Majority system
The majority system is a calculation rule that is used when adjudicators make placement recommendations. This is primarily the case in dance sport . In addition, the skating system is used if there is no space .
Procedure
requirements
There must be an odd number of adjudicators for the majority system to work. These give a placement recommendation for each participant, which means that each judge can only assign each place once.
Calculation method
The places are awarded one after the other, starting with the first place. For this purpose, the placements are processed one after the other, also starting with the first place. Later in the procedure, the space to be allocated and the examined placement do not have to match.
- Clear majority - If only one participant who has not yet been placed has an absolute majority for the placement examined, he wins the place to be awarded. Then the next place is assigned by examining the next lower placement (higher place numbers).
- Several participants with a majority - If there are several unplaced participants who have received a majority for the examined place, the winner is the participant who received the greater number of placements for this place or better. If several of these participants have an equally strong majority, the place numbers that make up this majority are added up and the person with the lowest total receives the place to be allocated (since he then received more "better" places). If the total is also the same, the next lower ratings for this participant are added one after the other until the place is allocated or all ratings have been taken into account and two or more shared places are allocated. The next free place is then allocated by examining the same ranking (or if there are two participants with the same majority, the losing participant receives the next free place).
- No participant with majority - If none of the not yet placed participants achieved the majority for the examined placement, the place is allocated by examining the next placement.
Strengths and weaknesses of the system
A disadvantage of the majority system is that it is not immediately obvious to the uninitiated. The arithmetic mean of the placement recommendations is often formed intuitively , but it does not make sense for a fair placement. It would be different with the award of points. A small example should make this clear:
Participants A and B received the following ratings:
| Start number | Ratings | arithm. Average | ||||
|---|---|---|---|---|---|---|
| A. | 1 | 1 | 1 | 1 | 7th | 2.2 |
| B. | 2 | 2 | 2 | 2 | 2 | 2 |
After considering the arithmetic mean, B would be placed first and A second. Firstly, this would not correspond to any of the judges' wishes and, secondly, the fifth judge's score would have a disproportionately high weight. Avoidance of the latter is a strength of the majority system.
History in dance sport
The original version of the majority principle was formulated by the English-speaking author Arthur Dawson . After some improvements in 1947 and 1948, the system was not changed again until June 25, 1956 by the Official Board (effective September 1, 1956). The system was adopted for German tournament sports, with the numbering of the original article also being adopted in the regulations (Paragraph 2 in the appendix to the DTV tournament sports regulations (TSO)). (Since the rules about the judges (1 to 4) are regulated elsewhere in the TSO or in the scoring guidelines, they are not listed in the appendix to the TSO.)
Examples
In the following examples, a “participant” is used neutrally. Depending on the type of tournament, this can be a couple, a formation or a single person.
Clear majority for each place
| Start number | Ratings | ||||
|---|---|---|---|---|---|
| 11 | 1 | 1 | 2 | 1 | 2 |
| 12 | 2 | 2 | 1 | 3 | 1 |
| 13 | 3 | 3 | 3 | 2 | 3 |
The ranking is calculated on a table, on which it is noted how many ratings the participant has received for a place and which place the participant gets. However, this is only filled in as far as the placement requires (in order not to create unnecessary confusion). The other fields are marked with "-". Often the individual judges are also listed in the scores (here denoted by A to E).
For this example the following results (majorities are marked here and in the following examples with an asterisk):
| Start number | Ratings | Places | Result | ||||||
|---|---|---|---|---|---|---|---|---|---|
| A. | B. | C. | D. | E. | 1 | 1-2 | 1-3 | ||
| 11 | 1 | 1 | 2 | 1 | 2 | 3 * | - | - | 1 |
| 12 | 2 | 2 | 1 | 3 | 1 | 2 | 4 * | - | 2 |
| 13 | 3 | 3 | 3 | 2 | 3 | 0 | 1 | 5 * | 3 |
The participant with starting number 11 received first place from three judges. Since this corresponds to the majority with five judges, he receives first place ( a "-" is entered in fields 1-2 ( 2 and better ) and 1-3 ( 3 and better )).
The participant with starting number 12 only has two first places. Since with two ones and two twos he got a total of four ratings 2 and better (entered in field 1-2 ), he has a majority for second place.
The participant with starting number 13 could not get a ranking for first place ("0" in field 1 ). Also there are not enough 2 and better places (here only one). For third place, the participant has the majority and thus receives third place.
Several majorities
| Start number | Ratings | Places | Result | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| A. | B. | C. | D. | E. | 1 | 1-2 | 1-3 | 1-4 | 1-5 | ||
| 11 | 1 | 1 | 1 | 5 | 2 | 3 * | - | - | - | - | 1 |
| 12 | 2 | 3 | 3 | 1 | 1 | 2 | 3 * (4) | - | - | - | 2 |
| 13 | 3 | 2 | 2 | 2 | 5 | 0 | 3 * (6) | - | - | - | 3 |
| 14th | 4th | 4th | 5 | 3 | 3 | 0 | 0 | 2 | 4 * | - | 4th |
| 15th | 5 | 5 | 4th | 4th | 4th | 0 | 0 | 0 | 3 * | - | 5 |
Columns 1 to 1-5 are checked: The first place is clear because only the participant with the start number 11 has a majority: Participant 11 has three ones, while participant 12 only got two ones. Participant 11 is now rated and a "-" is entered for 1-2 to 1-5 .
Column 1-2 is now considered: Participant 12 has three ratings 2 or better , just like participant 13 with three twos. This means that two participants have an equal majority (if there are five judges, three are required for a majority). So the sum of the evaluations is considered, but only those that make up the majority. It is written after it in brackets. Second place goes to participant 12 (1 + 1 + 2 = 4), while participant 13 (2 + 2 + 2 = 6) receives third place. If no decision had yet been made with the total, the lower scores would also have to be taken into account for these two participants. (See another example below.)
Further in column 1-3 : Nothing is decided there, as none of the remaining participants received a majority for this.
Column 1-4 now brings the decision for the two remaining participants: The participant with starting number 14 has a majority of four ratings for 4 or better , while participant 15 also received a majority. But that's only three ratings 4 or better , so fourth place goes to participant 14 and fifth place to participant 15.
Not a majority
It can easily happen that none of the participants was able to win a majority. Then the other places are also taken into account to determine a winner:
| Start number | Ratings | Places | Result | ||||||
|---|---|---|---|---|---|---|---|---|---|
| A. | B. | C. | D. | E. | 1 | 1-2 | 1-3 | ||
| 11 | 1 | 1 | 2 | 2 | 3 | 2 | 4 * | - | 2 |
| 12 | 2 | 2 | 1 | 1 | 2 | 2 | 5 * | - | 1 |
| 13 | 3 | 3 | 3 | 3 | 1 | 1 | 1 | 5 * | 3 |
Column 1 does not bring a majority to any participant, since participants 11 and 12 could only combine two ones and the fifth one went to participant 13. Therefore, column 2 or better ( 1-2 ) must now be considered.
There you can see that participant 11 only got four ratings that were 2 or better . Participant 12, on the other hand, only had ones and twos and was able to combine all five places better than two . The participant 13 only has a rating of 2 or better with the one one and thus no majority. The first place therefore goes to the participant 12, the second place to the participant 11.
The third column ( 1-3 ) allows the only space still to be allocated to go to participant 13.
Shared places and wins with 2nd place
Thanks to the majority system, it is possible for those who have only received second places to win: if there is no majority for first place, the next places must also be included in the scoring. If a participant got all (or many) twos, he may have the greatest majority here:
| Start number | Ratings | Places | Result | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| A. | B. | C. | D. | E. | 1 | 1-2 | 1-3 | 1-4 | ||
| 11 | 1 | 1 | 3 | 3 | 4th | 2 | 2 | 4 * (8) | 5 * (12) | 2.5 |
| 12 | 2 | 2 | 2 | 2 | 2 | 0 | 5 * | - | - | 1 |
| 13 | 3 | 3 | 4th | 1 | 1 | 2 | 2 | 4 * (8) | 5 * (12) | 2.5 |
| 14th | 4th | 4th | 1 | 4th | 3 | 1 | 1 | 2 | 5 * | 4th |
First, the column of the first places should be considered again: Participants 11 and 13 each received two ones, participant 14 a one. This means that no participant has a majority and column 1-2 must be taken into account.
Since all two went to the participant with the starting number 12, nothing changes in this column for participants 11, 13 and 14. However, with his five twos, participant 12 won a majority and thus first place. Since there are no other participants with a majority here, we continue with the third column.
In the third column ( 1-3 ), participants 11 and 13 were able to achieve a majority. Participant 14 does not have a majority with two scores for places 3 or better and is therefore automatically fourth. Since the total for participants 11 and 13 is also the same (1 + 1 + 3 + 3 = 8 and 3 + 3 + 1 + 1 = 8), columns 1-4 must also be used for these participants (as in the previous one Example for first place). But that doesn't make a decision either, since both participants each got a four: They both have five ratings of 5 or better with a total of twelve. As a result, this place is shared: The participants share second and third place and receive 2.5 points as the end result.
Common mistakes
In a previous example it was pointed out that only participants for whom a majority has been found have to be evaluated to the end. This example takes a closer look at this case.
| Start number | Ratings | Places | Result | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| A. | B. | C. | D. | E. | 1 | 1-2 | 1-3 | 1-4 | 1-5 | ||
| 11 | 1 | 1 | 1 | 2 | 5 | 3 * | - | - | - | - | 1 |
| 12 | 2 | 4th | 5 | 1 | 2 | 1 | 3 * (5) | 3 * (5) | 4 * | - | 2 |
| 13 | 5 | 2 | 2 | 5 | 1 | 1 | 3 * (5) | 3 * (5) | 3 * | - | 3 |
| 14th | 3 | 3 | 3 | 3 | 3 | 0 | 0 | 5 * | - | - | 4th |
| 15th | 4th | 5 | 4th | 4th | 4th | 0 | 0 | 0 | 4 * | - | 5 |
The first place is easy to determine, because only participant 11 could achieve a majority with three ones.
For places 2 or better ( 1-2 ) there are two participants: Participant 12 and Participant 13. Since both the strength of the majority and the sum of the scores (1 + 2 + 2 = 5) are the same, the others must Ratings are also considered. The third places are also included and it is determined that participant 14 has the majority there. Still, he doesn't get second place.
Namely, only participants 12 and 13 may continue to be considered. The rule requires that they (who have a majority in column 1-2 ) have to be rated to the end.
So looking at the 2 or better ratings did not bring any improvement - both participants have a majority of three ratings with a total of 5 (through the ones and two, which already led to a draw).
But the 4 now brings the decision: Only participant 12 received a four, so in column 1-4 for participant 12 it is stated that the majority is now made up of four ratings, while participant 13 still only has three ratings of 4 or better . Second place goes to participant 12 (the only participant who still had a majority in the 2 or better ) and participant 13 gets third place. So that all belonged to the processing of column 1-2 , only that the worse ratings had to be included.
Then it continues with column 1-3 : Participant 14 clearly has the majority and - although he has received all three - only gets the next free, i.e. fourth place.
Participant 15 will receive the last placement to be awarded: fifth place.