Good questions for a student-advisor compatibility test There are online a good amount of tests aimed to assess "compatibility" between two persons in a given life or work commitment situation; for instance, between coworkers, roommates, lovers, dungeons'n'dragons players.

Basically, the idea is asking questions to which there is no true correct answer, but different possible viewpoints based on personality, opinions and general attitude. Two people can check easily if they are on the same page on a number of controversial points, and early discussion helps identifying possible reasons for disagreement.

It would be interesting to come up with similar questions for the phd student/advisor relationship. For example,


  A good advisor should:
  
  a. provide detailed guidance and tell their student what to investigate in great detail, even on a day-by-day basis.
  
  b. leave their student free to choose their work agenda, but arrange regular meetings to check on their status and make sure they don't go astray.
  
  c. give their student a problem and tell them to come back when they have an interesting result, even if it is months later.


I would like to gather several specific questions of this kind as answers to a community wiki question.
Let me continue along the lines of @paul and @pete in a shortened quest for an answer.

I have been a teacher, although at this time I simply "work for" University of Richmond in a staff position. Lately I have been musing over a similar question involving the interaction between MDs and their patients. As patients we can forget that there is a sense in which we are hiring the doctors, and that the doctors are doing work /for/ us. While it is an asymmetric relationship, it is possible to bring it into balance.

The interview is likely to be short from the {doctor|advisor} side: A cardiologist is unlikely to be of much use for my orthopaedic problems, and an advisor is likely to be able to cut short the interview rather quickly if the subject matter is ill suited. So, let's suppose the question is really "How do I as a {patient|student} select a {doctor|advisor}?" It is a search for compatibility, yes? 


"How did you get into this line of work?" I always ask this. I want my doctor to have gone into medicine for the same reasons I got into computer science.
"What has kept you in this line of work?" I really want the answer to match my own reasons for having worked with computers and software every day for the past four decades: I cannot imagine doing anything else.
I know what success/victory conditions are for myself. So I ask "In my case, what does success look like for you?" 


You are likely to spot failure/incompatibility in five minutes; which allows you to move on to the next candidate. If you can talk at ease for 15 minutes, you likely have found someone with whom you are compatible. Remember: the match need not be perfect to be successful.

So in your case, you are looking for answers involving a continued desire to have substantive interactions with students (rather than just "problems"), and someone who likes to frame and revise the problem, but allow the student to work alone as evidence of success.