I don't know much more about the transition - only that the professor is becoming the new head effective [date], and that they have the support of the department.
Do I send congratulations (because it's a promotion) or condolences (because apparently some professors don't actually want the promotion, and only become the head of department reluctantly)?
Edit: what about the outgoing head of department? I clearly shouldn't send condolences in that case, but should I send congratulations?
That would depend on how well I knew the person. If they were a very close friend of long standing, I'd probably offer condolences, just as a joke. But that would take a special relationship.
In the general case, only congratulations are in order.
If you have to ask this question of us, then don't send "Condolences".
It really is that simple.
Send a message expressing your enthusiasm for their upcoming chairpersonship, your trust that they will steer the department well, and your willingness to support them as needed to achieve their goals for the department.
At base, "condolences" and "congratulations" are saying "a bad/good thing just happened", information that the recipient was already in possession of. The important part is what you say after the condolence/congratulation.
If you suspect that the person is taking on the job reluctantly, it is presumably for the good of the department that they have agreed to do so, and the appropriate sentiment to offer is not condolences but thanks.
A benefit of this approach is that it is also appropriate if the new chair was not reluctant to take the job. And it works for the outgoing chair, too.
If they didn't want the appointment, they almost certainly could have turned it down and it would gone to someone else. So, I would offer congratulations.
I would consider that offering condolences is appropriate if you know the professor well enough to be confident that they will understand that it is a joke and not be offended by it. Otherwise, congratulations is the safe thing to offer.
As others have commented/answered, being department chair is often treated as a duty more than a prize. That doesn't mean anyone is forced to take the position or that it is a bad thing. It's just a reflection of the fact that most professors enjoy research and teaching more than administrative duties. (Of course, some professors do want to move to a career in university administration.) The joke is a succinct way of acknowledging that the position comes with heavy responsibilities that will leave less time for research, teaching, and family.
I want to add that department chairs are not meant to dictate what the other faculty do and a good chair will wield their power in consultation with their colleagues. Treating the position as a duty rather than a privilege is a way of emphasizing that.
In these days, especially, although also forever, being a dept chair has tooooo many impossible responsibilities. Sure, there is some "power", but unless one reeeeally highly values power and is not disturbed by responsibility... it is a negative trade. Yes, in my experience, in math in the U.S., a significant number of people willing/hoping to be dept heads are not really competent, either in terms of appraising the mathematical work of the faculty, or in dealing with people.
A very few people have been willing to "do good"... but very often have been completely obstructed (and vilified) by "good-ol' boy network" kind of action.
So: a few people do take up chairperson jobs in a positive way... but often not so positive, but greedy... and, even when motivated in the best possible way, will be completely blocked (and insulted) by people who have their own agendas.
Allure, why are you sending any wishes to them in the first place ? If you are part of that department, then your views/thoughts have already made themselves apparent expressly or otherwise. It's easy for anyone to know who is in favor or against them regardless of words said. So there's no need to formalise it. It's also better not to accord too much importance to our honoring of selected people: it makes us look like people trying to achieve importance through association - rather like universities awarding honorary degrees. The real test of your relationship with the new head will come soon enough. Save your powder till then.
If you are a member of another department and have occasional formal or informal meetings with the new head then just say nothing.
If you are just a personal friend, then you have to call it as you feel it.
Department chair has almost double the salary and the position is rotated at my university.
There is no reason to be sad someone is getting an extra 100k.
