Single Transferable Vote (STV) — How Does it Work?

October 2, 2017

Single Transferable Vote: What’s That?

Single transferable vote, or STV for short, is the voting method used when one wants to run a preferential vote on a given position, but has multiple vacancies for that position; for a regular preferential ballot, there is only one vacancy. As far as the overall feel of casting an STV-based ballot is concerned, from the eye of a voter, there is no difference between an STV and a regular preferential ballot. It is only when we get to the tallying portion that the magic starts to happen.

The name says it all: this voting method involves transferring votes. But, how? What does this mean? 

Results are calculated through the process of redistributing votes in rounds, based on the voters’ indicated preference for a candidate. Low-ranked candidates are eliminated. Transferring votes from those eliminated candidates helps get other candidates across the line. Additionally, candidates that have surpassed the quota and therefore have already secured a spot also have their surplus votes redistributed. 

ElectionBuddy specifically uses Meek’s STV, which is a modified version of conventional STV. We will address Meek’s STV below!

The Single Transferable Vote Quota: Droop Quota

STV quota formula
STV formula

There are a few different ways to calculate a quota; ElectionBuddy uses a Droop quota. Calculating a Droop quota involves some simple mathematics. First, the total number of submitted votes in an election is divided by the number of available vacancies for the position, plus one. Then, 1×10^-9 is added to the quotient, and the result is truncated to nine decimal places. For example, if we have 115 votes cast in an election where the position up for election has three vacancies, we would calculate the quota using the formula on the left.

Single Transferable Vote: Round #1

The first round is very straightforward: the first preference on each ballot is a vote for that particular candidate. The votes are tallied. Any candidate(s) who have at least the minimum number of votes required, as dictated by the quota, win. So, in our above example, a candidate would need to obtain, at minimum, 28.750000001 votes to win.

Now, we need to decide how to transfer votes. Surplus votes are the first choice to be transferred; but, if no candidates surpassed the quota, the candidate with the fewest votes is eliminated. Their votes get transferred to other candidates. When two candidates are tied for last place, a candidate is randomly selected for elimination.

Subsequent Single Transferable Vote Rounds: To Transfer, or To Eliminate?

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: transfer the votes 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!

Logically, when a candidate is eliminated, all of their votes need to be redistributed. But, when a candidate has surplus votes, only some of their votes are redistributed, because they still need to have votes in order to be elected!  So, 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, we transfer votes in fractions, which keeps the vote distribution fair and unbiased for all candidates. 

With regards to our previous example: imagine a candidate received 41 votes. That candidate has just over twelve surplus votes to be distributed (41-28.750000001=12.249999999). The surplus votes get transferred at 12.249999999/41, or 0.298780488, of their value.  So, when transferred at such a small amount of their total value, the re-distribution of votes results in 12.249999999 total votes being transferred.

The rounds of transferring surplus votes/eliminating candidates and transferring their votes continue until you are left with enough winners to fill the position. 

Exhausted Votes and the Dynamic Nature of the Single Transferable Vote Quota

The quota changes when a vote is “exhausted”. A vote becomes exhausted when a voter has no next most-preferred candidate to transfer votes to. When there is no next most-preferred candidate for a voter, then once their ranked candidates are eliminated, the voter’s vote is eliminated with the last eliminated candidate. This affects the quota because it impacts the numerator of the quota formula — the total number of votes cast decreases.

Meek’s Single Transferable Vote Method

Conventionally, once a candidate has reached quota, that’s it – they have won a seat, and so they are excluded from any subsequent rounds of vote transferring (unless the quota changes). Meek’s STV, as previously mentioned, is a modified version of conventional STV. The candidates who have hit quota continue to be apart of the receiving and transferring of votes. Each candidate is assigned a keep factor that identifies the percentage of votes that they get to keep per round. So, any candidate under quota has a keep factor of 1, because they will keep the entire portion of their votes to attempt to reach quota. Candidates above the quota will have a keep factor of less than one. This is because their votes will always have a portion transferred away to keep them at quota.

The Benefit of Meek’s Single Transferable Vote Method

The main benefit of Meek’s STV is that it is beautifully democratic, especially when compared to other STV methods. 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. This is why we use it in our STV calculations. 

Constantly adjusting and cycling votes around sounds complicated, and if you don’t like math, it is definitely a little complex. Take a look at this guide to evaluate the difficulty for yourself!

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