More than one couple have a majority for the same place.
There are 7 judges so the majority is 4.


1. 
1^{st} and 2^{nd} places are awarded based on
a simple majority (Rule 5). 


2. 
When we count “3^{rd} and higher places” both #63 and
#64 have achieved a majority. The greater majority has been attained
by #63 and is, therefore, awarded 3^{rd} place with #64
awarded 4^{th} place. 

WALTZ


Judges

Places

Result

No

A

B

C

D

E

F

G

1

12

13

14

15

16

17

18


61

1

1

2

1

4

2

1

4















1

62

6

2

1

5

2

1

2

2

5













2

63

2

4

3

3

6

3

3



1

5











3

64

3

3

5

2

1

5

4

1

2

4











4

65

4

5

6

4

3

6

5







3

5







5

66

5

6

4

6

5

4

6







2

4







6

3. 
We are about to award 5^{th}
place but we are going to tabulate the next column on the worksheet
which is “4^{th} place and higher.” Neither of the two
remaining couples have a majority so we move to the “5^{th}
place and higher” column. #65 has 5 “4^{th} place and
higher” marks and #66 has 4. #65 is, therefore, awarded 5^{th}
place and #66 6^{th} place. 



The important thing to remember here with Rule 6 is that more
than one place can be awarded while working in one column of the
work sheet. The placement being assigned may not coincide with
the column/marks that you are working with. The second thing to
remember is that all the couples assigned a place must have
achieved a majority when they are assigned a position. 

If two or more couples have an equal majority for the same position.
Now is the time to add together the placemarks and not just count them.
There are seven judges so the majority is 4.
1. 
#71 is awarded 1^{st} place by virtue of a majority of
“1^{st} place marks.” We now move to the second column,
looking for “2^{nd} place and higher” (Rule 5), or even
different majorities (Rule 6). We find, however that there are
two couples, #72 and #73, who have an equal majority of “2^{nd}
and higher” place marks. 



WALTZ


Judges

Places

Result

No

A

B

C

D

E

F

G

1

12

13

14

15

16

17

18


71

3

1

6

1

1

2

1

4















1

72

2

2

1

5

3

1

3

2

4^{(6)}













2

73

1

5

4

2

2

6

2

1

4^{(7)}













3

74

5

4

2

4

6

5

4



1

1

4^{(14)}

6







4

75

4

6

3

3

5

4

6





2

4^{(14)}

5







5

76

6

3

5

6

4

3

5





2

3

5







6

2. 
Add (not count!) the placemarks for each couple
that has the majority. Adding the four “second and higher” place
marks for #72, (2+2+1+1) gives a total of 6. Doing the same for
#73 gives a total of 7. 


3. 
The couple with the lowest total (sum) is awarded
the position. Therefore, #72 is awarded 2^{nd} place and
#73 is awarded 3^{rd} place. 


4. 
This process continues until all couples with the
equal majority have been awarded positions. You then go back to
the remaining couples in the section. We continue with the “3^{rd}
place and higher” column to award 4^{th} position, even
though we are working in the “3^{rd} and higher” column. 


5. 
OK! Next question, “Same majority, same sum . . .?”
Hang in there for just a moment. 




6. 
Continuing with the example. 


7. 
Count the number of “3^{rd} and higher.” None of the three
remaining couples, #74, #85, and #76, have achieved a majority.
Moving on to the “4^{th} and higher” column we find that
#74 and #75 have an equal majority whereas #76 does not. 


9. 
We now focus only on the two couples #74 and #75 who
have an equal majority. Adding the place marks together they both
have an equal total (sum) of 14. The problem is still not resolved. 


10. 
As far as “4^{th} place and higher” is concerned
the two couples #74 and #75 are still tied. We, therefore, move
to the next column “5^{th} and higher” to try and break
the deadlock. Counting the “5^{th} and higher “ place marks
we find that #74 has a majority of 6 and #75 a majority of 5. #74
is awarded the 4^{th} place by virtue of the larger majority,
(effectively back to Rule 6) and #75 is awarded 5^{th} position. 


11. 
We now move back to the “5^{th} and higher”
column for #76. Counting their “5^{th} and higher” place
marks gives a count of 5, a majority, and they are therefore awarded
6^{th} place. 


12. 
The third part of Rule 7 defines a tie. There are situations where no matter
how many rules you apply you cannot separate the couples. In
the event of two couples having an equal majority and also an
equal sum, we go to the next column, FOR THESE COUPLES ONLY.
If the next column still gives us an equal majority and sum we
go to the next column, and the next until we reach the last possible
column. For 6 couples this will be “6^{th} and higher,”
for 7 couples “7^{th} and higher,” and for 8 couples “8^{th}
and higher.” Remember that if you have more than 8 couples you
will not be running a final!
If we still have a tie at the last column then each couple is
awarded the average or mean of the positions that we are working
with. If we have two couples and we are looking to place 3^{rd}
and 4^{th} each couple will be awarded the 3½^{th}
position, (3 + 4 = 7 ¸ 2 = 3½). For a 3way tie
for 3^{rd}, 4^{th}, and 5^{th} positions,
each couple is placed 4^{th}, (3 + 4 + 5 = 12 ¸3 = 4).
This describes the mathematical methodology that the scrutineer
uses to calculate the results. When the compere announces the
results, they are all listed as the highest of the positions involved
in the tie. In the example above the first two couples are announced
as being tied for 3^{rd} place. In the second, the three
couples are tied for 3^{rd} place.
Rule 7 is as complicated as it gets when working
with the individual dances.


If no couple receives a majority for the position under review.
After Rule 7, Rule 8 is simplicity itself. If no couple achieves a majority of 1st place marks then you move on to the “2nd place and higher” column. If there is no majority there you continue onto the next column and the next until one or more couples achieve a majority.
When one or more couples are found with a majority, subject to Rule 6 and Rule 7 the 1st place is awarded. We then continue in a similar manner to allocate all other positions.
There are 7 judges so the majority is 4.
1. We are looking for 1st place marks. No couple has a majority. We move on to the “2nd and higher” column. No couple has a majority in that column either. Moving on to “3rd and higher” we find that couples #81 and #82 have a majority of 6 and 4 “3rd and higher” place marks each. Subject to Rule 6 we award 1st place to #81 and 2nd place to #82.

WALTZ 

Judges 
Places 
Result 
No 
A 
B 
C 
D 
E 
F 
G 
1 
12 
13 
14 
15 
16 
17 
18 

81 
3 
3 
3 
2 
5 
2 
3 
 
2 
6 
 
 
 
 
 
1 
82 
4 
4 
4 
3 
2 
3 
2 
 
2 
4 
 
 
 
 
 
2 
83 
2 
2 
6 
6 
4 
1 
4 
1 
3 
3 
5 
 
 
 
 
3 
84 
1 
6 
1 
5 
1 
4 
6 
3 
3 
3 
4 
 
 
 
 
4 
85 
4 
5 
5 
1 
3 
6 
1 
2 
2 
3 
3 
6 
 
 
 
5 
86 
5 
1 
2 
4 
6 
5 
5 
1 
2 
2 
3 
5 
 
 
 
6

2. We are now looking to award 3rd place. Tallying the “4th and higher” column we find that both couples #83 and #84 have a majority of “4th and higher” place marks. Again using Rule 6 3rd place is awarded to #83 and 4th place to #84.
3. We are now looking to award 5th place. Tallying the “5th place and higher” column both #85 and #86 have achieved a majority. Rule 6 places #85 in 5th position and #86 in 6th.
4. Remember the column that you are working with may not coincide with the position you are looking to award.
So, with Rule 5, Rule 6, Rule 7, and Rule 8 you can work out the results for a single dance with simple majorities, multiple majorities, tied majorities, and no majorities!

Compilation of the final summary.
Final
Summary

No

Dances

Total

Result

W

T

V

SF

Q



91

1

1

1

1

1



5

1

92

4

2

2

2

2



12

2

93

2

3

3

3

3



14

3

94

5

5

6

4

5



25

4

95

3

4

5

7

7



26

5

96

6

7

4

5

6



28

6

97

7

6

7

6

4



30

7

98

8

8

8

8

8



40

8

We now move on to Rule 9, Rule 10, and Rule 11. These apply to multipledance sections as found in Ballroom and Latin competitions. It covers the whole gambit from the DBeginners class containing three dances, Waltz, Tango and Quickstep or ChaChaCha, Rumba and Jive to the Championship sections of five dances and the combinations of six, eight, and ten dances.
All of the results, and only the results not the individual placemarks, are transferred into a new table called the “Final Summary.” These results are then simply added together, not counted, to give a total. The couple with the lowest total is awarded 1st place in the section; the next highest total is awarded 2nd place, and so on until all couples have been placed.
Final
Summary

No

Dances

Total

Result

S

C

R

J




11

1

2

1

1




5

1

12

2

1

2

2




7

2

13

3

4

3

4




14

?

14

4

3

4

3




14

?

15

6

6

5

7




24

5

16

5

5

7

8




25

?

17

7

7

6

5




25

?

18

8

8

8

6




30

8

After having transferred the individual dance results to the “Final Summary” we see that #91 has the lowest total of 5 and is therefore awarded 1st place. #92 has the next lowest total and is awarded 2nd place. We continue in this way for all couples with #98 being placed 8th.
In the event that two or more couples have an equal total for the position under review, then there is a tie for that place. We use Rule 10 and Rule 11 to break the tie for multipledance sections in the same way that as we did for the individual dances and a single dance section.
#11 and #12 are placed 1st and 2nd, respectively. #13 and #14 both have the same total and cannot be placed, we need Rule 10 and Rule 11 to break the tie. They will be awarded 3rd and 4th places. #15 has the next lowest total and is placed 5th. #16 and #17 are tied and require Rule 10 and Rule 11 to break the tie for 6th place. With the largest total of 30, #18 is placed 8th.

If there is a tie for a place in the Final Summary.
Rule 10 is the most involved of all the Rules. There are several sections to Rule 10. Let’s try and be simple and take it one section at a time.
Final
Summary

No

Dances

Total

Result

W

T

SF





101

1

1

3





5

1

102

2

2

1





5

2

103

6

4

2





12

3

104

5

3

4





12

4

105

4

5

5





14

5

106

3

6

6





15

6





















One important point, before we start. Whilst working
within Rule 10 we are not looking for the majority of anything. It
is another case of the more the better!
1. 
There is a tie for 1^{st} place under Rule 9 for the section.
You must now look, in the Final Summary, to see which of the tied
couples has won the most 1^{st} places (won most dances).
Couples #101 and #102 both have a total of 5. However, #101 has
achieved 2 1^{st} places whilst #102 has only 1 (in the
Final Summary). #101 is therefore awarded overall 1^{st}
place and #102 overall 2^{nd} place. 


2. 
It is important to note that if more than two couples are tied
for 1^{st} place then after one of the couples has been
awarded the overall 1^{st} place the remaining couples are
actually tied for 2^{nd} place. You must therefore count
“2^{nd} and higher” places for the remaining couples to
try and award the overall 2^{nd} place. If you have a tie,
the couples all have the same number of places, then, as before,
you add the places together to provide a total. The couple with
the lowest total is awarded the place and the remaining couple is
awarded the next place. 


3. 
Here the similarity, with the previous singledance rules, ends. If the two
couples have the same number of places and the same total you
do not go to the lower places to break the tie. At this point
the couples are tied under Rule 10 and you must apply Rule 11
to break the tie.
#101, #102, #103, and #104 all have a total
of 12 and therefore must be considered for 1^{st} place.
#101 has more 1^{st} places (2) than the other and is
therefore awarded the overall 1^{st} place. The remaining
couples are now tied for 2^{nd} place, so we must count
“2^{nd} and higher” places to award the position. #102
has more “2^{nd} and higher” places than the others and
is therefore awarded the overall 2^{nd} place, (even though
the couple did achieve any 1^{st} places). We are now
left with #103 and #104 to be considered for the overall 3^{rd}
place. We now count “3^{rd} place and higher”. #103 (3)
has more than #104 (2) and is therefore awarded the overall 3^{rd}
place. #104 being the only remaining couple in the Rule 10 is
automatically placed overall 4^{th}.

Final
Summary

No

Dances

Total

Result

W

T

SF

Q




101

1

6

4

1




12

1

102

6

2

2

2




12

2

103

2

1

6

3




12

3

104

3

4

1

4




12

4

105

5

3

5

5




18

5

106

4

5

3

6




18

6






















Having placed the first 4 places we must now
award 5^{th} place. #105 and #106 have the same total
so we count “5^{th} and higher” places for the two couples.
#105 has the most (4) and is awarded the overall 5^{th}
place. #106 as the last in this Rule 10 is awarded 6^{th}.
It is important to notice that although we
had four couples with the same total under the Rule 10 we only
placed one couple at a time. Rule 10 is repeatedly applied to
place each couple. Rule 10 for 1^{st} place (count the
1^{st} places), Rule 10 for second place (count “2^{nd}
and higher” places), Rule 10 for third place (count “3^{rd}
and higher” places), and Rule 10 yet again for 4^{th}
place (count “4^{th} and higher” places).
If you have a tie under Rule 10 and cannot
award places then you apply Rule 11. The actual process, however,
is to temporarily leave those couples and places that you cannot
award and continue with the remaining couples and positions under
Rule 10. You then go back to the tied couples and apply Rule
11. This keeps the process structured and logical, believe me!

In summary you will have a tie under Rule 10 and need Rule 11 if:
When allocating the overall 1^{st} place all the
tied couples have the same number of 1^{st} places for the individual
dances or if none of them have any 1^{st} places.
For all the other positions if the couples have the same
number of places for the position under review and the totals of those
places is the same you have a tie. You will also have a tie if none
of the couples have any places that are the same or higher than the
position under review; you are looking to place 3^{rd} and none
of the tied couples have any “3^{rd} or higher” places in the
Final Summary.
A final and very important point to remember. You
need to know how to handle the positions in the Final Summary that include
fractions such as 2½, and 3½. When evaluating place marks in the Final
Summary table a fraction is considered to be a place mark for the next
highest whole number. 2½ is viewed as 3 and 3½ is viewed as 4. We cannot
leave this as simple as that. If when you have considered the place
marks and the couples in the tie have the same number of place marks
then, as above, you must add the place marks together to give a total.
When you do this you include the fractions at face value!
Let’s try another example to sort it all out.
1. 
#102 and #107 both have
a total of 8. #102 has the most 1^{st} places and is
awarded overall 1^{st} place. With only two in the tie
#107 is awarded overall 2^{nd} place.



Final
Summary

No

Dances

Total

Result

W

T

VW

SF

Q



101

7

6

5

6

5



29

R11

102

1

3

2

1

1



8

1

103

5

5

6

7

6



29

R11

104

6

7

7

5

7



32

7

105

4

4

3

3

3



17

3

106

3

2

4

4

4



17

4

107

2

1

2

2

2



8

2











2. 
#105 and #106 have the
next highest total of 17. We are now trying to place overall
3^{rd} place and must therefore count “3^{rd}
and higher” places. #105 has 3 and #106 has 2. #105 is therefore
awarded overall 3^{rd} place and #106, the only other
couple in the tie, is awarded overall 4^{th} place.



3. 
#101 and #103 both have the next highest total of 29. We are
trying to place 5^{th} place and must therefore count “5^{th}
and higher” positions. They are both tied with two “5^{th}
and higher” places. We must now add them to get a total. Both
have the same total of 10. These two couples are therefore tied
under Rule 10 and need to go to Rule 11. They will be awarded overall
5^{th} and 6^{th} places, but we will leave them
for the moment. 


4. 
We now move to 7^{th} place. On inspection we see that
there is only #104 with the highest total of 32. That couple is
therefore awarded overall 7^{th} place. 


5. 
By now you probably have a headache and your eyes are rolling.
If you have made it this far pat yourself on the back have a drink
and then come back for the home straight, Rule 11. 

When there is still a tie after Rule 9 and Rule 10.
Rule 11 is fairly simple to apply. Effectively you take all of the place marks given to the tied couples and process them as if it was a single dance. So if you have two dances in the section, say the Waltz and Quickstep and seven judges, in a Rule 11 all 14 place marks will be treated as if it was one dance.
There has to be a sting in the tail, with Rule 11 it is when more than two couples are tied under Rule 10 and move to Rule 11. Rule 11 is applied to all tied couples and the “best” couple is awarded the overall placing under review. The remaining couples in the tie then revert to Rule 10. If there is a tie under Rule 10 for the remaining couples we go forward again to Rule 11. After awarding the next overall position to the “best” couple this time around we revert back again to Rule 10 for the remaining tied couples. This procedure of Rule 10 followed by Rule 11 is repeated until all of the tied couples have been awarded an overall placing. It is important to note that as with Rule 10, Rule 11 only places one couple at a time. The only time when two overall places are awarded is if there are two couples in the tie or you are placing the last two couples in the tie.
The answer to your question is Yes! You can still have a tie under Rule 11. At this point we, the scrutineers, throw in the towel; there is no Rule 12! You have an unbreakable tie. To get rid of the problem you pass it to the Chairman of Adjudicators to decide. Typically if the tie is for 1st place a danceoff takes place between the tied couples. For the minor places the couples are, typically, awarded the tied position.
Having initially stated that Rule 11 is simple lets work through an example:
1. #111 is the outright winner as the only couple to acquire any 1st places. They are awarded the overall 1st place.
2. #115 has the next lowest total and is therefore awarded overall 2nd place.
3. #112 and #114 have the next lowest total and are tied for overall 3rd place. They both have one 3rd place, the position under review. WE do not go to lower positions to break the tie, so they are tied under Rule 10 and must go to Rule 11. All marks for both dances are considered to be for one dance. We are looking to place overall 3rd and start by counting the “3rd and higher” places. Both #112 and #114 have 7 “3rd and higher” places. We move to “4th and higher” to try and split the tie. #112 has 11 “4th and higher” places and #114 has 13. #114 has the most and is awarded the overall 3rd place with #112 being awarded the overall 4th place. (Whilst in Rule 11 we actually apply Rule 5 through Rule 8 to the marks for each tied couple.)

WALTZ


Judges

Places

Result

No

A

B

C

D

E

F

G

1

12

13

14

15

16

17

18


111

1

1

1

1

1

1

1

7















1

112

5

3

5

4

3

3

3





4











3

113

4

5

4

5

5

5

4







3

7







5

114

3

4

3

3

4

4

5





3

6









4

115

2

2

2

2

2

2

2



7













2


Quickstep


Judges

Places

Result

No

A

B

C

D

E

F

G

1

12

13

14

15

16

17

18


111

1

1

1

1

2

1

1

6















1

112

5

3

3

4

3

4

4





3

6









4

113

4

5

5

5

5

5

5









7







5

114

3

4

4

3

4

3

3





4











3

115

2

2

2

2

1

2

2



7













2

Final
Summary


Rule
11

NO

Dances

Tot

Res

No

Places

W

Q








3

4





Res

111

1

1






2

1

112

7

11





4

112

3

4






7

4

114

7

13





3

113

5

5






10

5









114

4

3






7

3









115

2

2






4

2









4. #113 has the next lowest total of 10 and is awarded overall 5th place.
Right that’s it, plain and simple. That is the Skating System, used most Saturdays by “Yours Truly” and the other scrutineers.
The following section includes a Final Example for you to try.
Solution
1. There are five judges for the dances. The majority is therefore 3
Foxtrot
2. Count the number of 1st places for each couple. The total is in the “1st” column. There is no majority so move to the “2nd and higher” column.
3. #115 and #116 both have the same total of 3 “2nd and higher” marks, which is a majority. The sum of these 3 marks is also equal (4). To break the tie we must move to the “3rd and higher” column.
4. #115 and #116 still have the same tie as neither achieved any 3rd place marks from the judges. Counting the “4th and higher” column we find that #115 has 3 “4th and higher” marks and #116 has 5. Both of these are a majority. By virtue of the larger majority #116 is awarded 1st place and, being only a twocouple tie, #115 is awarded 2nd place.
5. We must now go back to the “3rd and higher” column for the remaining couples. #114 has a majority of 3 “3rd and higher” place marks and is given 3rd place.
6. Moving onto the “4th and higher” column for the remaining couples we find that none of them has a majority, so we move straight on to the “5th and higher” column.
Note:
Do not get confused by the marks for #115 and #116 in the “3rd and higher” and “4th and higher” columns. They are part of placing those two couples 1st and 2nd and are not included in any further inspections.
7. Counting “5th and higher” we find that #111 and #118 both have a majority of 3 “5th and higher” place marks. The sum of these 3 place marks is lower for #111 (11) than for #118 (12). As a result of the lower sum #111 is given 4th place and #118 gets 5th place.
8. We now inspect the “6th and higher” column for the remaining three couples. #112 has a majority of 3 place marks and is placed 6th.
9. In like manner #117 has a majority of 4 “7th and higher” place marks and is given 7th place.
10. #113 is the only couple left and is given 8th place. For correctness you should take the trouble to enter the place marks for #113 in the "8th and higher" column. The work sheet is then 100% correct and complete.
11. Finally copy the results into the “F” column in the Final Summary work sheet.
Tango
12. A similar process is followed for the Tango. In summary:
13. #115 takes 1st place because of a lower sum of “2nd and higher” place marks. It is a twocouple tie with #116 who is automatically placed 2nd.
14. #114 takes 3rd place, having a sole majority of “4th and higher” place marks.
15. Likewise #118 is given 4th place with a sole majority of 3 “4th and higher” place marks.
16. A sole majority of “5th and higher” place marks gives #111 5th place.
17. Next is #113 in 6th place with a sole majority of “6th and higher” place marks.
18. When the “7th and higher” column is inspected, #117 has a greater majority (5) of “7th and higher” place marks than #112 (3). #117 is, therefore, placed 7th and #112 is placed 8th.
19. Copy the results into the “T” column in the Final Summary work sheet.
Final Summary
20. Each couple’s positions are now added to give a total. In this example they are 9, 14, 14, 6, 3, 3, 14, 9
21. #115 and #116 both have the lowest total of 3 and are considered for 1st place. Each has won one 1st place and are, therefore, tied under Rule 10. We must use Rule 11 to break the tie. Leave them for the moment. These two couples will eventually take 1st and 2nd place
22. The next lowest total is #114 with 6. #114 can immediately be awarded 3rd place.
23. We must now allocate 4th place. #111 and #118 both have a total of 9 and the sums are equal at 9. They are also tied under Rule 10. Rule 11 here we come again, but leave it for a while!
24. We have three remaining couples, #112, #113, and #117 each with a total of 14. We are looking to allocate 6th place. #117 has not achieved any 6th places and therefore immediately drops out, being awarded 8th place. #112 and #113 have both achieved one 6th place and are therefore tied under Rule 10. A third visit to Rule 11 to break a tie.
25. Well here we are at last Rule 11:
#115 and #116 for 1st and 2nd place
#111 and #118 for 4th and 5th place
#112 and #113 for 6th and 7th place
Do not forget. We are now treating the two dances with five judges each as a single dance with ten judges. The majority whilst in Rule 11 is 6
26. We have to allocate 1st place. Inspecting the 1st place marks for #115 and #116 show a total of 4 and 2 respectively. There is no majority and 1st place cannot be awarded. We move to “2nd and higher” place marks. Both couples have a total of 6 “2nd and higher” place marks. They are still tied. Summing these 6 place marks gives a sum of 8 for #115 and 10 for #116. By virtue of the lower sum #115 is awarded 1st place and #116 is awarded 2nd place.
27. We must now consider #111 and #118 for 4th place. Inspecting the total of “4th and higher” place marks for each we find that #111 has a total of 4 place marks and #118 has a total of 5. Neither of these represents a majority. We now inspect the “5th and higher” place marks. #111 has a total of 7 “5th and higher” place marks and #118 has a total of 6. By virtue of the larger majority #111 is awarded 4th place and #118 gets 5th place.
28. We finally move to #112 and #113 to allocate 6th place. Inspecting “6th and higher” place marks for each, shows a total of 4 “6th and higher” place marks for #112 and 5 for #113. Yet again neither of these is a majority. Considering the “7th and higher” place marks, #112 has a total of 7 and #113 a total of 5. Both of these are a majority. The greater majority for #112 gets them 6th place and #113 gets 7th place.
You’ve finished... CONGRATULATIONS!!!

     