Have you used such grading policy in your teaching? I have seen a grading policy for a course with two midterms. Under this policy, if a student scores better in the second midterm than in the first one, the first test will be "forgiven" and the weight shifts to the second one. For example, if midterm 1 and are 15% each and a student got 60 for midterm 1 and 80 for midterm 2, then the weigh of the two exams become 0% and 30%. I can see the good side of the policy is to encourage students making progress. But I worry that this will cause students complain about unfairness, particularly those who can't take advantage of this policy.

Any thoughts would be appreciated.
The version we use in my calculus class says that we drop the lowest score out of homeworks and midterms. There are 4 midterms, worth 15% each, and the homeworks are worth a total of 15%. The rest is decided by the final. When calculating the final grade, we drop the lowest score out of the midterms and homeworks, and calculate the grade as if each is worth 75/4 % instead.

Some students (the ones who read the syllabus) that have good scores on the first three tests and the homeworks elect to not take the fourth test. Other (less wise) students put all their faith in tests and don't do any homeworks. Most students still do all the homeworks and take all tests.

We think of it as a way to allow the students to have one bad day, without destroying their grade in the course.