gregbo (gregbo) wrote,

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"Man I won, but I didn't beat him!"

These were the words of Apollo Creed (Carl Weathers) in Rocky II, when his trainer tried to convince him not to fight Rocky Balboa again, because of the terrible beating Rocky gave him in their first fight.

Might some Swing competitors say this after seeing their final placements? Let's see …

Most Swing competitions use a system called Relative Placement (RP) to determine the final placements of contestants. You can follow the link for a more in-depth explanation, but briefly, judges rank the contestants in order, then the RP algorithm produces the final placements based on determining the largest majority of the highest placements.

So, let's take a sample from a hypothetical contest (which is also in the RP document linked to above):


Four judges placed Couple A 2nd, and three placed Couple B first. Under the RP algorithm, Couple A would beat Couple B, because a majority of twos beats both a minority of ones and a majority of threes. (With seven judges, four is a majority.)

But did Couple A really beat Couple B? Maybe not …

Looking a bit more closely at each judge's placements, we see that six judges actually placed Couple B higher than Couple A. In other words, the vast majority of judges thought Couple B danced better than Couple A in this contest!

This type of pairwise comparison between couples was a topic of debate recently among WCS dancers. As it turns out, the question of whether a pairwise comparison of couples' judges' placements is a stronger measure of victory than RP is relevant. Such questions were asked (and answered) by the Marquis de Condorcet, among others, in the development of social choice theory. I would not be surprised if this issue comes up again, especially if it would make the difference in one of the major Swing competitions, such as the US Open, which just concluded recently.
Tags: dance, swing, wcs

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