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  1. § Dan Wallach Email said on :
    The real question is whether your auction mechanism would make it rational for a judge, from the same country as the contestant, to give a correct ranking for the contestant rather than to try to strategically improve their ranking.

    Your proposed mechanism and the current mechanism both imply the absence of a penalty for a referee who tries to game the system. Now, imagine a mechanism where you apply the Vickery auction principal to every ranking given by a referee. If you give one perfect 10.0 and everybody else gets a 9.5, then the 10.0 disappears. Something like that could well allow a U.S. judge to rank a U.S. gymnist, but it would be awfully strange when none of the gymnists learn their score until the last one has competed!
  2. § joe® Email said on :
    Heya Dan! Very good points! If the mechanism allows an increase in the competence and precision of the judging pool, it would be that more effective.

    I did briefly consider a mechanism that worked across the field of gymnasts, but I felt that it would be weird if all of their scores could change after each successive performance. I mean, that competition looks nerve-racking enough! (especially for the Chinese who seem to spend their whole lives working for one moment).
  3. § A Mom Email said on :
    Actually the first score for each gymnast was 16.725, not 16.780. The official score displayed is calculated after removing the highest and lowest B scores for each woman. What the first tiebreaker does is to take only the execution score (B score) which was the average of the middle 4 judges and look at who scored highest. In this case since the athletes were already tied and their A scores (start value) were equal at 7.7, the first tiebreaker made absolutely no difference. Liukin got 9.025 for the B score and so did He. The second tiebreaker calculation you discuss is correct and thank you for providing this information.
  4. § joe® Email said on :
    I really really appreciate this correction; I'll update the post first thing tomorrow. I'm not surprised I got it wrong! Thanks for commenting.
  5. § Ed Felten Email said on :
    What you are trying to do seems impossible. Here's why.

    Consider a single judge. The judge has two mental rankings of the gymnasts: the "fan ranking" F, which measures how much the judge *wants* each gymnast to win, and the "judge ranking" J, which measures how well the judge thinks each gymnast actually *performed*. (To simplify the argument, let's assume that J is unpolluted by F, that is, that the judge's observation of the gymnasts' performance is not biased by the judge's desires.)

    You want to find a mechanism that causes the judge to give scores that advantage the gymnasts according to J, while ignoring F. But no such mechanism can exist.

    To see why, imagine that we have a mechanism that causes a judge to provide scores S(J,F) depending on the judge's two rankings. For our mechanism to work, S(J,F) must produce scores that advantage gymnasts according to J but not according to F (that is, according to the judge's honest appraisal of performance, and not according to who the judge wants to see win).

    The problem is that a judge can always mentally swap F and J before deciding what to do. The judge behaves as if her favorite gymnasts performed the best, while pretending to be rooting for the gymnasts who actually did perform the best. She provides the output S(F,J) instead of the desired S(J,F). The result is a score that advantages gymnasts according to the judge's (hidden) rooting preference, and not according to the judge's (hidden) observation of performance.

    You can't stop a judge from mentally swapping J and F, because the swap occurs entirely within the judge's head. It follows that no mechanism with the desired property can exist.

    The only way out of this mess is to rely on external indicators to predict a judge's fan ranking, for example by assuming that a judge will prefer gymnasts from her own country. This is essentially what the existing rules do.
  6. § joe® Email said on :
    Hi Ed! I think the answer lies somewhere inbetween. That is, I think you're ignoring the interaction between a judge's score and the other judges' scores. With my mechanism, it doesn't matter what J and F are unless they are extreme compared to the other judges' scores, in which case they are replaced for something not as extreme. Maybe I'm not following your analysis.
  7. § Ed Felten Email said on :
    Part of my point is that a judge can't be forced to reveal J and F directly. You can't stop a judge from deliberately ignoring errors by gymnasts she likes, or from pretending to root for gymnasts she doesn't actually like.

    So, for example, the harder the system tries to correct for a judge's fan ranking, the more the judge has an incentive to pretend to act as if she has a different fan ranking.

    You can't just ask a judge to reveal J and F because they'll have an incentive to lie. They'll give high performance rankings to gymnasts they like, and they'll pretend not to like the gymnasts they actually do like.
  8. § joe® Email said on :
    That's the great part about a second-price mechanism here, it doesn't matter what they're revealing, J or F or some combination of the two, if it the result is extreme, it is swapped out for something less extreme. The real criticism I was hoping someone would point out is collusion. Because there is no "one value" that wins (as in the case of an auction), but a suite of values that are averaged, it's easy for two judges to collude on a low or high score and strategically effect the result. Sigh.
  9. § Jack Lerner Email said on :
    Under your system, Joe, what is to stop judges from gaming the system by guessing what the top or bottom *acceptable* score might be, i.e. what the second-best or -worst score might be, and giving that score instead of a lower/higher, theoretically objective score? The same-country judge wants to give a 9.3, but knows it will be thrown out, so he or she gives a 9.1 instead, when objectively he or she thinks that the gymnast really scored an 8.9. I guess your method might put a cap on unduly high scores (barring collusion), but it seems to me that as Ed says it can't eliminate bias altogether.
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