What is being petitioned?
Sotnikova's coronation engendered outrage from figure skating fans, a highly emotional response in defence of a beloved champion. However, the petition for an investigation is not solely about ensuring a second gold medal for Yuna Kim. There are practical reasons for the petition: the sport suffers from a lack of credibility due to the secrecy surrounding the way the sport is judged. The petition seeks to reveal which judges provided which sets of scores. It's the lack of transparency that lends itself to the widespread perception that the event was rigged to favour the Russian skater.
From the change.org petition:
Superior technical points for Sotnikova: This is the MAIN opposition we are getting. But I am not concerned about the technical points; yes Adelina's program was composed of "more jumps (by 1) and more difficulty" I do NOT doubt that. What this WHOLE petition is concerned with, at least for my rationale for organizing it, is the GOE's (Grade of Execution) for both SHORT and FREE program which are grades given by judges to how the skater performed each jump/skill - I demand this SUBJECTIVITY to be TRANSPARENT and NOT ANONYMOUS ANYMORE!
In figure skating, athletes are often rewarded for their body of work, or ability to consistently produce high quality routines. More succinctly, skaters benefit from having a certain "pedigree" when it comes time for the judges to reveal their scores. Throughout the course of a figure skating season, judges will have seen a skater perform their routine at multiple events; there is no mystery when they step onto the ice to skate for gold. How then, did Sotnikova improve her performance so drastically on the biggest stage? This is something that baffles Kurt Browning. How could Sotnikova better her previous best by such a wide margin in such a short period of time?
Figure skating is different from most athletic competitions in that the medals are not decided by who has the fastest time, or who jumps the highest or farthest. It's decided by an anonymous panel of judges who give their subjective assessment of a fast-moving sequence of events on the ice. At least when the sport used the 6.0 scale for technical and artistic merit, the nationality of each judge was attached to his/her score. Now, the ISU utilizes a much more complex, but equally abstract, method that is far more confounding for the fans. The change in scoring system was implemented in 2005 in response to the 2002 Olympic scandal. Yet, here we are, questioning whether corruption has reared its ugly head yet again.
Given no clear understanding of how the skaters are judged, we can only rely on comparisons. It's the only way to make any sense of the sport when the numbers are so inaccessible. How did Sotnikova score higher than Mao Asada in the free skate? If the argument is that Adelina landed one more triple jump than Yuna, then what about Mao's flawless skate that included a perfectly executed triple axel? Of course, Mao could not win the overall title after a poor short program, but shouldn't she at least beat Sotnikova in the long program? In a sport that is already saddled by too much subjectivity in its scoring, these types of clear inconsistencies only serve to exacerbate the problem even further.
This is not just a matter of Sotnikova's performance versus Yuna Kim's. Some believe that Carolina Kostner skated a better program than Sotnikova; Kostner landed as many triple jumps as the gold medallist, and is held to be vastly superior in the components department. All this means that, as many as three women could lay legitimate claim to have beaten Adelina in the free skate. The most puzzling point of comparison is between Sotnikova's Sochi free skate and Yuna Kim's Vancouver world record skate. Sotnikova was awarded 149.95 in Sochi while Kim scored 150.06 four years prior. Are we to believe that the judges (albeit not the same panel) view the performances as essentially one in the same? There is a very wide gap between the two.
How do we explain all these discrepancies? That this story has not gone away shows it is not just sour grapes from bitter Yuna Kim fans. Hopefully the petition leads to some answers. It's not enough to retroactively award a gold medal to Yuna Kim. She's already lost out on the glory of the moment, that is gone forever. At least the International Skating Union has an opportunity to ensure that this sort of thing doesn't happen again. This is bigger than Yuna Kim, it's about the betterment and long-term survival of the sport.
Further reading: overview of the situation via Christine Brennan at USA Today, including some possible avenues for investigation regarding the make-up of the judging panel.