There is nothing arbitrary about how the Court operates. They are the actual real life processes by which the Supreme Court goes about its job of interpreting the Constitution.
There is no conflict between them being arbitrary and being real life processes. If they are not arbitrary, then they must be in either the Constitution or the statute law, although even statute law could be arbitrary, like various age limits for drinking, driving, etc. If they are merely the rules of the Court, the Court could, change or waive them if they wishwsm and probably have in the past.
I suspect you are using a different defintion of arbitary than hoosiermama. Here are four from the American Heritage dictionary:
1. Determined by chance, whim, or impulse, and not by necessity, reason, or principle: stopped at the first motel we passed, an arbitrary choice.
2. Based on or subject to individual judgment or preference: The diet imposes overall calorie limits, but daily menus are arbitrary.
3. Established by a court or judge rather than by a specific law or statute: an arbitrary penalty.
4. Not limited by law; despotic: the arbitrary rule of a dictator.
I believe she was using #3 or close to that, while you seem to be using something more like #1, with emphasis on whim and impluse.
Using definition #3, the Court’s decision in Marbury v Madison of 1803 was “arbitary” since Article II does not establish a priniciple of Judicial Review as a function of the Supreme Court and yet that “arbitrary” decision has become the primary modus operendi of the Court for the last 206 years.
Interesting riff on “arbitrary.” What would you call J. Brennan’s mysterious kill-your-babies penumbra?
It's obvious the SCOTUS in recent years, rather than protecting the Constitution and its guarantees of civil liberties of American citizens against statist repression, often does the opposite. So let's not get into a knee-jerk defense of everything the SCOTUS may do.
And, BTW, there is something arbitrary about the SCOTUS deniying Certiorari on 99% of petitions without a word of public comment on why such petitions are denied.