On many exams, professors give students e.g. 4 questions, then say "Answer any three." The point, I suppose, is to:
1. Avoid penalizing students for random blind spots.
2. Create safety valve for badly-written questions.
In practice, though, it seems like giving students a choice of which questions to answer makes exams a noisier measure of student knowledge. The problem: Empirically, there is a very low correlation between "knowledge of the subject" and "ability to identify the easiest questions." So bad students often hone in on the easy questions and get full credit, while good students often try to do the hard questions and fail.
It's particularly bad when some questions are so easy that every student who attempts them gets 100%. Then students who fail to notice how easy the question is (and given time pressure, it's easy not to notice that a question is easy until you try to answer it) get much lower scores largely because of luck.
In any case, if you're worried about problems (1) and (2), there's an easier solution. For (1), just give a large number of smaller questions. Then random blind spots won't matter much. And for (2), just grade on a curve. Then the occasionally badly-written question won't lead to low average performance. (Again, this works better if you have lots of small questions instead of a few big questions).
Anyone care to defend the "drop a question" approach?