I would disagree.
I think that there is a platonic ideal of school figures and those were scored on how closely the execution matched the ideal.
But with freeskating, there's doing the basic thing correctly, and then there are variations that enhance the basic skill or that reflect different ways of doing it right and better than just "right." That's where the positive GOEs come in, or uncaptured mental extra credit under a holistic judgment. If there's only one way to make an element better, then the better-est it could be might be the ideal. But if there are multiple ways to make it better, then the standard good is not the ultimate ideal and neither is only one of the possible improvements.
Actually, I don't disagree with anything that you are saying here. Maybe we are just misunderstanding each other. But the fact that there are multiple variables that define the success of technical elements is not the same thing as saying that each of those variables, in principle, is not definable (can be mapped in a systematic way to a range of numerical increments).
And, yes, the number of discrete variables means that the number of permutations is also large, but again, they are mathematically finite.
Certain variables/aspects are only bounded by the limitations of human capability and physics (e.g. how "deep" an edge can go, or how fast they can skate, or the number of rotations, "hang time"/delay, and distance in a jump), but, again, these can be mapped to a numerical range of scoring effect.
This is what was meant by the proposition that the technical elements can be viewed though a pragmatically Platonic lens.
Yes, very broadly. But there are cultural differences among practitioners and officials as well as among fans. The skating community can try to reinforce common standards within its own boundaries. But the the individuals will also have outside influences. And subcommunities of fans will develop their own common criteria that may draw more on the values of the outside
Just as a random example, some expert and nonexpert viewers might swoon with delight a the sight of a male skater with impeccable body line and pointed toes. Others might feel deeply uneasy at what they perceive as feminine characteristics on a male body, to the point that watching male skaters with these qualities gives them the creeps. (Obviously, they wouldn't last long as officials or coaches if that were the case. But as fans they could continue to enjoy women's skating and the more macho, perhaps less refined male singles and pair skaters.)
Again, no disagreements from me. I really think we're on the same page, but looking past each other.
-Sure, there are cultural differences, but those differences don't prevent viewers from learning to understand and appreciate other (human) cultural cues if they make a good-faith effort. The ability to do so is one of the things that defines human beings as members of the same species. On the other hand, if a tentacled sentient mollusk from Neptune vibrated its antennae in a certain way while releasing electromagnetic pulses that we can't detect, then I'm not sure that we would be capable, even in principle, of knowing what was being communicated, or of feeling the same way about it even if we could.
-On your more earthy (and earthly) example, I would suggest that the negative response to the male skater is a reflexive, unexamined reaction, similar to those of the crowds laughing all the way out of Marcel Duchamp's Armory exhibition (and I say this as someone whose personal taste runs to ladies skating vs. mens). But I would bet that a good portion of those crowds was able to understand and even appreciate Duchamp's merits a couple of decades later, once the world got used to the modernist perspective. In other words, I'm certainly not arguing that viewers (or even judges) are infallible, or can immediately adapt to unfamiliar things (and this is probably why there are a lot of "warhorses" in terms of music and choreographic style; this is a competition, and for most competitors, any possible acclaim for artistry some years down the line just wouldn't make up for missing the gold by looking like an oddball right at this moment

).
Nevertheless, so long as those unfamiliar things are human, other human beings can learn to appreciate the point of view, as well to develop a sense of judgment as to greater/lesser within that perspective. And even, to extend this further, to be able to judge why a certain tango-inspired skating performance was better than a certain ballet-inspired one. This is why, on the same principles, a film competition feels justified in placing a comedy next to a tear-jerker drama in the category for "Best Picture". IMO, what we all share in terms of the basis for aesthetic response, albeit "very broadly", is ultimately more innate and hardwired than the aspects on which we differ. Everything else, particularly the cultural conventions, is detail, and can be learned.
The numbers are inevitably a compromise. It's more convenient than giving a verbal evaluation (to communicate) or mental or penciled tickmark (to keep track) of where each skater is good, better, or not so good and by how much.
To re-emphasize, I am not against numerical scoring of itself. Any competitive endeavor, almost by definition, must have some numerical basis, however simple. Where I question COP is in the implied
precision of the scoring
for the artistic components (PE, CH, I), because the scoring increments cannot be persuasively shown to correspond to a set of discrete variables with fairly precise gradations of incremental fulfillment (in contrast to the "technical" elements).
I have no idea what that means and don't have time to google.
Sorry, I should have been more mindful that the fan bases of skating and boxing are generally pretty far apart

. In boxing, each round of the boxing match
must have a winner, who will be awarded ten points for that round, irrespective of whether the performance in that round was better or worse than the winning performance in another round of the bout. In each round, the winner always gets 10 points, and the loser gets a score relative to winner's performance.
So if there are 30 skaters in the short program, then there should be an average of 3 in each slot? Or can there be slots of 8.5, etc.?
Are these scores given for whole programs or several scores from each judge for different aspects of the program (e.g., 5 separate components)?
As per my caveat, this is just a preliminary idea off the top of my head. But for the sake of discussion, how about this:
-Each "artistic" component (that is to say, this only applies to PE, CH and I, because I consider skating skills and transitions to be, in concept if not always in actual practice, "technical" and hence more amenable to precision) is scored separately. For each of these components scores, the skater receives a rank relative to the field. So if there are 30 competitors, there are 30 rankings.
-Each ranking number (e.g. #1, or "the best") can have, say a maximum of 2 or 3 names in that slot. In other words, two or three skaters can be tied in the #1 slot. Similarly for the #2 slot, and so on. This doesn't mean that it's mandatory for judges to put in the maximum number of names in each ranking slot. This is only if the judge feels that there is no clear choice for that ranking slot. So (assuming a maximum of 3 skaters per ranking slot) you could end up with, for example, 2 skaters ranked #1, 3 skaters at #2, only 1 skater in the #3 slot, and so on. What this means is that there may be 30 rankings, but they may only go down to, say, #20 (since there are multiple names in slots in some cases).
-The scoring differentiation between the ranking slots is up for debate. But a very simple example would be for the #1 ranking skater(s) to receive 10 points, the #2 slot(s) to receive 9 points, and etc. on a linear scale. I haven't completely thought through the scale of increments, but it could also be curved, either more sharply at the top or at the bottom, depending on whether you want to incentivize the top performances and/or more heavily penalize the worst. And to answer your question directly, a particular slot could certainly have 8.5 points. The big-picture theme, though, is that the increments are pre-determined and are not discretionary on the part of the judges.
-I am currently envisioning that the artistic components scores would be given by each separate judge for each separate component, as is the current practice. The key difference is that the judge is only responsible for determining greater than/lesser than/equal to, strictly relative the the field of that particular competition, and with no discretion for determining the precise magnitude of the scoring differential.
Since these are comparative scores, they could only be given after the fact. How do you keep track in large fields?
Here is the best (in the opinion of 5 of the judges, IIRC) men's short program from 1996 Worlds:
http://www.youtube.com/watch?v=IyGkx7b_Dc0
It was also the 2nd out of 30 performances that day.
What kind of notes do the judges need to keep to remind them to give 3 or 4 hours later that that was the best performance of the day? They can't give the best-in-field score in real time, because for all they knew that could end up being only be the 4th or 5th best performance of the day.
How do they remember that the first skater of the day was, in their opinion, 25th best overall? That's what the placeholder scores were for under 6.0, with some advantages from the flexibility of tiebreakers and some disadvantages in that the numbers corresponded only roughly to absolute skill levels as understood given the state of the sport at that point in skating history.
What the program components scoring is trying to do is to peg the numbers to those somewhat-less-rough mental consensuses about "absolute" skill level rather than comparing them directly to other skaters in the same event.
So I have a few questions about how your proposal would work.
*How many numbers does each judge give to each performance?
*How do they keep track of comparisons among many skaters across the several-hour duration of a large event?
Ahh, you've got me, here

. You're absolutely right that the logistical problem of handing out purely
relative scores in a competition is probably the biggest issue. My very preliminary thoughts as to a possible solution (and I say again for the eighth time that this is just an idea that I've been playing around with for a pretty short time):
-Have a separate panel of judges (who can be members of the general judging pool, but who are designated to judge only the artistic components at this particular competition). The artistic rankings (and, hence, the artistic component scores) are punched in and tabulated at the end of the SP and the FS. Thus, the "overall" score will only be known at the end of that day's competition. This involves some incremental cost. One could theoretically have this done by one panel of judges responsible for both the technical as well as the artistic scores (as currently done), but this would leave open the charge that the judges can "manipulate" the artistic scores to achieve a desired result. How to achieve this as a practical matter is a separate issue; I'm just focusing on the concept for the moment. It would actually be even better, I think, if the "artistic" panel didn't know what the skaters received in their technical scores, but I haven't fully worked out the mechanics of that

.
I think it's even conceivable that this type of scoring procedure might heighten the audience thrill factor, particularly in cases where the technical scoring is close, and the overall results very much hinge on the artistic aspects, which the audience generally feels they can more readily relate to.
Please see above.
I disagree that there is a theoretical version of perfection. I think there are multiple, potentially contrasting, theoretical versions of excellence. So several different skaters in the same well-skated high-level event might come close, in different ways, to the best imaginable performances of their different programs with their separate areas of excellence. If we want to come up with a winner, there needs to be a way to distinguish at a finer level than either 10 or 9 for the whole program (not sure if that's what you're proposing).
I think this was addressed in the discussion of the ranking/scoring increments above.
See, I think that's actually a much harder question when you have more than 6 skaters to keep track of.
The few very best and very best in the event will be memorable. But how do you distinguish between 10th best and 13th best if they skated several hours apart without some external mental benchmark to compare them to?
My own personal viewpoint is that it might actually be easier to correctly rank the skaters on artistic components if done after all the performances are completed, and with more than a few minutes to make an assessment per score (the subject for scoring is both complex and holistic). It might, for instance, cut down on the cases where a skater received low marks simply because the skater wasn't in the final group.
The judges will still be able, unofficially and privately, to keep a rolling tabulation as the competition moves along, and he'll still be able to utilize almost all of the "outside" principles of assessment that he/she has always done. Just not any reference to any skate (either personally ideal or historical) outside of that competition in assigning ranks, and the official rankings are only inputted and tabulated
after the judge has seen
all of the performances.
Is this proposal for program components/second mark only and there would still be more absolute/cardinal scoring of the elements?
Taking control of the increments (margin of victory) in components away from the judges would mean that the base values would more often determine the results.
Or if you're proposing to use this for technical content too, then it takes away precision in evaluating the tech content.
As I tried to make clear in both my previous and this current post, this idea proposes to apply this "new" scoring convention only to the "artistic" components of PCS (PE, CH, and I), and not to SS and TR, and certainly not to TES. The scoring of those elements/components would stay as is.
Under the above, I don't see how this would mean that base values would more often determine the results.

I'm not in any way going all Tom Cruise in proselytizing for this idea. It's just a musing that I thought would make for interesting discussion, possibly highlighting some of the issues along the way.