A competition is made up of categories, each category is made up of one or more rounds, each round is made up of one or more heats. A specific heat is referred to as an event and is often given an event number within a running order.

The structure of a competition describes the range of categories offered, the number and size of heats that comprise each round and whether repechages are used. The following terms are used:

• A Final is the last round danced in an event.
• A Preliminary Round is any round that isn't a final.
• A Repechage allows competitors a second chance if they didn't get through the first preliminary round.

A repechage can give anyone who misses the first cut a second chance to progress to the next round. This is especially helpful if the first round hasn't been seeded or where heats have noticeably different numbers of better dancers.

A repechage guarantees that people will get at least two dances at a competition. This is particularly appreciated when there are few other categories that a dancer may enter. However with the appearance of more fun and creative categories the need for repechages has diminished.

• Etymology: comes from the French verb pêcher to fish, hence it means "to fish again ", i.e. have another go! (This is also a good way to remember the spelling)
• If you do not make it to the next round then you are in the repechage.
• This means that you are guaranteed to have at least two dances.
• Competitors who make it through the repechage are mixed with those who made it straight through to the next round.

For example, a round with 48 entries could be split into heats in a variety of ways:

• 2 heats of 24
• 3 heats of 16
• 4 heats of 12
• 6 heats of 8
• 8 heats of 6

Schedules are tight and the more heats there are the longer the competition takes to complete.

For judges, 8 heats of 6 could be more tiring than judging 3 heats of 16. However if there are more than 10 entries on the floor then the judges need more time to look at each entry.

Whether or not heats are seeded we want to be sure that the top 3 entries can make it through to the final should they start the competition in the same heat. This means that in the absence of a repechage at least 3 entries should go through from each heat.

With split floors and more than 8 couples on a floor we start to lose sight of who we're watching and, from a competitor's point of view, who we're presenting to (if applicable / encouraged).

Heats run on split floors cannot be judged across a round.

We could just have two large heats of 24 entries and take the top 3 from each into the final. However going from 48 entries to 6 means than only one in 8 competitors gets to go through. This seems particularly harsh and would not be popular with competitors. Therefore a compromise is required between keeping the number heats down yet numerous enough to give competitors the feeling of progressing through heats, semi-finals and finals for a given category.

Registration is the process whereby competitors can register their details and select the categories they wish to enter.

How many events competitors can enter depends on the competition. Competitors may be able to compete both as a lead and as a follow. The MJPI has separate points tracking for lead and follow.

Competitors may be seeded for the following reasons:

1. We want to initially spread out top dancers in high level events.
2. We want to mix entries from different studios.

Seeding only has an effect at the start of a competition when the first preliminary round of a category is filled with entries.

We can automatically seed entries by examining the points of each entry and their corresponding studio to give an overall optimal seeding.

We normalise each competitor's points for their respective role by subracting the baseline points for the event level they are in. We then take the natural log of the sum of the squares. This has the effect of converting points with a range of a couple of hundred to a seeding with a range of less than 10. When we sort on the seeding and dance studio we end up with competitors in each heat with a range of dance studios and abilities.

Each event requires judges to score the competitors. Most ranking algorithms work best if an odd number of judges is used in order to produce a majority winner. Usually five or seven judges are allocated per round, in the case of Dance With A Stranger (DWAS) two groups of judges are required: one for the lead role and one for the follow role, in which case ten or fourteen judges are used.

The role of the judges is to provide ranking data for the ranking algorithms based on how the competitors meet the judging criteria for the event they are in.

Judges can be ranked in order to eliminate ties without having to resort to a head judge.

We can allocate judges in two ways:

• Session Judging
• Event Judging

Session Judging is where a group of judges judge all events within a certain time period usually associated with a particular round or group of categories. For example the same judges might judge all semi-final freestyle events, but a different judge could judge the finals for the same categories.

This approach is simpler to coordinate but requires that judges are comfortable judging a wide range of events each with different criteria.

Event Judging is where the same group of judges judge every heat and round for a particular category. This tends to be preferred by most judges because the criteria stay the same for each event within the same category.

Teams and Showcases are scored in a different way from other categories due to the different music played for each entry. Entries are scored one after the other under a variety of score headings. The same judges score all the entries within a performance category.

• In a given round the aim is to play music of a similar genre for each heat.
• Genre, Mood and BPM (beats per minute) will be similar for all heats within a given round except for Music Mashup.
• Genre, Mood and BPM will vary between rounds of the same event.
• For most events we choose music that dancers are likely to know.
• Heats can have one or more songs.

Given that the better dancers have reached the finals the music becomes more challenging. Finals can have a range of formats comprising one or more of the following:

• Single song
• Slow and fast song
• Spotlights where each couple perform a dance
• Clustered spotlights (2 or 3 couples dancing at one time)

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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).

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