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Borda Count Explained: How Positional Points Pick a Consensus Winner

Borda does not ask who you love, it asks who everybody can live with. Each position in your ranking awards points, and the highest total wins. Here is the arithmetic, the Nauru variant, and the strategic weakness every board should know before adopting it.

VD
vote.direct team
An ordered stack of ranked bars descending in weight, illustrating how Borda count awards points by position

Quick Answer

The Borda count reads a ranked ballot as a set of points. With N candidates standing, a first-place ranking earns N minus 1 points, second earns N minus 2, and so on down to zero. Points are added across every ballot and the highest total wins, or for a board, the highest totals fill the seats.

Borda rewards broad acceptability rather than passionate first-place support. A candidate ranked second by almost everyone can and often does beat a candidate ranked first by a third of the room and last by the rest.

This article is general information, not legal advice. Confirm what your governing documents allow before adopting a new method.

How the Points Work

With five candidates on the ballot:

PositionClassic pointsDowdall points
1st41
2nd31/2
3rd21/3
4th11/4
5th01/5

A candidate a ballot leaves unranked earns nothing from it. That is the standard reading for truncated ballots: each point represents a head-to-head win the ballot is asserting, and a ballot that never mentions a candidate asserts nothing on their behalf.

A worked example

Four candidates, one seat, 100 members, classic scale so first place is worth 3.

Candidate1st2nd3rd4thPoints
Tanaka40102030160
Ubaldi2550205195
Vargas30153520155
Weiss525254590

Tanaka leads on first preferences with 40 and would win outright under plurality. Ubaldi wins the Borda count with 195, because 75 members put Ubaldi first or second and only 5 put them last. That is Borda doing exactly what it is designed to do, and whether you regard it as the right answer is a governance judgment, not a mathematical one.

The Dowdall Variant

Dowdall, used by the parliament of Nauru, replaces the linear scale with a harmonic one: 1, then a half, then a third. The drop-off is far steeper, so first preferences carry much more weight and the method behaves partway between Borda and plurality.

If your bylaws mention Nauru or name "the Dowdall system", that is the scale they mean. Both are available as a setting on the same question.

The Known Weakness

Borda is unusually sensitive to strategic ranking and to which candidates are on the ballot at all.

  • Burying. A voter can rank their favorite first and then deliberately rank the strongest rival last, below candidates they actually prefer less. It is a cheap and effective way to move points.
  • Clone candidates. Adding two similar nominees can lift or sink a related candidate's total by shifting everyone's positional points, even though no voter changed their mind.

Neither is a reason to avoid Borda. It is a reason to use it where the field is stable and the electorate is not adversarial, such as committee selection, award panels and priority ranking, and to think harder before using it for a contested board seat.

Borda Compared

BordaCondorcetInstant runoff
What it optimizesAverage rank positionHead-to-head winsMajority after eliminations
CountingOne passOne pass over pairsMultiple rounds
Elects the head-to-head winnerNot alwaysAlways, when one existsNot always
Vulnerable to buryingYesLessLess
Multi-seatYesNoNo, use STV

Running a Borda Count Online

Borda is the Ranked choice question type with the counting method set to Borda count. The ballot is an ordinary ranked ballot, identical to the one used for instant runoff and STV.

Two settings:

  • Point scale. Classic, meaning N minus 1 down to zero, or Dowdall.
  • Seats. How many candidates win. The highest point totals take the seats.

Weighted elections multiply a ballot's points by its weight, consistent with every other count on the platform. Point totals are compared at the platform's display precision, so two totals that render identically are treated as the tie they appear to be, and a tie at the last seat is reported rather than resolved by lot.

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

Frequently Asked Questions

Q: What is the Borda count?

A ranked voting method where each position on a ballot awards points, first place earning the most, and the candidate with the highest point total wins.

Q: What is the Borda count formula?

With N candidates standing, a first-place ranking is worth N minus 1 points, second is worth N minus 2, and so on to zero for last place. Unranked candidates receive nothing.

Q: What is the Dowdall system?

A Borda variant used by Nauru where the points are 1, one half, one third and so on. The steeper drop-off makes first preferences count for far more than under the classic scale.

Q: What is wrong with the Borda count?

It is vulnerable to burying, where a voter ranks a strong rival artificially low, and to clone candidates changing totals without anyone changing their mind. It suits stable, cooperative fields better than contested elections.

Q: Does the Borda count elect the same winner as ranked choice voting?

Often, but not always. Borda rewards broad acceptability while instant runoff rewards majority support after eliminations, so a candidate ranked second by nearly everyone can win under Borda and lose under instant runoff.

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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