Who Woulda Won?

Relative placement is the official scoring system used in WSDC competitions. It works by finding, for each placement, the competitor who has a majority of judges ranking them at that place or better.

The system processes placements in order (1st, 2nd, 3rd, etc.). For each placement, it counts how many judges ranked each remaining competitor at that place or higher. This is the cumulative count. A competitor is placed when they achieve a majority at some cumulative count.

When two or more competitors reach a majority in the same cumulative count column, tiebreakers apply:

• Greater majority: The competitor with more judges at or above that column wins the tie.
• Quality of majority: If still tied, sum the actual placements given by the judges who contributed to the majority. The lower total (better quality) wins.
• If still tied, take the next cumulative counts for the tied competitors, and so on until the tie is broken.
• If all cumulative counts are exhausted and there are still two tied competitors, take a head-to-head vote between the two.

In the working table below, each competitor's row shows their individual judge placements, followed by cumulative counts. Where a quality of majority score was needed to break a tie, this is shown in parentheses. The cell where a majority is first reached is highlighted. If you roll over a cumulative count cell, the cells of the contributing individual judges are highlighted.

This system is also known as (part of) the Skating System. It is used in many partner dance competitions, including WCS, Lindy hop, salsa, bachata, zouk and ballroom.

The Borda count assigns points based on each judge's ranking. With n competitors, a 1st-place ranking is worth n−1 points, 2nd place is worth n−2, and so on down to 0 for last place. Each competitor's points are summed across all judges. The competitor with the highest total wins.

The implementation below breaks ties using a recursive Borda count: The tied competitors are re-scored using only their relative rankings among each other, effectively running a smaller Borda count within the tied group. This process repeats if the tiebreak itself produces another tie.

The Borda count tends to favour broadly acceptable candidates over polarising ones, since it rewards consistent mid-to-high rankings rather than requiring outright majorities.

The Schulze method uses head-to-head voting between pairs of competitors to produce an overall ranking. Where majority votes are cyclic (A beats B, B beats C, C beats A), it uses beatpath strengths to resolve the conflict.

The first table below is a pairwise preference matrix. Each cell shows the number of judges who ranked the row higher than the column. Cells are highlighted in green if more judges preferred the row than preferred the column.

The second table below shows the strongest beatpath strengths. A beatpath from A to B is a sequence of pairwise victories. Its strength is the weakest link in the chain, as given by the smallest majority. For example, if A beats X 5–2, X beats Y 4–3 and Y beats Z 6–1, the beatpath from A to B has strength 4. If no beatpath is available, it is recorded as zero. As you roll over this table, it will show the beatpath giving the strength in each cell.

A competitor has a Schulze win against another if their strongest beatpath to that opponent is stronger than the opponent's beatpath to them. Competitors are ranked by how many Schulze wins they have, with Schulze ties counting as half.

The implementation below breaks ties using the sum of winning beatpath strengths.

The Schulze method is a Condorcet method: If there is a candidate who beats every other candidate in a pairwise head-to-head vote (a Condorcet winner), this method is guaranteed to pick that winner. You can tell if there's a Condorcet winner from the pairwise preference matrix: if a row is all green (except the cell on the diagonal), the competitor in that row is the Condorcet winner.

Sequential instant runoff voting (IRV) determines placements one at a time. To find 1st place, it runs a full IRV election among all competitors. The winner is removed, and IRV runs again among the remaining competitors to find 2nd place, and so on.

Each IRV election works as follows:

• Count each judge's top-ranked competitor (among those still in the race) as a first-preference vote.
• If a competitor has a majority (more than half of all votes), they win.
• Otherwise, the competitor with the fewest votes is eliminated, and their votes are redistributed to each judge's next preferred competitor.
• This process repeats until someone achieves a majority.

Because dance competitions use a small number of judges (relative to an election), ties are common. This implementation breaks ties as follows:

• If there is a tie for fewest votes, a restricted vote is taken among those competitors tied for the fewest votes, with each judge voting for their highest preference among those tied. If there is one competitor with the fewest votes in this restricted vote, they are eliminated. Otherwise, this process repeats among those tied for fewest votes until a unique eliminee is found.
• If all competitors are tied, it will not be possible to reduce the field using a restricted vote. Instead, the judges' 2nd preference votes are tallied, and the competitor with the fewest such votes is eliminated. If all competitors remain tied, 3rd preference votes are taken, and so on. If some but not all competitors remain tied, the next restricted vote returns to 1st preference votes.