incentives, or why grading policy lies somewhere between economics and foreign relations

In this post, I plan to cover the issue of grading policy, particularly in relation to FCPS and TJ.
First of all, what is the purpose of grades? I propose that it is twofold:

1. Grades are intended to give an objective measurement of both achievement and effort in order to provide colleges and others with an idea of how the student performs in a typical academic environment, as opposed to on a standardized test.
   
2. Grades are intended to provide an incentive to students that drives them to put more effort into their academic pursuits than they would otherwise, that is, to provide external pressure to those without internal pressures.

Second, how well does the standard letter grade system with this purpose?

Does it provide an objective measurement?

For the most part, yes, but different teachers do apply different standards. This is hard if not impossible to fix. The hope, of course, is that differences between teachers get averaged out in any one student's GPA over the course of their four years of high school.

Does it provide the proper incentives?

Absolutely not. The critical part of any continuous incentive system (e.g. wages) is a strictly positive marginal increase in the incentive's value over the performance variable being targeted by the incentive. In calc terms (yay), d(I(p))/d(p) > 0. This is not satisfied by any threshold-based system. With a numerical grade of 92%, for instance, there is a strong incentive to perform that does not exist at a grade of 94%.

Third, why does everyone involved seem to have an agenda?
The PTSA wants TJ students' grades to improve even without an actual increase in effort, while the school board wants actual growth in performance and effort. The school board is concerned with every student in the county; the TJ administration and PTSA are not. From a viewpoint outside TJ, what PTSA wants would look both elitist and unjust: maybe TJ's courses are all honors, but wouldn't the addition of a 0.5 quality point for all TJ courses be unfair to those to whom that quantity of honors courses simply isn't offered? If the purpose was really an incentive, why apply it to every course? Doesn't it become less of an incentive and more of a simple boost without reason and without a corresponding increase in absolute performance?
From a purely self-interested point of view, of course, anything that benefits others without affecting yourself is functionally equivalent to something that hurts you more directly. An A seems better when compared with a B+ than when compared with an A−…

Can’t we all just spend more time doing the work and less time arguing about how we should be graded on it? This is precisely what a continuous, letter-free system would enable. Directly converting from the numerical percentage to a numerical GPA actually makes everything easier, while removing the abomination that is arbitrary thresholds from the equation entirely. No matter what your grade, you would have the same incentive to perform as anyone else.