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Relative Placement How - To
This document is to be used with
"The Relative Placement System of TNGSDC 10/94.” The TNGSDC Relative Placement Tally System assumes
that all judge's scores are equal; one judge should not be able to
significantly alter the outcome of a contest. At least five judges are required to use the relative
placement scoring system. Odd numbers of judges are better than even number of
judges to obtain majorities (5 out of seven is easier to resolve than four out
of six). A head judge is required to break tie scores. A judge may not give tie
(i.e., duplicate) scores between any two couples in the contest. For complete
details, please refer to "The Relative Placement System of TNGSDC
10/94." 1. Convert all raw scores to ordinals. Look at each score for a given judge, and assign places, giving the highest score first place, the second highest second place, etc., until all places for all couples are assigned for each judge. Raw Scores Scores
Step-by-step example: Judge I
Raw scores converted to ordinals Scores
2. Count all
first place votes for each couple, then first through second, etc., until a
majority for a place is reached. The tally columns to the right represent 1st
through 1st (1 >1), 1st through 2nd (1>2), etc. The example below places
couple 5 in first place since three out of five judges have them in first. Once
a couple has been awarded a place, you do not need to consider their scores to
place the remaining couples.
3. Repeat for
all places, until you have ties in the number of votes. Below, second place is
awarded to couple 3 - they have a majority of votes (again, three out of five)
for second and above. Continuing on, counting the number of placements for
third and above, we find a tie between couple 4 and couple 1.
4. Resolve ties by adding the sum of placements
received for the ordinals in which they are tied. In this case, add the placements from I st
through 3rd. Sums are in parenthesis. The lower the sum, the higher they place (1st, 2nd,
3rd, 3rd beats 2nd, 3rd, 3rd, 3rd). Award the next place to the couple tied for that
ordinal.
5. Continue until
all places are awarded.
The above examples cover most scoring situations you
may come across. For more details on other tie situations, refer to the text,
The Relative Placement Scoring System Rules, by Jeff Kletsky. Addendum - Disadvantages of other scoring systems · AVERAGING RAW SCORES Using raw scores and averaging the results is NOT
recommended. It is easy for one or two judges to sway the contest in their
favor. Mathematically speaking, the judge with the widest range of scores, from
highest to lowest, will have the most influence on the scores. Taking the raw
scores from the exercise on the previous pages, note that the results come out
quite differently. Raw Scores
Judge 5 had a major influence on the scores. Judge 5
had a very wide range of scores. The single low score given to Couple 5 by
Judge 5 lowered the them from first to second, despite the fact that 3 out of 5
judges had them in first place. Here is another example: At first glance, the scores seem to be relatively
even. Raw Scores
Relative Placement - Majority Tally (above
raw scores converted to ordinals and tallied)
Once we convert the raw scores to ordinals it is easy to see how the panel as a whole has judged the contest. Using the raw scores would have resulted in a disaster! A fifth place couple winning first, a second getting fifth, etc.! This occurred because most of the judges had scores within only a half point range while Judge 5 had a scoring range of a point and a half. Normally this is not necessarily bad by itself; however, in this case, it was enough to sway the scores... · USING
SUMS OF ORDINALS INSTEAD OF MAJORITY TALLY Simple sums of ordinals are NOT
recommended. Using the scores from the previous example
(the one used to illustrate the problems with point scoring,) we see that using
placement totals have a few problems...
Taking a sum of the placements has given us a
different placement result for couples 2 and 3. Note that the majority of
judges clearly had couple 2 place higher than couple 3. But if we use totals,
the final placements would be reversed. There is also a tie for 4th place. Looking at the
scores, anyone would clearly break the tie by seeing that couple 4 had more
judges placing them higher than couple 5, therefore they should get 4th place.
When we start to use that logic, we might as well use RPS for the whole contest
anyway... Still not convinced? In the example below, a clear
majority has awarded one couple first, second and third places. Taking a sum
instead of looking for majorities may result in placement that disagrees with
the majority of the judging panel. Looking for majorities eliminates the
possibility of one or a minority of judges (in this case, judge four and five)
from "taking over" the judging for the contest.
In the above example, three out of five judges clearly
had couple 1 in first; yet using sums would mean that couple 1 would get 2nd
place, because judge 5 scored them in fifth place. Using sums, couple 4 would
be awarded 3rd, despite the fact that couple 3 had four votes out of five for
them in third place. Using the columns on the right, you can see that the RPS
majority tally system eliminates the tendency of one judge to sway the results
of a contest. Also, mathematically speaking, the larger the field
(more contestants) the more potential there exists for numerical variation, in
which using sums would result in even wilder results. A judge could easily
“bury” a contestant/couple by giving them the lowest score. Using the sums
means that the worse placement counts more. |
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