How does a departmental library decide what new books to order? Who decides what books a department (say, of mathematics, at a public university in the US) shall order for its library? Is there usually a formal process?

I am somewhat surprised that I have found essentially no answer to this on the internet, nor on my library's website.
My department shares a "library representative" with several other departments in my university. If you want a book purchased, you tell the library representative. Occasionally, there will be an allocation of funds to purchase new resources, and the library representative will send all faculty a note to submit requests by such-and-such date.