The part that seems oddest to me is the eliminating of the two, because that is random, and in a close competition, which judges are eliminated could make the difference between 1st and 2nd or between on the podium or off. That seems to be introducing an element of luck into a system that is trying to be more standardized. We have 9 experts there - why not use all of their scores? And are the same judges eliminated in for all skaters in the event - or is re-randomized for each skater? Or even each element?
Yes, it is fair. In s subjective sport it is really the fairest way. If one judge is giving Rachel Flatt all 10s and +3s and it is totally out of line with what was presented, that judges should be dropped as being too high, the same would be true if a judge gave Yuna Kim all -2s with 5.5s.
You're talking about two different things. The random selection
ivy brings up has nothing to do with judges scoring skaters too high or too low.
1)
Random selection. Extra judges are assigned to the panel, and the computer randomly picks some of these judges to have none of their scores for the whole competition.
The point of this, combined with anonymity, was to confuse federations, etc., who were trying to pressure judges to judge in certain ways and to check up on whether they did. But it didn't actually help that purpose very well, and paying for extra judges to sit on the panels and not contribute to the results was too expensive.
So this is not done any more. No need to worry about random selection any more. We can still worry about the anonymity and the mixing up of the order of judges' score columns between each skater, because that is still done in international senior event. (It's not done in all IJS events.)
When this was done, it was random. So if there was a judge who was extremely biased or actively trying to skew the results, the random selection might eliminate all of their scores from the calculations, or it might keep them on the smaller subset of the panel whose scores actually counted. There was a chance that they would have zero effect on the results. But there was also a larger chance that an honest judge would be randomly dropped and the biased judge would have a larger effect on the results than if all the judges sitting and scoring were actually used.
2)
Trimmed mean. For each element GOE and for each component, the highest and lowest mark is dropped. This is
not random. Which judges' scores get dropped changes for each element and for each component depending on which judges happened to be highest or lowest for that particular element or component. Often there are several judges who gave the same highest mark or the same lowest mark, so one of them gets dropped from the averaging but it's meaningless to say which of the two enthusiastic judges who gave +3 for the same spin (for example) was the one whose score was dropped.
The trimming will take out outlying scores that result from judges seeing things differently from everyone else on the panel (probably a mistake by the outlying judge, but possibly s/he saw a detail that everyone else missed) or from judges making data entry errors.
(This is a good thing, except in the rare cases when only a lone judge saw the element correctly.)
It will also often take out scores from judges who consistently score higher or lower than the rest of the panel for all the skaters, or who use a wider range of numbers to reflect the differences they perceive between the skaters.
(This is probably a bad thing, assuming the judges are honest and competent but just happen to use numbers a little differently than the majority.)
If a cheating judge is way out of line consistently, giving a pretty-good skater stellar marks or a stellar skater mediocre marks, that would get all or most their scores trimmed for those skaters.
(Good thing, but it still means another judge whose scores for that skater/element/component were similarly high or low will not get dropped, as would have been the case if the cheating judge had judged honestly.) They might do a good job with the rest of the field and not get trimmed any more than the other judges for the other skaters.
A judge who is actively trying to manipulate the results in favor of a specific skater can probably adjust their marks to give little boosts here and there to their favorites and little dings here and there to the favorite's rivals without getting most of their scores dropped. They can't guarantee a win for their favorite, but they can nudge the averages in the direction they want, which in close contests can definitely make a difference.
If a judge is just incompetent and their scores are too high or too low or all over the place in inconsistent ways because they just don't have enough knowledge of what they're seeing and what the scoring rules are compared to the rest of the panel, then their scores will often be dropped.
(Good thing.)
If many of a judges' scores are consistently out of line over several competitions, for whatever reason there's a process for identifying those judges. Again, this might happen because the judge is cheating or strongly biased without realizing it, because the judge is incompetent, or because a competent judge just happens to use a higher or lower or wider scale than the rest of the panel. The latter will be able to give good explanations when flagged. If the judge gets several assessments and can't defend their decisions, they can be demoted. So it's in the best interest of judges who aren't as competent as their peers to improve their competence.
And it's in the best interest of judges who are trying to manipulate results to do it as subtly as possible so they don't get caught.
The extreme examples
mousepotato gives are not likely for that reason.