Asymmetric information and high school effort grades

In high school, I remember thinking how our grading system was a total farce. We weren’t graded on ‘results’, allegedly. Instead, our teachers gave us a grading based on our ‘effort’. There were 5 grades in total:

C – Commendable
G – Good
S – Satisfactory
D – Disappointing
U – Unsatisfactory

To me this was complete nonsense, because effort is not observable! What the teachers did was to look at the end product, and use that to infer some ‘perceived’ level of effort to base their grading upon. This isn’t the same thing as actually judging effort. I knew this because, quite often, my end product was pretty good and although it required minimal effort, I ended up with the top grade of C. Similarly, there were times where I put in a lot of effort, but got a poor effort grade because my end product was not so good.

Asymmetric Information

This situation is a classic example of ‘asymmetric information’. This is where one person (or party) can do some action, or has some information, that the other person cannot observe fully.

In terms of effort, this means that students could get away with putting in much less effort because teachers cannot accurately observe or measure it. On the flip side, teachers may misread a student’s effort based on their work.

My effort

I’m going to construct a fairly trivial model in the context of my high school effort grades to make things a little bit interesting.

The table above shows the effort grades as I described before. In the 2nd column, I have assigned values to each grade, so that, for example, I’d get a reward of 3 if I got a G. In the 3rd column, is the minimum effort level I need to put in to obtain each grade, given a perfect world where effort was directly linked to grade. So if I put in somewhere in between 50% and 75% effort, I should get an S grade.

Again, for simplicity, suppose I am doing a piece of schoolwork that has just 2 outcomes: good (g) and bad (b). These outcomes are chosen from the 5 reward values that correspond to each effort grade. The probability of my work being good is e (i.e. the amount of effort I put in) and the probability of it being bad is 1 – e.

Of course, putting in effort is costly for me. I want to get away with as little as possible. Suppose the cost of the effort I put in is given by the function 2e2. This means my expected payoff is:

ge + (1-e)b – 2e2

What would my optimal effort be? We just need to differentiate this function with respect to e and set it equal to 0 to obtain my optimal effort level e*:

e* = (g-b)/4

What does this mean? My effort level depends on the difference between the grade that I get when I do good work and the grade that I get when I do bad work. Suppose my teacher decided to give me a C if I did good work and an D if I did bad work. This kind of thing happened often with teachers that were ‘nice’ and didn’t want to make students feel too bad if the work wasn’t good. They assumed that people still put in some effort and so wouldn’t give us a U unless we did something particularly crazy. Then g-b=3. So my optimal effort would be e=3/4, or 75%.

As a result of the teacher’s benevolence, I could get away with putting in less than 100% effort, and still stand a chance of achieving a C grade! According to the table above, this shouldn’t be possible since a C grade should only be given to students who put in 100% effort.

However, the flip side is that you could get particularly unfair teachers. They might only ever give a G if your work was good, and wouldn’t hesitate to give you a U if your work was bad. In this case, g-b is still the same as before, and so my effort is still 75%. But I’m in a worse situation. No matter whether my work is good or bad, this teacher will always give me a worse effort grade than the nice teacher. And yet I’m still exerting the same effort!

Of course, there were also some teachers who almost always gave me the same grade, regardless of my work. Quite common was the ‘G’ teacher. They didn’t want to spoil kids by giving them a C and making them feel too happy, but they didn’t want to demoralise either. This means that I’d have no incentive to put any effort in whatsoever!

The bottom line

This model is perhaps mathematically a bit silly. It’s not hugely sophisticated. But it explains my point quite simply and elegantly. Sure, your effort is vaguely linked to the effort grade you get. But at the end of the day, regardless of how much effort you actually put in, your grade mainly depends on:

  1. The personality of the teacher
  2. Your actual end product

There’s no objectivity or concreteness in trying to grade effort – something that you can’t reliably observe! Just one of the many reasons that I don’t miss high school at all…

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