Recall and Entry Listings

Usually the heat entry listings are printed on paper and displayed near the marshalling area. The term 'recall' is used in the context of when competitors are recalled to enter the next round. Online recall is where competitors can access the same information online.

How Heats are Filled

The heats in the first round are filled according to any seeding in place and by mixing entries from different studios to make the heats more exciting and varied.

For subsequent rounds, entries from the previous round and repechage (where applicable) are sorted in descending order of score, heats are then filled automatically to give the most even spread of ability.

Example: 24 entries going into 4 heats (6 entries per heat)

• Entry 1 goes into Heat 1, Entry 2 to Heat 2, Entry 3 to Heat 3, Entry 4 to Heat 4
• Entry 5 goes into Heat 1, Entry 6 to Heat 2, Entry 7 to Heat 3, Entry 8 to Heat 4
• Repeat until all entries have been allocated to a heat.

This ensures that the best entries do not end up in the same heat.

Allocating Floor Positions

Floor positions are allocated randomly. Therefore there is always the slim chance that an entry may find themselves in the same position for each event. A future development would be a more intelligent floor positioning algorithm to avoid this.

Strong Ranking versus Weak Ranking

A judge has to produce data that is used to rank all the entries in a heat or round. There are two types of ranking:

• A Strong Ranking is a ranking without ties.
• A Weak Ranking is a ranking with ties.

Judges need to be able to rank all competitors in the time available. This then determines the type of ranking used for each round. The higher the number of entries the harder it is to rank the entries within the time available.

Where there are 8 entries or less, a judge can comfortably produce a strong ranking.

For more than 8 entries, judges use a weak ranking. Two common variations used in dance competitions are:

• Yes or No (Selected or Not Selected). This is equivalent to ranking competitors between 1 and 2 with ties allowed.
• Yes, Maybe or No (Selected, Alternate or Not Selected). This is equivalent to ranking competitors between 1 and 3 with ties allowed.

Competitors can be ranked across an entire round or within a heat. If split floors are used then competitors can only be ranked across each heat.

Preliminary Rounds

In preliminary rounds there is often a wide range of abilities and a large number of competitors usually arranged in at least two heats. A weak ranking is sufficient to provide enough information to determine which entries go through to the next round.

Final

For finals we are aiming to get an overall strong ranking in order to award 1st, 2nd and 3rd places. Judges are required to give a strong ranking which will provide enough information to separate the entries.

Variation Among Judges' Ranks

It is important to understand that variation amongst judges' scores is expected. Each judge will view different parts of the competitors' performance and will also apply the judging criteria slightly differently, therefore it is reasonable to expect some variation in the scores supplied by the judges (see analysis of actual data below). Potential factors include:

Factor 1. Consistency of a Competitor's Performance

• A heat occurs over a length of time (e.g between one and a half and three minutes) where all competitors dance at the same time.
• Judges cannot watch all competitors simultaneously for duration of the heat.
• For a given competitor, Judge A might see their best 20 seconds and rank them high while Judge B might see their worst 20 seconds and rank them low.
• It would therefore follow that the more consistent a competitor's performance the lower the variation of the resulting ranks.

Factor 2: Variety of Criteria

Modern Jive is one of the most flexible partner dance styles around. There's even a mathematical principle behind this - basically it's all down to its lack of specific footwork. So much variation is possible that it is impossible to rigorously rank and weight criteria for competitors to judged against especially where there is variation in how Modern Jive is taught. To quote a national champion, judge and studio co-owner:

"If I watch Ballroom I see a floor of people trying to look the same, when I watch Modern Jive I see a floor of people trying to look different."

• While criteria are often listed in order of importance, there is no absolute scale showing the weight of each criteria and as mentioned above, it is not possible to come up with one nor would we necessarily want one.
• Each judge will have a slightly different internal comparative scale which they use to come up with an overall feel for how well a competitor performs.
• By having a variety of judges, the winning competitor is the one who scores best in the eyes of all the judges.

Factor 3: Similar Level Performance from Competitors

• The closer a heat is, the wider the variation of scores.
• The judges have to produce a ranking even if they think that all the competitors meet the criteria to the same extent. So how each judge finally splits the ties will vary such that the final rankings could all be completely different.

Ranking

Ranking is the process where the judges' scores are fed into an algorithm and a final overall ranking is produced for each round.

The main challenge is to combine the judges scores in such a way that the best couple or dancer wins. This may sound fairly obvious but due to flaws with some algorithms the best couples do not necessarily win!

Finals can sometimes have up to 3 songs (slow, fast, spotlight), so we must be able to combine the judges' scores for each song.

Performance categories such as Teams and Showcases often have a number of criteria, for example: timing, teamwork, technique, choreography, performance, costume etc. Some of these criteria may be weighted, for example, costume is not usually considered as important as the other criteria. Again, any ranking system must be able to combine scores for each criteria to give an overall ranking.

Breaking Ties

Another challenge is how to deal with ties. In some dance competitions ties are broken by the head judge or by examining scores from previous rounds.

The MJPI scoring system calculates the overall ranking using three different methods or algorithms. If there is a tie from the first method then the second one is used and so on. If there is still a tie after the third method then judge rankings are used to finally break any remaining ties.

Results & Scores

Once all the finals have been scored the competition has come to an end and all that remains is to publish and share the results. The results are usually given for competitors who place 1st, 2nd or 3rd. An individual's scores are then sometimes made available online.

These all tend to come under the term Ranked (or Preferential) Voting Systems as they are often associated with elections either at a national or regional level. There are other Voting Systems, notably Range Voting. Many electoral voting systems are not particularly fair but are easy to explain to the public. So ease of interpretation of the system used wins over a fair election 😥

A Condorcet Method is "any election method that elects the candidate that would win by majority rule in all pairings against the other candidates, whenever one of the candidates has that property". It is often useful to know if a particular ranking algorithm or election method is a Condorcet Method.

Schulze Method

This is our preferred ranking algorithm. It passes more tests of fairness than the others below and is a Condorcet method which the others below are not.

This is a ranking algorithm similar to Ranked Pairs. It very easy to implement in software. We also use the Schulze method to work out a final ranking from Yes / No / Maybe scores.

Skating System

The Skating System has been in use since 1937. In Dancesport competitions there can be as many as 10 different dances and this system aims at picking the overall best performers. However it is not a Condorcet Method and in less 2% of cases the best couple does not win! (Refer to statistical analysis performed by Xavier Mora Dancesport adjudicator and Professor of Mathematics, Barcelona Universty).

• Used by Dancesport and other dance styles
• Odd number of judges 3, 5, 7, 9 etc to reduce likelihood of ties.
• Competitors are scored across the round.
• The multi-dance aspect does not satisfy the Ostrogorski Paradox as mentioned in Professor Mora's paper (the Schulze Method handles multi-dance finals with greater fairness).

Relative Placement

The World Swing Dance Council uses Relative Placement and it is also used by other dance styles. It is similar to the Skating System but with a couple of minor differences.

• 3 options for judging competitors in preliminary rounds: selected, not selected, alternate.
• Judges do not have to mark a specified number of competitors to go through nor do they have to select a certain number across all heats.

There are many discussions regarding the fairness (or rather unfairness) of the Skating System and Relative Placement. Neither are Condorcet Methods nor are not listed as standard voting systems in mainstream or academic articles. Their main advantage is that they can be calculated by hand, however computers have meant that fairer systems can now be used instead.

Borda Count and Raw Scores

Borda Count deals with raw rankings / scores and is not recommended as it is not a Condorcet Method.