29 October 2013

Costly Signaling: The Quest for a 90.0%

I remember that during my senior year of high school, there was some unofficial competition among friends to get the lowest final grade possible without ``Asian-failing." That is, to do as poorly as possible on graded assignments without getting the dreaded B+. The GPA cutoffs was set such that an A [93%, 100%] was a 4.0/4.0, A- [90%, 93%) was a 3.8/4.0, and B+ [87%, 90%) was a 3.3/4.0, so dropping from an A- to B+ is a much bigger deal than dropping from an A to A-. This game was certainly fun to play, but at that time I didn't understand the reasons that we participated.

It turns out that costly signaling could explain this phenomenon. Costly signaling, or the handicap principle, is a behavior that is costly for all groups, but more costly for the ``worse'' group than it is for the ``better'' group. In this case, better and worse are in terms of ability to do well in class and cost is the expected grade, which is related to the probability of sinking below 90% and the probability of being able to rescue a failure. I assume that the less smart kids have less control over their performance on assessments since they probably (1) can correctly answer fewer questions and (2) are more prone to make trivial errors.

Riskier variations include playing the game below senior year, during which grades are more valuable (since colleges will see them), or at MIT. I wonder how the brave souls at the Institvte would do, since the cliff between an A- (5.0/5.0) and a B+ (4.0/5.0) is massive.

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