval top-two (MATT)
"Maximum approval top-two" (or "MATT") is a voting system that was proposed by User:RobLa, based on discussions that happened on the election-methods mailing list in 2018.

MATT uses the following steps:


 * 1) The candidate who receives the highest approval rating (the "front-runner") qualifies for the general election
 * 2) * Example: if there are 100 voters, and 40 approve of "A" and "B", 30 approve of only "B", and 30 approve of only "C", then "B" advances to the general election, since "B" is approved by 70% of voters.
 * 3) A second candidate (the "complementary candidate"), who maximizes the approval of the electorate, also qualifies (i.e. by having the highest approval among voters that did not approve of the front-runner). If two candidates both satisfy an equal part of the remaining electorate, the candidate with the highest overall approval rating advances.
 * 4) * Example: if there are 100 voters, and 40 approve of both "A" and "B", 30 approve of only "B", and 30 approve of only "C", then
 * 5) ** "B" advances with 70% approval (per step 1)
 * 6) ** "C" advances (per this step). "B" satisfies 70% of the electorate, and "C" satisfies the other 30%.  So, 100% of the voters will be satisfied with one of their choices in the general election.

Majority approval filter (MAF)

 * Draft 4 published December 28, 2018

This set of rules is broken into three parts: 1) The goal of MAF, 2) the definition of "Pools" of candidates advanced to the general election in this system, and 3) the rules for populating the Pools of candidates. It is written with some effort toward legal precision and legal document tools-of-the-trade (e.g. the use of capitalized "defined terms"), but more work is needed.

Goal
A set of rules for holding a primary election with an Approval Voting-style ballot, providing motivation for all candidates to achieve the highest approval rating, and resulting in a general election Ballot Satisfaction Score of at least 75%. The "Ballot Satisfaction Score" is the percentage of the electorate which approves of at least one candidate on a given ballot.

Pools
Candidates advancing to the general election must qualify for one of the following "Pools". Candidates that don't qualify for one of the Pools below are "Non-advanced Candidates". By default, all candidates are Non-advanced Candidates until they qualify for one of these Pools:
 * "Supermajority Candidate Pool" - all candidates who receive greater than 75% approval
 * "Plurality Candidate Pool" - all candidates who receive greater than 50% approval, but do not qualify for the Supermajority Candidate Pool. If no candidate receives greater than 50% approval, this pool will contain the leading candidate, who may have less than 50% approval.
 * "Opposition Candidate Pool" - a subset of candidates who receive greater than 40% approval, but do not qualify for the Plurality Candidate Pool

Rules
Sequential steps for filling the above Pools with qualified candidates:
 * 1) Select the candidate who receives the highest approval rating. This is the "Top Candidate" and automatically qualifies for the general election ballot by one of the following rules:
 * 2) * 1a. If the Top Candidate receives greater than 75% approval, add this candidate to the Supermajority Candidate Pool.
 * 3) * 1b. If the Top Candidate receives less than 75% approval, add this candidate to the Plurality Candidate Pool.
 * 4) Complete the Supermajority Candidate Pool and the Plurality Candidate Pool using the following rules:
 * 5) *2a. Add any Non-advanced Candidates with greater than 75% approval to the Supermajority Candidate Pool
 * 6) *2b. Add any Non-advanced Candidates with less than 75% approval, but greater than 50% approval to the Plurality Candidate Pool
 * 7) Evaluate the Ballot Satisfaction Score (defined above) using the following rules:
 * 8) *3a. If the Ballot Satisfaction Score is greater than 75%, candidate selection is complete. Skip to step 6
 * 9) *3b. If the Ballot Satisfaction Score is less than 75%, proceed to step 4.
 * 10) If there is one or more candidates in the Plurality Candidate Pool, attempt to add an equal number qualified candidates to the Opposition Candidate Pool, evaluating each Non-advanced Candidate using the following steps
 * 11) *4a. Find the Non-advanced Candidate with the highest approval score.
 * 12) **If this candidate has less than 40% approval, determine if this candidate qualifies for the Opposition Candidate Pool in step 5.
 * 13) **If this candidate has greater than 40% approval, add this candidate to the Opposition Candidate Pool, then proceed to step 4b.
 * 14) *4b. Compare the size of the Plurality Candidate Pool and the Opposition Candidate Pool
 * 15) **If the Plurality Candidate Pool has more candidates than the Opposition Candidate Pool, skip back to step 3.
 * 16) **If the Opposition Candidate Pool contains an equal number of candidates to the Plurality Candidate Pool, proceed to step 5.
 * 17) If the Ballot Satisfaction Score is greater than 50%, skip to step 6.  If the Ballot Satisfaction Score is under 50%, ensure at least two candidates advance to the general election using the following steps:
 * 18) *5a. If there are no candidates in the Opposition Candidate Pool, find the Non-advanced Candidate with the highest approval score. If this candidate increases the Ballot Satisfaction Score by more than 10% (the "Candidate Differentiation Threshold"), add this candidate to the Opposition Candidate Pool, and skip to step 6.  Otherwise, advanced to step 5b.
 * 19) *5b. Consider each Non-advanced Candidate in order of approval score. Find the first candidate who increases the Ballot Satisfaction Score by more than the Candidate Differentiation Threshold (10%), and add this candidate to the Opposition Candidate Pool, and skip to step 6. Otherwise, advance to step 5c.
 * 20) *5c. Find the Non-advanced Candidate with the highest approval rating. Add this candidate to the Opposition Candidate Pool, and advance to step 6.
 * 21) Candidate selection is complete. Advance all candidates in the Supermajority Candidate Pool, the Plurality Candidate Pool, and the Opposition Candidate Pool to the general election.

History

 * MAF (note: Full discussion history of this method can be found at Talk:Majority approval filter)
 * 2018-12-28 - Draft 4 published at , based on conversation documented at Talk:Majority approval filter)
 * 2018-12-07 - Draft 3 published (with clarifying edits continuing through 2018-12-10). See December email thread "[EM Approval-based replacement for jungle primary ]" for more discussion about the evolution of this draft
 * 2018-11-22 - Draft 2 published in 2018-11-22 email from RobLa (and also available at User:RobLa/MAF drafts
 * 2018-11-20 - first draft published on electowiki.org and as "Replacing the jungle primary" by User:RobLa (and also available at User:RobLa/MAF drafts)
 * MATT: Full discussion history of this method and it's counterpart (Majority approval filter) can be found at Talk:Majority approval filter)
 * 2018-11-20 - first draft published on electowiki.org and as "Replacing the jungle primary" by User:RobLa


 * Majority approval filter (MAF; history of the page formerly known as "MAF") - a primary election voting method that is guaranteed to advance all candidates receiving a majority approval score to the general election
 * Maximum approval top-two (MATT; page history for MATT) - a simplification of MAF that is guaranteed to advance no more than two candidates.