Single Transferrable Voting (STV)

An organization's bylaws and rules may dictate what voting method must be used or are looking for a voting system to best present winners according to the voter population's overall preferences by using a Ranked Choice method, such as Preferential Voting.

Single Transferable Vote (STV) is a subset of Preferential Voting where voters rank their choices, and is used when there are multiple positions or vacancies open. The voting process is the same as Instant Runoff Voting (IRV) also known as Ranked Choice Voting (RCV) or Alternative Vote (AV), but the tallying calculation accounts for the transfer of these votes.

While Weighted Voting will work with Preferential Voting if there is only a single-seat position when there are multiple vacancies to select multiple winners in which STV is used weighted voting is unable to be applied within the calculation of the results.

The reason why STV and weighting are not compatible in ElectionBuddy is that we were unable to find a demonstration of an accurate result that is calculated by any sort of preferential voting method with weights. In other words, the overall results may not truly reflect the actual preferences of the electorate because of the weights.

For more information about other voting and tally methods, please see Voting Systems and Calculating Winners

The Voting Process

Voters rank the candidates in order of preference, with “1” being the highest (most preferred) ranking. For example, if there are three candidates, the voter places “1” beside their first choice, “2” beside their second choice, and “3” beside their third choice.

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The ballot is no different than any other preferential vote, but the tallying system is what makes STV unique.

How Results Are Calculated

Results are calculated through the process of redistributing the votes and eliminating low-ranked candidates in rounds to try and get a candidate across the quota of votes required to win. To generate a quota, the total number of submitted votes in a vote is divided by the number of available vacancies for the position plus one. Then, 1/109 is added to that quotient, and the result is truncated to 9 decimal places. For example, if we have 115 votes cast in a vote where the position up for voting has three vacancies:

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In the first round of tallying, the first preference on each ballot counts as a vote for that particular candidate. Any candidate who has at least the minimum number of votes required, as dictated by the quota, is automatically considered a “winner”. In our above example, the candidate would need to have at least 28.750000001 votes to win.

If there is at least one candidate who surpasses the quota, then their surplus votes are transferred. If no candidates surpass the quota, the candidate with the fewest votes is eliminated, and their votes are transferred to other candidates. If candidates are tied for last place, then a candidate is randomly selected for elimination.

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Exhausted Votes

The quota can change if a vote is “exhausted”. A vote becomes exhausted in the event that the voter has not indicated a different candidate to transfer their vote to, or all of their other indicated candidates have already been eliminated. If the voter has not indicated a preference for their vote to be transferred to, then once their final ranked candidate is eliminated, the voter’s vote is eliminated with the candidate. This affects the quota because it affects the numerator of the quota formula: the total number of votes cast is decreasing.

Transferring Rules

No matter whether the votes are coming from an eliminated candidate, or from surplus votes from a candidate above quota, the transferring process is the same. Votes are transferred to the next highest-ranked candidate, as indicated by the voter. However, there is a big difference between transferring surplus votes and transferring votes from an eliminated candidate. When a candidate is eliminated, all of their votes get redistributed, but when a candidate has surplus votes, only some of their votes are redistributed. Depending on which votes are considered “surplus”, the outcome for other candidates can change: if two voters indicated a candidate who has surpassed quota for first place, but their second-choice rankings are different, the outcome for the next candidate could be affected depending on which of the two voters’ ballots are considered “surplus”. To solve this problem, fractions are used to determine the outcome, which keeps the vote distribution fair and unbiased for all candidates.

In the above example, imagine a candidate received 32 votes, over 3 greater than the quota of 28.750000001 votes. That candidate has a little over 3 surplus votes to be distributed (32-28.750000001=3.249999999). The surplus votes are transferred at 3.249999999/32, or 0.101562499, of their value. After all votes had been redistributed, 3.249999999 total votes were transferred.

Meek’s STV Method

ElectionBuddy uses Meek’s STV to transfer votes. The candidates who have hit the quota continue to be a part of the receiving and transferring of votes. Each candidate is assigned a keep factor that identifies how much of the votes they receive should be transferred away. So, any candidate under quota will have a keep factor of 1, because they will keep the entire portion of the vote and not transfer anything away.

Candidates above the quota will have a keep factor of less than one because their votes will always have a portion transferred away to keep them at quota. Because the candidates are always getting votes, even if they’ve reached or surpassed quota, the voter’s votes are always going to their intended candidates, even though a portion of that vote may be transferred away.

For more information, please see Reference Meek Rule on Proportional Representation Foundation and a read of Meek's method.

The difference between a regular preferential vote and STV is the number of vacancies. The basic IVR vote has one vacancy (a single seat). When multiple vacancies exist, STV accounts for all preferences when tallying the votes. During the tally, surplus votes are “transferred”, based on the ranking assigned to the candidates at the time of voting, in order to ensure that all vacancies are filled. To transfer votes, ElectionBuddy uses Meek’s STV Method. This will be explained in more detail in “How the Results are Calculated”.

Using STV for Ranking

STV is a great voting method when it comes to filling multiple vacancies, but there are some limitations to it that may make other voting methods a better option.

STV sets a quota that needs to be hit during each round. What STV doesn't do is rank each option; it just specifies which option achieved the necessary quota and continues to calculate rounds of voting based on the ranked voting choices by the voters until the vacancies are filled. Single Transferrable Voting (STV) will help you understand why a ranking is not possible given the calculation.

If ranking the winning candidates is the goal, you can download the results and manually calculate a winner using a method such as the Borda Count You can also use Plurality Voting (also known as 'First Past The Post') and run multiple rounds of votes as separate new votes, more commonly known as 'runoff votes' until you have determined the rank order. Or you can do Scored Voting, but voters can assign the same score to multiple choices.



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Apr 25, 2024