How to use the ranked choice voting calculator
- Enter one group of ballots per line: a count, a colon, then the ranking with > between the names.
- A ballot may rank only some of the candidates. Names that differ only in capital letters count as the same candidate.
- Read the instant runoff rounds and the winner.
- Compare the result with the Borda count and the head-to-head table.
Formula
Instant runoff: count each ballot for its highest-ranked candidate still in the race. A candidate with more than half of the active ballots wins
Otherwise remove the candidate with the fewest votes and count again. Ties for last are broken by an earlier round, then by name
Borda: with n candidates, first choice earns n - 1 points, second n - 2, down to 0
Condorcet winner: a candidate who beats every other candidate head to head
A ballot that ranks no remaining candidate is set aside, and the majority is counted on the ballots still in play.
Nine ballots and three candidates
Four ballots rank A > B > C, three rank B > C > A and two rank C > B > A. In round 1 the counts are A 4, B 3 and C 2, and nobody has more than 4.5, so C is removed. C's two ballots move to B, which makes B 5 and A 4. B has more than half and wins. B also has the most Borda points (12 against 8 and 7) and beats both rivals head to head (5 to 4 against A and 7 to 2 against C), so it is the Condorcet winner too.
The three methods do not always agree. With 33 ballots A > B > C, 32 ballots B > C > A and 35 ballots C > A > B, A beats B, B beats C and C beats A, so there is no Condorcet winner. Instant runoff removes B and elects C with 67, and the Borda count also gives C 102 points to A's 101.
Three ways to count the same ballots
Instant runoff looks only at first choices in each round, so a candidate who is everyone's second choice can be removed early. Borda counts every ranking and rewards broad appeal, but a candidate can win without being first on any ballot. A head-to-head count looks for a candidate that beats every rival in a straight contest. Each method answers a slightly different question, and none is the single correct rule.
Showing all three together lets you see whether the result is robust. When they agree, the winner does not depend much on the rule. When they differ, the disagreement is worth knowing about.
Ties and short ballots
When two candidates tie for the fewest votes, the one with fewer votes in the most recent earlier round where they differed is removed, and if they never differed the names are compared in alphabetical order. The result says which rule was used. This tool does not draw lots or follow any particular election law, so check the rules that apply to your vote. For a different kind of draw see the Tournament Bracket Generator and the Random Name Picker. To turn vote totals into seats use the Proportional Seat Allocation Calculator, and for scoring options on criteria the Decision Matrix Calculator.
Assumptions and limits
- Each ballot ranks its candidates from first choice to last with no ties.
- Unranked candidates score zero Borda points and lose to every ranked candidate head to head.
- The ballots shown are examples. Use your own ballot counts.
- Up to 40 lines and 8 candidates are accepted.
Frequently asked questions
What is an exhausted ballot?
One whose ranked candidates have all been removed. It is not counted in later rounds, which is why the majority threshold can drop.
Why can the winners differ?
The methods use the rankings differently. Instant runoff uses only first choices each round, while Borda uses every position and head-to-head compares pairs.
What does None mean for the Condorcet winner?
No candidate beats all the others, which happens when preferences go in a circle: A beats B, B beats C and C beats A.
How do I enter a ballot that ranks one candidate?
Write the count, a colon and the name alone, for example 10: A. The ballot counts for A until A is removed.