Should we ask ambiguous questions on an exam? 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 &quot;what's in my pocket&quot; 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.
I think the focus on ethics is a bit misguided. If your professor genuinely believes that asking ambiguous, &quot;what's in my pocket&quot;-type questions (a closely related concept is that of a &quot;gotcha&quot; question) on an exam is an appropriate testing strategy and serves a useful pedagogical purpose, then I cannot say that they are behaving unethically.
So the problem as I see it is not that the professor is behaving unethically, but simply that if they believe such a thing then they are wrong. I can't support this with any scientific argument based on research; but just based on my own experience with teaching, one major reason why I'm pretty sure this plan will not work  as your professor expects is that students in the US (and other countries I'm familiar with) have been conditioned to expect, over their many years in the educational system, that all exam questions, in STEM and related technical subjects at least, have a single, unambiguously correct, answer (unless explicitly stated otherwise).
Now, a professor might be of the view that this is poor preparation for real life, where situations are typically much more vague and nuanced, and a suboptimal way to develop critical thinking skills. So it's tempting to think &quot;why don't I design an exam that simulates real life more closely, and this way test for more of the things that really matter and encourage students to really think&quot;. This is well-intentioned, and perhaps even correct in an idealistic sense of being closer to the Socratic method. If you were gathered together with a small group of students on an island somewhere and had all the time in the world to develop their intellect, and no earthly concerns about schedules, tuition, the need to test and grade hundreds of students in X amount of time with Y resources with no easy chance for a do-over if something goes wrong, etc., then asking such questions would be a wonderful method to stimulate their thinking.
On the other hand, here in the real world, the conditioning I mentioned is so powerful, and the conditions under which students are tested so stressful and unforgiving, that asking questions with more than one correct answer (without stating that explicitly in the question) is a very clear recipe for trouble. A lot of students are already so stressed out and anxious taking tests that it's difficult to them to think creatively or be resourceful in an exam setting. What I expect will happen is that many of the students will obssess over whether A or B is really the correct answer (despite your professor saying they &quot;shouldn't obsess over this minor detail&quot;), will get confused and spend unreasonable amounts of time on this issue, will end up not having enough time for other questions they are perfectly capable of solving, and will end up frustrated and hurt and feeling that they have been treated unfairly over this testing strategy. And of course, they could complain, leading to a nasty headache of a problem for you and the professor to have to explain to the undergraduate program chair.
Here's a final thought to consider: it's hard enough -- by which I mean essentially impossible -- to get students to believe you're treating them fairly when you're bending over backwards not to create problems of this type and &quot;just&quot; giving honest, error-free, clear exam questions each of which tests one unambiguous snippet of knowledge. Even then, some students will still manage to come up with explanations for why they did poorly that somehow put the blame on you and your teaching/testing/grading practices and not on themselves for not studying hard enough. So the way I see it, things being hard enough already, why make them intentionally even harder still? This particular headache is easily avoidable. Let the professor try out their creative teaching ideas during the semester and not in the high-stakes, pressure-cooker environment of an exam. For the exam, my advice would be to stick with standard principles for designing exam questions that follow the same conventions everyone else uses and that students are used to. Anyway, that's my unscientific two cents.