Tie votes in STAR Voting are rare - well over 10 times less common than with choose-one voting- but as with any voting method they can occur, especially in small demos or elections without many voters.
Standard Tie-breaking Protocol
In most cases, ties in STAR voting can be broken by referring back to the ballots themselves:
Step 1: Ties in the scoring round should be determined in favor of the candidate who was preferred (scored higher) by more voters. If there are only two candidates this will be the majority preferred candidate, if there are multiple tied candidates this will be the candidate(s) preferred over all other candidates. (See section below on Condorcet winners and losers.)
Step 2: Ties in the Runoff Round should be broken in favor of the candidate who was scored higher if possible.
Step 3: In the event that a tie can not be resolved as above, the election will be called as a tie and broken randomly, unless a further tie breaking procedure was adopted in advance of the election and was publicly disclosed.
Establish tie-breaking protocols in advance of the election
The body hosting the election is responsible for establishing tie-breaking protocols in advance of it's elections. In the event that no protocol has been specified, and the election has already been conducted the standard tie breaking protocol above should be used as the default.
Key considerations for resolving ties:
- Resolve ties as described above in steps 1 and 2 if possible.
- If there are remaining ties, a coin toss or random tiebreaker is a valid option.
- If desired, you may want to pick an additional tie-breaking protocol that is more determinative.
- Set additional protocols in stone before the election!
Additional Tiebreaker Options
- Five Star Tiebreaker: If an additional tie breaking protocol is desired, (beyond steps 1 and 2 above,) break the tie in favor of the tied candidate who received the most five star votes as follows: Determine how many voters gave a five star rating to each of the tied candidates. The candidate who received the most five star ratings wins.
- Random Tiebreaker: If an additional tie breaking protocol is desired, (beyond steps 1 and 2 above,) break the tie randomly. Common examples of a random tiebreaker include a coin toss, a name draw, or in cases where candidates names appeared on the ballot in a randomly generated order, electing the candidate whose name appeared first.
What if we want to use a different tiebreaker protocol that isn't listed above?
There are a number of fair and valid ways to break ties. STAR ballots can be run with another voting method such as with this Condorcet tiebreaker if desired. (The Five Star Protocol above is essentially a Plurality or Approval Voting tiebreaker.) As long as a protocol is fair and is chosen in advance it can be used, however, we recommend against using more complex tiebreakers for the sake of transparency, and because it's unnecessary.
What is a preference matrix?
A preference matrix is a chart which shows all the voter preference data from a given election.
When do I need a matrix and why?
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.
A preference matrix is a great reference point for looking at the additional data which can be gleaned in STAR elections. It may also be helpful for breaking ties in the scoring round.
Another reason a matrix might be needed is if ballots are not being tallied centrally, or if ballots will be counted in sets as they come in. Creating a matrix for each sub-set of ballots allows each set to be fully tallied on it's own and then be compiled with other sets of ballots later. This is a feature known as summability. Ballot summability means that with STAR Voting local audits and/or partial 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 additional data is available.
How do I create a preference matrix?
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 you're using.
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 likely have found your winner and can stop here, completing a full preference matrix is completely optional. In the example below Allison won with 35 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, for example, Allison vs Bill, Allison vs Carmen, and so on. Record the number of ballots which preferred each candidate in each head-to-head match in the corresponding box.
Tiebreaker Example #1:
In the example above we have a tie in the scoring round. Bill and Carmen are tied for 2nd highest scoring candidate with 32 stars each so we'll need to break the tie to determine who should advance to the runoff. Looking at the preference matrix we can determine that Bill is preferred over Carmen, (five voters prefer Bill over Carmen, but only four voters prefer Carmen over Bill,) so this is a simple tie that can be easily resolved. Bill advances to the runoff.
In the runoff, we find that Allison and Bill are both preferred by the same number of voters, (5 each,) but looking at the scores we find that Allison was scored higher overall so this is another simple tie that can be easily resolved. Allison wins the election.
Tiebreaker Example #2:
In the example above, Allison, Bill, Carmen, and Doug are all tied for highest scoring with 78 stars each. Looking at the preference matrix we find that there is a three way tie in the runoff as well! Allison is preferred to Bill, Bill to Carmen, and Carmen to Allison. (This is known as a Condorcet cycle.) Doug is not preferred over any of the others so he is not one of the tied candidates.
Ties like these should be resolved by a tie-breaker chosen and agreed to in advance such as one of the options listed above.
What are Condorcet winners and losers and how do I identify them?
A Condorcet winner is a candidate who in head-to-head match-ups was preferred over every other candidate. A Condorcet loser is a candidate who was not preferred over any of the other candidates.
You can use a preference matrix to quickly compare any two candidates head-to-head to find Condorcet winners and losers.
In this election Allison is preferred head-to-head over all other candidates, which makes her the Condorcet winner. Doug is not preferred over any of the others, so he is the Condorcet loser. If Doug was eliminated, then Bill would become the new Condorcet loser.
STAR Voting usually elects the Condorcet winner if there is one. If STAR elects a different winner, it's because determining Condorcet winners only takes into account preference order but doesn't take into account the strength of support (total score) for the candidates.
STAR Voting finds winners by maximizing both strength of support and number of supporters.
If you are running an election and have additional questions or would like guidance please email us at [email protected]
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