- Joined
- Jun 21, 2003
This question came up, in disguised form, on another thread. When scores are averaged, extreme values can play a disproportionate role in determining the outcome. Two or three resolute conspirators can thwart the will of the majority of the judging panel simply by highballing their favorite and lowballing his/her rival. This cannot happen in ordinal judging, where a majority of first place ordinals is guaranteed always to carry the day.
Here is an example, one that is not far-fetched in the least. Suppose the program component scores for the nine judges came out like this:
Skater A: 9.50 9.00 9,00 9,00 9,00 9.00 8.50 8.50 8.25
Skater B: 8.50 8.75 8.75 8.75 8.75 8.75 9.25 9.25 9.25
Throw out highest and lowest and we have
9.00 9.00 9.00 9.00 9.00 8.50 8.50
8.75 8.75 8.75 8.75 8.75 9.25 9.25
Nothing out of the ordinary, and if the scores were all mixed by by randomization there is nothing to comment on.
And yet … 5 judges out of 7, and 6 judges out of 9, thought that skater A performed the best. But skater B wins by a score of 62.25 to 62.00.
This situation, where a determined minority cabal can dominate the majority, could not happen if we used the median (middle score) instead of the mean. The median is simply the maximally trimmed mean -- we throw out the highest four and the lowest four instead of the highest one or two and the lowest one or two. In this example the median scores are
Skater A: 9.00
Skater B: 8.75
which certainly captures the opinions of the majority in this example.
What do you think? Would this be a better system?
Here is an example, one that is not far-fetched in the least. Suppose the program component scores for the nine judges came out like this:
Skater A: 9.50 9.00 9,00 9,00 9,00 9.00 8.50 8.50 8.25
Skater B: 8.50 8.75 8.75 8.75 8.75 8.75 9.25 9.25 9.25
Throw out highest and lowest and we have
9.00 9.00 9.00 9.00 9.00 8.50 8.50
8.75 8.75 8.75 8.75 8.75 9.25 9.25
Nothing out of the ordinary, and if the scores were all mixed by by randomization there is nothing to comment on.
And yet … 5 judges out of 7, and 6 judges out of 9, thought that skater A performed the best. But skater B wins by a score of 62.25 to 62.00.
This situation, where a determined minority cabal can dominate the majority, could not happen if we used the median (middle score) instead of the mean. The median is simply the maximally trimmed mean -- we throw out the highest four and the lowest four instead of the highest one or two and the lowest one or two. In this example the median scores are
Skater A: 9.00
Skater B: 8.75
which certainly captures the opinions of the majority in this example.
What do you think? Would this be a better system?
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