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Single Transferable Vote Explained: Quotas, Surpluses and Transfers

STV is the method that makes a board actually look like its membership. It is also the one people find hardest to explain. Here is the quota, the surplus transfer and the exclusion rule in plain language, with a worked count and the three published rulebooks.

VD
vote.direct team
A funnel narrowing many candidate cards down to a few elected seats, illustrating single transferable vote transfers

Quick Answer

Single transferable vote is ranked-choice voting for more than one seat. Voters rank candidates. A candidate is elected on reaching a quota, and from then on the count stops wasting votes in two directions: surplus votes above the quota transfer onward at a fraction of their value, and candidates with no path to a seat are excluded and their votes transfer at full value.

The result is proportional. A faction holding a third of the ballots wins roughly a third of the seats, without anyone having to organize a slate.

This article is general information, not legal advice. Confirm what your governing documents require before your board relies on any method described here.

The Quota

The quota is the number of votes that guarantees a seat. STV uses the Droop quota:

quota = total valid votes / (seats + 1), and a candidate is elected on holding strictly more than that.

With whole votes this is the familiar floor of V divided by S plus 1, then add one. With weighted ballots, where a member might hold 1.5 shares, it is the same rule without the rounding.

Why seats plus one? Because that is the smallest share that cannot be matched by every remaining seat-holder at once. With three seats, four people cannot each hold more than a quarter of the votes, so anyone who does has mathematically secured a seat.

SeatsQuota (share of votes)
1Over 1/2
2Over 1/3
3Over 1/4
5Over 1/6
7Over 1/8

The Count, Step by Step

  • 1First preferences. Every ballot counts for its top choice.
  • 2Elect anyone over quota. They are in.
  • 3Transfer the surplus. An elected candidate keeps exactly a quota. Everything above it is surplus, and every ballot they hold moves to its next continuing preference carrying a reduced value: its current value multiplied by the surplus divided by that candidate's total. All of their supporters share proportionally, rather than a lucky subset having their votes transferred whole.
  • 4Otherwise exclude the lowest. With no surplus outstanding and seats still open, the candidate with the fewest votes is excluded and their ballots transfer at full current value.
  • 5Repeat until every seat is filled.
  • 6Exhausted ballots. A ballot with no continuing preference left stops counting, at whatever value it carried. This is why deep rankings matter to voters who care about the last seat.
  • 7Short circuit. When only as many candidates remain as there are unfilled seats, they are all elected, because quota can become unreachable once enough ballots exhaust.

A worked example

Three seats, 1,000 ballots. Quota is 1,000 divided by 4, so a candidate is elected on more than 250.

StageAdeyemiBhattCostaDupontEriksen
First preferences40024018011070
Adeyemi surplus (150) transfers250285205145115
Eriksen excluded250300240210out
Dupont excluded250320315outout

Adeyemi is elected at stage one with 400, keeps 250, and the 150 surplus is spread across every one of their ballots at 150/400 of its value. Bhatt crosses quota at stage two. Eriksen and then Dupont are excluded, and Costa takes the third seat. Notice that the 400 first-preference votes for Adeyemi did not go to waste, and neither did Eriksen's 70.

The Three Rulebooks

"STV" names a family, not one procedure. The differences matter when a result is close, so bylaws often name a specific rulebook. All three are supported:

RulebookWhere it comes fromDistinctive feature
Scottish rules (WIGM)Scottish local government electionsWeighted Inclusive Gregory Method. Every ballot a candidate holds transfers at a reduced value. The default.
Meek methodNew Zealand local elections, by statuteIterative. Keep factors are recalculated until every elected candidate holds exactly a quota, and the quota itself falls as ballots exhaust.
ERS97Electoral Reform Society, 1997, 3rd editionThe hand-count rulebook UK societies and unions name in their standing orders. Deferred surpluses, batch exclusions, two-decimal transfer values.

If your standing orders say "counted under ERS97", that is a real and specific instruction, and the count follows the numbered clauses.

Ties

Every published STV rulebook eventually says to draw lots. We never do.

Where a tie is procedural and provably cannot change who wins, the count refers to earlier stage totals, a reproducible published rule. Where a tie actually decides who takes the last seat, the result reports it, names the seats it blocks, and leaves the decision to your board under its own bylaws. A certificate that records a coin flip as an election result is not worth printing.

Running STV Online

STV is the Ranked choice question type with the counting method set to Single transferable vote. The ballot voters see is an ordinary ranked ballot, identical to instant runoff, so switching method does not change the voting experience.

Set the number of seats, and optionally the rulebook. Every stage of the count is published: quota, per-stage totals, transfers, values and exclusions, so a member can follow exactly how the seats were filled.

Elections up to 25 voters are free, and paid elections start at $4.99.

Frequently Asked Questions

Q: What is single transferable vote?

A proportional multi-seat method where voters rank candidates, a candidate is elected on reaching a quota, and both surplus votes and votes for excluded candidates transfer to later preferences instead of being wasted.

Q: What is the Droop quota?

Total valid votes divided by the number of seats plus one. A candidate is elected on holding strictly more than that figure. It is the smallest share that guarantees a seat.

Q: What is the difference between STV and ranked choice voting?

Instant runoff, usually called ranked choice, fills one seat by eliminating the lowest candidate each round. STV fills several seats and adds surplus transfers. The ballot is identical, only the count differs.

Q: What is the difference between the Scottish, Meek and ERS97 rules?

Scottish rules transfer every ballot an elected candidate holds at a reduced value. Meek recalculates keep factors iteratively and lets the quota fall as ballots exhaust. ERS97 is a hand-count rulebook with deferred surpluses and two-decimal transfer values.

Q: What happens to my vote if my first choice is already elected?

The portion of your vote above what that candidate needed transfers to your next preference. Your ballot keeps working rather than being locked to someone who already had enough.

Ready to run one? Create your election, or compare every method in the voting methods series.

This article is general information, not legal advice. We recommend you do your own research and confirm anything you plan to act on. Where this article states law, the section is cited so you can read the primary source yourself rather than take our word for it — that is what the citations are for. Election requirements also turn on your own governing documents, which we have not seen, and statutes are amended. For advice about your community, consult a qualified attorney licensed in your state.

We work hard to verify every citation against the primary source, but laws change and errors happen. If you spot an inaccuracy, email [email protected] and we will correct it. See our editorial standards for how these pages are researched and checked.

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