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Thread: Should the IJS use median scores instead of the trimmed mean?

  1. #61
    Landing 3As in my dreams! skatedreamer's Avatar
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    Quote Originally Posted by lilahozi View Post
    This only addresses the viewer. What about the SKATERS? I don't see anyone mentioning the most important group of people in all of this. Should skaters just dedicate all those hours and years to practice, and accept that they'll probably get rewarded with unfair scores? We may never achieve a perfect system, but we should aim for it.
    I don't think anyone is suggesting that. It's just that no matter how perfect the system and how honest the judges, there probably will always be some disagreement about results. Unfortunately, that's the nature of a judged sport. The goal is (or should be) to construct a system that everyone trusts and that minimizes the chance of cheating/manipulation as much as possible.

  2. #62
    Custom Title Mathman's Avatar
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    Quote Originally Posted by drivingmissdaisy View Post
    The paradox is that you have two skaters who are ranked against one another, and their relative rank can change based on what other people do. In SLC, after Michelle Kwan skated she was ahead of Sarah Hughes. Kwan was better than Hughes over the course of the SP and the LP, until Irina skated. Now Hughes was better than Kwan over the course of the SP and the LP, and a third skater was responsible for that flop.
    To me, that is not a paradox. Kwan was ahead of Hughes because of factored placements. Kwan had 1st in the SP and (temporarily, because the contest was not over yet), 2rd in the LP. This put her ahead of Hughes' 4th and (so far) 1st.

    Then Slutskaya skated and Kwan turned out not to be second best in the LP after all, but rather 3rd.

    How is it a paradox to say that Michelle was 2nd in the LP before Irina skated but 3rd afterward?

  3. #63
    Wicked Yankee Girl dorispulaski's Avatar
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    Quote Originally Posted by Mathman View Post

    I have never understood what is so "paradoxical" about flip-flops.The only reason we even attach the negative-sounding name "flip-flop" to this phenomenon is that we have counted our chickens before they hatch. Just tell the skaters, "hold your celebration until everyone skates."

    Me either.

    It ain't over till it's over.
    ---Yogi Berra
    That is all the explanation needed.
    Last edited by dorispulaski; 06-10-2014 at 06:37 PM.

  4. #64
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    Hmm median has its own problem as someone already pointed out. I think increasing number of judges significantly(at least in big competitions like worlds or olympics) will be more effective and realistic solution to deacrese the possibility of bad judging outcome(mathematically speaking).

  5. #65
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    Quote Originally Posted by Mathman View Post
    How is it a paradox to say that Michelle was 2nd in the LP before Irina skated but 3rd afterward?
    The paradox is how one skater can be better or worse than another based on more than just how they each skated individually. I think we all understand how ordinal system works but it is strange to conclude that Sarah Hughes was the best skater in SLC, but only because Irina was better than Michelle. If Irina was worse than Michelle, then Michelle would have been the best in SLC. The result is paradoxical, not how it was arrived to.

  6. #66
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    ^The equivalent political science theory to that paradox is called Independence of Irrelevant Alternatives: http://en.wikipedia.org/wiki/Indepen...#Voting_theory

    It exists with a lot of voting/ranking systems.

  7. #67
    Custom Title Mathman's Avatar
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    ^ However, it is worth pointing out that the example of Hughes, Kwan, and Slutskaya in 2002 is not an example of violation of independence of irrelevant alternatives. (Slutskaya was not "irrelevant" in the technical meaning of the term here. ) The Salt Lake City result was strictly due to factored placements, not to the kind of thing that is studied in social choice theory.

    Quote Originally Posted by drivingmissdaisy View Post
    Kwan was better than Hughes over the course of the SP and the LP, until Irina skated.
    I think this language is a little bit misleading. Kwan was not "better than Hughes" in the middle of the LP competition. All we know is that Kwan was better in the SP but worse in the LP. How much worse? We don't know yet. Being in temporary "second place" when there are still skaters left to skate does not mean anything in terms of the overall standings.

    To make the "paradox" go away, all the announcer has to say is, "So far Michelle is in second place in the LP. If this holds up she will win the gold medal. If this placement does not hold up then Hughes or Slutskaya will win."
    Last edited by Mathman; 06-11-2014 at 10:06 AM.

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