Complaint against supervisors

First - a meta comment. Getting out of abusive relationships with one's advisors can be really difficult, especially if said advisor is a big name researcher. That said, once the first signs are in, it is often better to cut your losses and get out of this relationship than to stay on in a bad situation.

I think that if you have some real complaint then you should make your case to the department administration (head, dean for graduate studies etc). If your university has student support resources (e.g. a student union, an ombudsman), get them involved as well. What happens next is very dependent on the advisor's status within the department, and on your department's administration.

If yours is not the first case, then your complaint can have serious repercussions towards your advisor. Informing fellow students about this person's behavior is also a viable strategy, as it may protect them from a potentially terrible experience.

The weight given to your complaint is highly dependent on what it is that you're actually complaining about. If your advisors gave you bad advice but otherwise kept their advisory roles (e.g. regularly met with you, provided you with necessary resources etc.) then this could be chalked up to style/bad luck. A lot of administrative matters are beyond your advisors' control, so maybe what you perceive as a failure on their part really has nothing to do with them. If you have written proof of malicious intent or gross incompetence, then you may have a case.

Since you have already graduating, I see no benefit to you in complaining, at least under a very narrow definition of benefit. There is some satisfaction in knowing that you made the world a better place by acting against an abusive/incompetent advisor, again, under the premise that your complaint has real merit.

I was planning to complain informally to the graduate office and say I had terrible supervision that I wouldn't wish on anyone.

In any complaints process, you need to first consider what it is you want to get out of the complaint. What is the outcome you want to occur? It sounds like you are already finished with your candidature, and you simply want to leave feedback. If this is the case then presumably the same effect could be obtained by framing your contact as "feedback" rather than as a complaint (especially since you have said you do not intend to use the formal complaint mechanisms). If your goal here is to encourage your supervisor to raise his game for future students, then it is possible to pursue this in a way that is encouraging to the supervisor (see below).

If you do indeed "complain informally" to the graduate office, then you should be aware that they probably will not have much scope for action. The university already allows informal feedback from students to staff, and has formal complaint mechanisms for serious cases. If you choose not to avail yourself of the formal complaint mechanisms then your contact will be treated as informal feedback, and so what happens then is really up in the air. Your feedback might be passed on to the supervisor, and might also be communicated to the department head, or it might just stay with the graduate office. If multiple complaints accrue against the same supervisor then this might spur some action, but it depends on the department.

My complaint will be made on the basis of persistent misleading advice and a total lack of advocacy in terms of university administration. I can support my case with emails and written feedback.

Those things are upsetting, and I'm sorry they happened to you. Nevertheless, more detail would be needed to see if these things actually constitute failures of supervision. Misleading advice is certainly annoying, but whether it is a supervision problem depends on what it was about. Research advice often involves educated guesses about how to pursue a problem, and this can lead to dead-ends, such that the initial advice may be misleading in retrospect. On the other hand, if the misleading advice concerned administrative matters, then it may be outside the scope of the supervisor's expertise, and instead be the proper domain of administrators. I'm not suggesting you don't have cause for complaint here - only that it is unclear from your description.

As to advocacy in terms of university administration, it is unclear from your description whether this falls within the scope of the supervisory relationship at all. Some supervisors do help students navigate the waters of the university administration, but there are limitations to their responsibilities. As a general rule, supervisors are not required to act as advocates for their students in administrative processes, though some may choose to assist in this area if they feel their students are not being treated fairly. Again, I'm not suggesting you don't have cause for complaint, but you will need to think carefully about whether the assistance you wanted from your supervisor is actually part of his role.

Is there any point to making a complaint against my PhD supervisors? I was never going to ask my supervisors for references but was wondering about other repercussions.

Assuming you have reasonable cause for grievance on these matters, if you want to give feedback on these matters informally, the best way to do this would be through direct communication with your supervisor. For maximum impact, I would suggest you frame your feedback carefully - make sure you put these issues in context, and acknowledge any positive work done by your supervisors. It is actually quite hard to supervise a PhD student, and it is often thankless work, so it would be best not to approach this matter from a purely negative perspective. You could start by telling your supervisors the things they did well in your candidature, and thank them for their work with you. After you have shown some appreciation for their work, raise the negative issues where you believe they did not assist you properly, describe what happened and how this caused problems for you. You might also offer positive suggestions for how you would have preferred those matters to have been handled.

Most academic supervisors are reasonable people, and if you give them constructive criticism, properly contextualised, they will try to take that on board to improve their work in the future. If you frame your feedback in a reasonable way, and are not belligerent, then there are unlikely to be negative repercussions. However, If you frame your feedback in a way that does not acknowledge any of the work they have done with you, or is unreasonably critical, then it probably will not do you much good.

Finally, if you are only proceeding informally, I would recommend you don't give evidence from emails and written feedback in the first instance. When giving informal feedback you are not expected to prove anything, and if you make a point of laying out a whole history of emails to prove your assertions, this will come across more negatively than if you just state the problematic issues, describe what happened in general terms, and say how this affected your candidature. If you were to proceed to a formal complaint then you would be expected to give evidence of your claims, but with informal feedback this is not expected.