My point is that it's a fools errand to try to develop a judging system that doesn't occasionally have results that looked at in certain ways are flawed. According to Arrow's theorem, is a certain arbitrariness to any election system ranking three or more candidates. The relevance of the difference in scales in technical and artistic merit is that it is another source of arbitrariness that leads to some unexpected results. Combine these things and you have a practical limit to how perfectly your judging system can work.
You seem to be under the impression that I think adding the technical and artistic scores is an unworkable thing. This is not my opinion. I think it is workable, but we cannot expect it to be perfect and come up with results that everyone will agree upon after the fact. In practice, judging systems don't have to be perfect. They just have to be sufficiently predictable that they give the contestants something to aim for. Furthermore, the scoring system must do more than be fair to each individual performance, it must be good for the sport as a whole.
If making a perfectly fair system were the highest priority, you would create a system based on technical merit alone, using an objectively measurable scale with so many deductions for every fault, etc. Such scores could be added objectively, the differnces between judges should only be lapses of observation or differences in vantage point. However, artistry is an important part of the sport, and while there is no accounting for taste, you still could reasonably add the judges artistic score, provided you train the judges to score the contestants on a similar scale. This introduces a small degree of arbitrariness (what is worth a tenth of a point artistically speaking), but if you disagree with the results, its a simple matter of a difference of opinion.
However, skating is a sport in which technical and artistic factors are important. As soon as you combine those two factors, you are guaranteed to have results that seem to be unfair or even arbitrary. If you fixed the rules to work better in this case, there will be future cases that are just as broken but in different ways.
It is important to the sport to combine these two factors, but it gurantees that there will be differences in opinon. The interests of the sport to maintain these two independent scales of performance overrule the interests of the contestants. Getting all prosecutorial over mathematically inevitable flaws is just poor sportsmanship.
If I were to suggest a system that would be more fair than the current one, sufficiently simple that an ordinary person can understand it, and scrupulously fair to each performance, I would suggest this. Score the performances independently for artistic and technical merit, add the judges' scores in each category separately and award two independent championships. A performance could potentially win up to two medals. If one couple were superior on both categories, they'd get a double-gold, a kind of superchampionship that would carry a kind of glory that would motivate contestants to work on both aspects of their performance.
In the current case, we'd have one couple walking off with an artistic gold and another with a technical gold. It may be disconcerting that there is no single championship pair, but this reflects the reality that neither pair was agreed by the judges to be superior in both categories. Any attempt to name a single champion will necessarily be unfair to one or the other pair.
Such a system avoids the arbitrariness of adding numbers awarded on incommensurable scales. It also avoids the Arrow theorem, which is about the impossibility of composing pairwise preferences into a composite preferences. The judges are not raking candidates, they are scoring them.
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