> Kahneman hypothesis implies that such teachers reward students only when their level of achievement is higher than it has ever been in the past and punish them whenever their achievement is below their highest level of achievement.
Not really, Kahneman is talking about doing better or worse than expected, not about your best or worst performance.
Regression to the mean arises when following up on any deviation from the mean – though of course the more extreme the deviation, the more pronounced the effect.
Similarly, the effect of regression to the mean is smaller when measuring longer periods of time (less measurement error means fewer fluke outcomes) but it doesn't disappear.
Of course, it's perfectly possible that strict teachers are truly beneficial even when accounting for regression to the mean, it doesn't have to be one or the other, and Kahneman certainly doesn't prove anything of the sort, but it does shift back the burden of proof to those who would claim that strict or even borderline abusive teaching is helpful.
> Not really, Kahneman is talking about doing better or worse than expected, not about your best or worst performance.
At a given point in time there are two quantities we need to worry about: how the teacher expects the student to perform at that point in time and the student's ability to perform at that point in time.
If the teacher is rational and has seen the student perform many times these quantities will be the same. I think the outcome is probably optimized if these quantities are the same at all times but in the real world there may large disparities in the values which can fluctuate over time.
Nevertheless, suppose it were the case that the values are always equal. Then Kahneman's hypothesis is obviously wrong. The student will perform better than expected roughly the same number of times they perform worse than expected (in the long run, obviously).
Regression to the mean exists, yes, but has no impact on the distribution of the events of being above the mean or below the mean.
I supposed that Kahneman would recognize this fact and he his reference to regression to the mean was based on a more complicated but much more realistic model where the expectation is not always aligned with reality. In such a model there must be a mechanism for relating the two quantities after each new performance/test/review.
I tried to think of how this model would work and suggested Kahneman meant that expectations were adjusted based on previous best values. I should have been clearer that other mechanisms were possible and that I was only guessing which Kahneman meant. Then I argued that based on my experience this is a poor model of how teachers punish/reward their students in general because it is unnatural and unhelpful to the task at hand. As this model is not valid his conclusion that people are incentivized to punish each other is specious.
Not really, Kahneman is talking about doing better or worse than expected, not about your best or worst performance.
Regression to the mean arises when following up on any deviation from the mean – though of course the more extreme the deviation, the more pronounced the effect.
Similarly, the effect of regression to the mean is smaller when measuring longer periods of time (less measurement error means fewer fluke outcomes) but it doesn't disappear.
Of course, it's perfectly possible that strict teachers are truly beneficial even when accounting for regression to the mean, it doesn't have to be one or the other, and Kahneman certainly doesn't prove anything of the sort, but it does shift back the burden of proof to those who would claim that strict or even borderline abusive teaching is helpful.