Tie votes in STAR Voting are rare -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.
In most cases, what appear to be ties in STAR voting can be broken by referring back to the ballots themselves:
- Ties in the Runoff round should be broken in favor of the candidate who was scored higher.
- Ties in the Scoring round should be broken in favor of the candidate who was preferred head-to-head by more voters. Multi-candidate ties are broken in favor of the Condorcet winner if one exists, and can also be narrowed down by eliminating any Condorcet losers. The info needed to do this is present in the preference matrix for the election. (See below.)
- Ties which can not be broken as above are considered a "True Tie."
Q: What is a preference matrix and how do I read one?
A: A preference matrix is a chart which shows all the data from a given election. Unless you are doing a hand count, a matrix is generated automatically and will be available with your election results.
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 anyways.
Q: 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 tabulated 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 step at the end:
- 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.
Q: What if two or more candidates are tied for 2nd highest scoring candidate in the scoring round?
A: Take the tied candidates and compare them head to head with eachother. If one is preferred by more voters then they should advance to the runoff. If needed you can also compare them each head to hear against the highest scoring candidate.
In this election Bill and Carmen are tied for 2nd highest scoring candidate with 67 stars each. Looking at the preference matix we can determine that Bill is preferred over Carmen, so this is not a true tie. 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. Allison wins the election.
Q: What if three or more candidates are tied for highest scoring candidate in the scoring round?
A: Take each candidate and compare them head-to-head with the others in the tie. This is known as a Condorcet method. (See below.) The two most preferred candidates advance to the runoff and the candidate preferred by more voters wins. If none of these candidates are preferred by more voters then it's a true tie.
Q: What is a Condorcet winner?
A: A Condorcet winner is one who in head-to-head match-ups was preferred over all others candidates. Finding Condorcet winners is helpful for breaking 3 way ties or ties with even more candidates if needed. If one candidate was preferred over all others they win the tiebreaker.
In the context of a 0-5 star ballot we determine which candidate was preferred by counting which candidate was scored higher on more ballots, just like in the STAR runoff. It's also essentially the same as a choose-one plurality election if there are only two candidates. Each ballot is one vote and the candidate with more votes wins.
Q: What is a Condorcet loser?
A: A Condorcet loser is a candidate who was not preferred over any of the others. In the event that you are trying to find two candidates to advance to the runoff and there is no Condorcet winner, you can at least eliminate any Condorcet losers.
Q: How do I compare candidates head-to-head and find Condorcet winners or losers?
A: You can use a preference matrix to quickly compare any two candidates head-to-head.
In this election Allison is preferred head-to-head over all other candidates, which makes her the Condocet 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.
Note: STAR Voting usually elects the Condorcet winner if there is one. If STAR elects a different winner, it's because a Condorcet winner 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.
Q: What do you do if there is a true tie?
A: True ties can happen in any voting method, so it is critical to set up a protocol for this in advance and agree upon it. Most organizations which run elections have a protocol in place in their bylaws or charter.
True ties can be broken by random selection. Alternately, if complexity is not an issue they can sometimes be broken using another voting method such as Minimax voting. Minimax itself was developed as a tiebreaker system for 3 way ties in Condorcet elections.
In this election, 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 Condorcet cycle as well! Allison is preferred to Bill, Bill to Carmen, and Carmen to Allison.
A close look also reveals that Doug is not preferred by anyone, Doug is a Condorcet loser and can be eliminated. This election is a three way tie between candidates Allison, Bill, and Carmen.
True ties in elections should be resolved by a tie-breaker chosen and agreed to in advance. Many organizations use a random method like a coin toss. If complexity is not an issue we recommend using another voting method which can process 0-5 star ballots such as Minimax to break the ties.
If you are running an election and have additional questions or would like guidance please email us at firstname.lastname@example.org