Rgirl, here is a quicky for now, with a promise of a more extended analysis later.
How would the judge or judges in your examples know if his/their score(s) would not be thrown out as the random one(s)?
They wouldn't. That aspect of the NJS would, at random, either strengthen or dillute the supposed conspirators' hand.
Or if he/they had the high or low scores in their chosen area?
The trimming of the mean muddies the conspiratorial waters and does mitigate the effect of low-balling your rival. Some observers think the ISU should go all the way in this direction and use the median score, instead of a modified mean, which would make the procedure impervious to manipulation of high and low scores.
But there are still two points to consider. If you artificially score your favorite way too high, even though that score is thrown out, that puts into the mix someone else's high score which otherwise would have been the one eliminated.
Second, as in the example of Sokolova and Czisny at Skate America, manupulating scores in the middle range (raising a score from 6.25 to 6.50) can have an effect in the final outcome, especially if a group of scoundrels all do it in concert.
Also, Rgirl asks re this example, "1.0 points x 5 components x 2.4 factor for SP and LP together / 7 (averaged over 7 judges) = 1.71," with 11 judges, the two high and two low scores thrown out, plus two random scores, wouldn't that be averaged over 5 judges instead of 7?
Yeah, I knew when I was writing it that I wouldn't be able to slip that one by you. I didn't want to compicate the explanation by having to consider separately, and then average over many competitions, the various cases where 0, 1, or more of the conspirators' scores were thrown out.
For the Grand Prix, I think there are 10 judges, 3 thrown out in the random draw, 1 high and 1 low thrown out. This means there are 7 actual judges before triming. There is a 2/7 chance that you will be trimmed, in which case your contribution is 0, and a 5/7 chance that you won't get trimmed, in which case your contirbution is 1/5 of the total. The weighted average of these effects is 1/7 x 0 + 5/7 x 1/5 = 1/7.
But this is a statistical average, not the outcome of any particular contest.
I think for the Olympics there are 12 judges, 3 eliminted in the random draw, 1 high and 1 low eliminated, then the other 7 averaged. (Is this right?)
To me, the bottom line is not whether it is easier or harder to cheat now or before. The New System is here, to Irina it's clear, to Michelle it's severe, it's a puzzle to Weir, the Olympics are near. In a close contest it is possible for unethical judges to skew the results.
Mathman