A preference matrix is a chart which shows all the data from a given election. Unless you are doing a hand count, a matrix can be generated automatically and will usually be available with your election results, depending on the platform.

A preference matrix is a great reference point for looking at the additional data which can be gleaned in STAR elections. In most elections a full matrix isn't needed. All that is needed to select the winner is to determine the preferences between the two highest scoring candidates. When an election is tabulated electronically the full preference matrix is generated automatically.

When might I need a matrix and why?

In the event of ties, the full set of voter preferences shown in the matrix can often be used to break ties in favor of the more preferred candidate.

When ballots are not all tallied centrally, creating of matrix for each sub-set of ballots allows each set to be fully tallied on site and then be compiled later. This is a feature known as precinct summability, and it means that with STAR Voting local audits and recounts are possible if needed. Summability is an important requirement for election security and integrity. STAR Voting and most voting methods are summable, but Instant Runoff voting, the type of Ranked Choice widely used around the world is not.

Preference matrices provide a lot more information beyond who won and lost, so they are often used in data analysis. One advantage of STAR Voting over choose-one is that all of this information is available.

Creating a preference matrix by hand is just like tallying a STAR election, but with an extra runoff for each pair of candidates:

• Total the scores given to each candidate in the election.
• Just like in the STAR runoff, the two highest scoring candidates are selected. Sort the ballots to find how many voters preferred each of those finalists. Ballots are sorted into three stacks: Ballots preferring one finalist, ballots preferring the other, and ballots who gave both the same score and thus have no preference between those two. If you are doing a hand count you will have found your winner and can stop here. In the example below Alison won with 89 points. She was preferred by 8 out of 10 voters, or 80%.
• To create a full preference matrix, repeat the step above for each pair of candidates.