I'm TAing an undergraduate course at a university in the US, and had a disagreement with the professor teaching the course about a question in an exam. Here's an abstract version of the relevant part:
Select the single most appropriate method, out of the list {A, B, C, ...}, to solve problem X.
Both A and B are appropriate to solve X, and objectively superior to any other method on the list. Weak arguments can be made for either of them being more appropriate than the other. After a debate with the professor, we agreed that the question is ambiguous.
My opinion is that we should not be asking such a question. I think students might waste a lot of time trying to find their presumed mistake, since the question asks for a single most appropriate method, and there isn't one. Therefore, I think we should either remove it, remove one of the two methods, or rephrase it to
Select a single appropriate method...
The professor argues that the ambiguity is not an error on our part. They suggest we'll give full credit to either choice of A or B, and say that students shouldn't obsess over this minor detail at the expense of other parts of the exam.
I feel like this is problematic in terms of ethics (because of the possibility of misleading students) and pedagogy (since I would like students to distinguish strong and weak arguments for a method being superior to another). I would like to know others' position and arguments on this issue.
I'm also very interested in references that address the pedagogical aspect, based on either research or experience. The only such reference I could find is this blogpost (in Hebrew), written by a teacher, that defines "what's in my pocket" questions to avoid as teachers.
Edit
I might have overdone the abstraction, and made the example trivial. Consider the question
Select the single most appropriate method, out of the list {A, B, C, ...}, to solve each problem in the list {X, Y, Z, ...}.
{A, B, C, ...} are standard methods, all taught in class. Each other problem, {Y, Z, ...}, has a unique method most appropriate for solving it, and the ambiguity rises only for X.