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Frutti di Bosco

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frutti di boscoGrading – grating. Oh, the agonies of grading student performance! Allow me to indulge (again) in a moment of self-pity. For an earlier Jeremiad, see here. It is a well-known fact – and one that is obvious to any folk psychologist upon reflection – that those students who missed a better grade by a hair feel worst and are most likely to plead with the instructor. Some go on to appeal to what they believe is a higher power (deans) if they remain dissatisfied; others offer to do extra work to improve their grade. Consider the simple world of grades at my university. There really are only two grades, A and B. No plusses and no minuses. The grade C is rare and is understood to be ignominious. A and B, in other words, respectively amount to success and failure in an environment where everyone expects to be better than average. By and large, 40% of the grades are A, 55% are B, and the rest C.

gradeTo work with frequencies, suppose in your class, there are 9 A and 11 B. The highest B complains and gets her way. Now there are 10 A and 10 B. What are the hedonic consequences? The 9 original A will be disappointed because their grade has been cheapened. The climber is happy, and the remaining 10 B are unhappy because their grade now signals worse performance on average; it is now more clearly a poor grade than it was before. Let the cycle continue. Again, there is one individual whose B is the highest. Suppose she pleads with success and receives an A. The 10 A that are already on record will feel worse, and so will the remaining 9 B. And so it continues. At the extremity, the last person with a B will plead into an A, will feel good, while the other 19 A feel worse because now their grade has lost all meaning. Conclusion: Do not yield to the first request to have a B turned into an A.

There is a flipside. No student will request the reverse, that is, the transformation of a low A into a high B. Surely, though, you could make it so even without that request. If you did, you would sacrifice the happiness of that one student for the increased happiness of all the others. The remaining A would feel good because their grade would bear a clearer mark of distinction, and the B students who are already on record will be pleased to see that their comparatively low grade has become a more common one. And the cycle continues. At the extremity, the last A standing will be transformed into a B, making that student miserable, while pleasing all others. The B is no longer the mark of failure. It is not the mark of anything, other than participation.

You see what you need to do to fully exploit this dynamic. Begin with a distribution of N-1 A and 1 B, and then whittle away until all grades are B. Happiness should increases monotonically – if irrationally. In the end, the students will realize their entrapment, and see how short-term increases in happiness undermined long-term happiness. It sounds like an addiction to grade change, no?

A parallel in economic psychology suggests itself. In most countries, the distribution of wealth is highly skewed, such that the modal, the median, and the average wealth are arrayed in this increasing order. Stated differently, the distribution looks like a J lying on its back with its foot sticking up on the left. What would be the effect on national happiness if the wealth of a few people increased at a time? These individuals would be happy, whereas those they leave behind and those they join would not be. All told, there would be more unhappiness than happiness. Put the process in reverse, and you’ll see that if a few people lose wealth, everyone else will be happy. Again, if you let this process run to its tragic conclusion you would have to conclude that the gradual immiseration of a society would be a happy thing in the moment, although general gloom would await at the end.


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