Approval-based primary election methods

From electowiki

Approval-based primary election methods are electoral systems based in the "approval voting" single-winner system, but allow for the selection of multiple candidates. They are designed as proposals to replace primary elections.

The "St, Louis method" is the only one in use in public elections, as it was adopted by the city of St. Louis for their non-partisan primaries in 2019.[1]


In 2018, User:RobLa led discussions about "MATT" and "MAF" on the election-methods mailing list.[2][3] They led to the creation of the "Maximum approval top-two" and the "Majority approval filter" pages here on electowiki.

  • "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.[4]
  • "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.

Neither MATT nor MAF took the world by storm.

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.[5] This method is called the "St. Louis method" on this wiki page and is described below.


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

Unified primary

Heading from the sample ballot for Heading from sample ballot for the March 2021 primary election in St. Louis, Missouri[6][7]

The unified primary method is the method currently used in St. Louis, Missouri, was used in the 2021 St. Louis mayoral election, resulting in the election of Tishaura Jones. This method is defined in a short paragraph on the St. Louis 2020 ballot petition:[1]

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.[8]

Maximum approval top-two (MATT)

"Maximum approval top-two" (or "MATT") is an approval-based primary system where voters use an approval voting ballot to select no more than two candidates to advance to the general election. It was proposed by User:RobLa, based on discussions that happened on the election-methods mailing list in 2018.[2][3]

MATT uses the following steps:

  1. The candidate who receives the highest approval rating (the "front-runner") qualifies for the general election
    • 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.
  2. 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.
    • 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
      • "B" advances with 70% approval (per step 1)
      • "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)

Majority approval filter (or "MAF") is another approval-based primary method, mainly devised by User:RobLa in 2018 (in discussion with Ted Stern and other members of the election-methods mailing list).[2] It's 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. The "Ballot Satisfaction Score" is the percentage of the electorate which approves of at least one candidate on a given ballot.

The goal of the system is to provide the least-objectionable approval-based system that would achieve the following:

  • Ensures the candidate with the highest approval rating isn't eliminated
  • Prefers a second candidate who may not be approved by voters who approved the top candidate, but has a high approval rating, too.
  • Prefers selecting two candidates who are approved by over 75% of the electorate, through a set of rules involving a "Ballot Satisfaction Score" and ensuring that at least one of the two advancing candidates are approved by 75%

There are many rules to ensure this outcome. While not as simple as the St. Louis method or MATT, it handles more oddball cases (where an "unjust" outcome may occur) than either of the former two methods.


  1. a b STL Approves. "PETITION FOR PROPOSITION D" (PDF). STL Approves.
  2. a b c Lanphier, Rob (2018-07-18). "[EM] A simpler approval based way of replacing the CA jungle primary". Retrieved 2021-02-06.
  3. a b Lanphier, Rob (2018-11-25). "Replacing the jungle primary". Medium. Retrieved 2021-02-06.
  4. User:RobLa and other editors (2018–2020). "Maximum approval top-two". Electowiki. Retrieved 2021-02-06.CS1 maint: uses authors parameter (link) CS1 maint: date format (link)
  5. Schlinkmann, Jesse Bogan, Mark. "The next mayor of St. Louis faces big challenges — and high expectations". Retrieved 2021-02-04.
  8. Schlinkmann, Mark. "Overhaul of St. Louis election system passes, residency rule repeal fails". Retrieved 2021-02-06.