For me, arbitrary means something like "not constrained by rules; able to be chosen at will". An arbitrary choice doesn't have to be "random" in the strict sens

For me, arbitrary means something like "not constrained by rules; able to be chosen at will". An arbitrary choice doesn't have to be "random" in the strict sense of being chosen by nondeterminstic chance, although people often use "random" to mean something similar to "arbitrary" in colloquial speech. It can have good or bad connotations: "Emacs's configurability means you can extend it in arbitrary ways" is good; "Russia is known for arbitrary detention of political dissidents" is bad.