Don't blame the messenger. I did not make these numbers up. I took them from the protocols.
One judge really did give Adelina a total of 31 in GOE points (before factoring, etc.) One judge gave the same skater, for the same performance, a total of 15.
For Kim, one judge awarded 27 points and another 16.
Here are two different explanations for these wide discrepancies.
Explanation number one. One judge gave Adelina 31 and Yuna 16. This judge thought that Adelina was great and Yuna not nearly so good. Another judge was of the opposite persuasion. He gave Adelina 15 and Kim 27.
Explanation number two. Both judges thought that the contest was close. The first judge was generous across the board, giving Adelina 31 and Yuna 27. The other judge was uniformly stingier, giving Adelina 15 and Yuna 16.
Which explanation (if either) is correct? We cannot tell from the protocols. As for the hope that the ISU would undertake an internal investigation and pass out sanctions, no. The procedure for deciding when "discrepancies are so large as to raise eyebrows" is quite carefully defined in ISU Communication 1631. None of these scores is sufficiently outside the "corridor" as to constitute an "anomaly" under the judges' review procedures.
I know you took these numbers from the protocol, and it is common to see discrepancies as judges can be quite different in their genorosity, some could be giving marks out like candy, 31/27, some could be stingy, 15/16.
However, you are *assuming* the most extreme scenario in your hypothesis, a difference of 12 points in (1), and then claim that the probability of that happening is *THE SAME* as a more plausible scenario, that judges awarding them a difference of 3-5 points in (2), in explaining Adelina's win.
That to me is a rather forced strawman to argue that the judges could have cheated technically.
By definition, cheating is a stealth act, your worst assumption would have put those 3 judges waaaay out there in terms of judging anomaly in comparison to the others, an anomaly that would immediately place these (1) judges in an unwanted spotlight, i.e. equivalent to the cheats shining a spotlight on themselves, a risk that would be too great to take for any rational cheat attempting to get away with an act of cheating.
In (1), the majority judged that Yuna skated better, but it comes at the price of extremely questionable allocation of points by 3 cheating judges, to the tune of awarding a difference of 10-12 points advantage to Adelina, and hoping that they would get away with it, in a sort of twisted pretzel logic.
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In (2), the majority judged that Adelina skated better, with 2 dissenting judges giving an advantage of 1 point to Yuna, which indicates they thought Adelina skated almost as well as Yuna.
The two are not at all equivalent in probability. Occam's Razor favors (2).