A preference matrix is a chart which shows all the preference data from a given election, ie. which candidates were prefered to who. 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?

Preference matrices provide a lot more information beyond who won and lost so they're often used in data analysis. One advantage of STAR Voting over Choose-One Plurality is that this additional information on voter preferences is available.

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.

Creating of matrix also allows for a subset of ballots to be fully tallied on site and in the moment, even if all the ballots for the election are not in hand yet. This is a feature known as summability, and it means that STAR Voting doesn't require centralization of ballots. It also means that STAR Voting is compatible with all the best practices in election security. Partial audits, risk limiting audits, local audits, and recounts are all possible if needed.

Summability is an important requirement for election security and integrity. STAR Voting, Ranked Robin, Approval Voting and most other voting methods are summable, but Instant Runoff voting, the type of Ranked Choice Voting widely used around the world is not.

Creating a preference matrix by hand

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.