We would probably have a better Supreme Court even if we had arbitrary requirements that make little sense but would be a better alternative to what we have now. For instance:
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All Justices must have the name Horatio (either a given name or by name change). No last names.
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Twenty years of experience required in horticulture, which because of the forementioned name change, is more like horatioculture.
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Must have read at least 3000 books of any type.
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Can juggle an arbitrary amount of oranges on demand.
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Has combat experience in either blunt or bladed weaponry in the event of a zombie apocalypse, with a skill level scaled to their age. Alternatively, skilled in the occult and necromancy (to turn the undead).
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Can create rhythmic song related to the laws being discussed in the event of spontaneous musicals.