At this point, readers possessing technical proficiency and a mistrustful temperament will be piping up: Where do all these assumptions come from? How do you know what the standard deviations are? (I made them up.) Shouldn't the deviations be smaller at the top of the grade range? (I don't care.) And what probability distribution, exactly, are you using? (A truncated normal distribution, you fussy creature.)
Trust me: None of these questions matter. However you compute, the point stands. A grading scale much too coarse to separate students' performances in a single class (for instance, the system with just two grades) can—if it is not too coarse—be perfectly adequate when we have a whole transcript to look at.
How coarse is too coarse? It's actually easy to tell. In the example above, Zoe and William weren't separated on the two-grade scale, because both got straight A's. And, in general, a grading scale is too coarse if there are a lot of students who get the same grade in almost every class they take. In my experience, very few undergraduates make straight A's all through college, let alone straight B+s. That indicates that the present system, inflated as it is, is good enough to rank our students.
Indeed, a 2000 Department of Education study found that just 14.5 percent of undergraduates nationwide had a GPA above 3.75. And Henry Rosovsky and Matthew Hartley, in their well-reasoned monograph, found "no large body of writings in which, for example, employers or graduate schools complain about lack of information because of inflated grades." (Certain of their informants did complain to this effect in "informal conversations.") Anyone who's read fellowship applications, or graduate school admission folders, knows that the best undergraduates aren't hard to pick out—they're the ones who excel in nearly every course, the ones with a healthy sprinkling of A+s, the ones whose recommendation letters read like mash notes.
So, Mansfield is wrong—which doesn't mean grade inflation is all right. There are still those moral, psychological, Marxist, and geopolitical questions to think of.
And underlying all these questions is a deeper one: Why do we grade? Is the point to give students information? To reward, punish, or encourage them? Or just to hand them over to law-school admissions committees in accurate rank order? Until we answer this question, there's little hope of making sense of grade inflation. It's as if we were bankers trying to formulate a monetary policy, but we hadn't quite decided whether dollar bills were a means of economic transaction or a collection of ritual fetish objects.
"In a healthy university," Mansfield says, "it would not be necessary to say what is wrong with grade inflation." There, again, he's mistaken. In a healthy university, we would talk about every aspect of grading, down to the bottommost questions about why we grade at all. I suspect we'd all find it much less tempting, under those circumstances, to project onto our students' GPAs our anxieties about moral leadership, honesty, and the rewards to be expected from hard work. That would be an improvement. Grades are—should be—many things. But ritual fetish objects they are not.