Our school has a mandate that in any evaluation component (say quiz1, quiz2, etc.), the grades to be given are A, B, C and D to students. There is a further mandate that in any evaluation component (quiz1 for instance), the % of students receiving A should not be greater than 20% of the class and the % of students receiving A or B should not be greater than 60% of the class. [This implies that suppose all 100 students in my class had scored full points in both quizzes, all of them, unfortunately, necessarily have to receive a grade of C or D. (This has not happened thus far, thankfully!)]
We had two quizzes, quiz1 (15% weightage in GPA) and quiz2 (15% weightage in GPA). Technically, the mandate above applies to quiz1 separately and to quiz2 separately.
Can it be shown that if we do combine quiz1 and quiz2 into a single component QUIZ (say quiz1 was out of 50 points, and quiz2 out of 50 points, QUIZ = quiz1 + quiz2 out of 100 points) with QUIZ having weightage of 30% of the GPA, and apply quantiles to QUIZ to figure out the atmost 20% As and the atmost 60% As or Bs, that student grades would be better:
(a)on average, or
(b)even stronger, individually that no student is worse off in his final GPA for the course?