Here is what I used to tell students assembled for commencement: "When the President of the University confers upon you your new degree, she will confer all the "rights, privileges, and responsibilities appurtaining thereunto."
Don't let that go unto your head. You have almost no new rights nor privileges; you may add the initials of your degree after your name, but outside academia, and before the Ph.D., almost no one does that.
What you do have are the responsibilities of an educated person, one example of which is the responsibility to help others understand the social and political implications of what's going on. That turns out to be a substantial amount of work. So, enjoy your new status and exercise your new responsibilities well! We're proud of you, SPSU grads!"
Separately, the president specifically granted "the right to wear the hood appropriate to your degree.," so, at least one actual privilege, although perhaps less important now than 600 years ago.