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I agree with this analysis. (As pointed out by gsrossano -- post 44 above -- the ISU has a different view, but never mind that.)

This is the point at which statistics raises it’s ever-curious head. We cannot expect that the average of this finite sample will be exactly the same as that “best number” representing the average score for all judges in the world. But we could hope that “probably” it is “pretty close.”Now consider all judges existing in the world at the present time. Let each judge do the same thing. In general, [each judge might give a different score,] so take average. Then you will get a unique number for each performance (or for each element under consideration). It may be viewed as the best number representing the performance.

Of course you cannot do this in reality. The only thing you can do is select some finite number of judges…

The job of statistics is to say how probable is “probably” and how close is “pretty close.” There is a formula for this, which works in many, many cases. It goes like this: “We can be 95% confident that the average of the finite sample will be off by no more than twice the standard deviation divided by the square root of the sample size.”

Hence the discussion of how large the size of the finite judging panel ought to be.

(The argument between Dr. Rossano and me on this thread is mostly about whether figure skating judging is – or should be -- the kind of thing that this sort of analysis usefully applies to.)

As a person who still likes ordinals (and the particular statistical ideas that apply in that case – one does not, for instance, take the average of ordinals), I found the following part of your post most fascinating.

Why would it be unfair? Who would it be unfair to? Why might a judge feel this way?Originally Posted bysteyn

I think perhaps the answer is that it seems “unfair” to our pyschological sense of how sports scoring "ought" to work. We have different emotions when our team clobbers the other guys 20 to nothing, compared to when we squeeze out a 5 to 4 victory in an overtime shootout.

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