Cute, you cut out the very next part of the definition, here let me get it for you: b : existing or coming about seemingly at random or by chance or as a capricious and unreasonable act of will Now clearly, to any human with an actual brain, I was paraphrasing, and I was still correct. Oh, and just to add on top, by these definitions, you used arbitrary incorrectly. Nice try though, it was kinda cute how you intentionally cut out part of the definition to try and make me look incorrect, I guess you just forgot that this is the internet though, and that I can go to the exact same website you did. Also, just the cherry on top, random is a synonym of arbitrary for a reason. Don't you feel better having learned something today? No need to thank me, I'm glad to help.
Wrong.
As I said before, 1 and 3a were the usages I intended, which have absolutely nothing to do with randomness and everything to do with individual preference, convenience, and discretion. Even your choice (and it isn't your usage we are talking about, is it?) "seemingly at random" isn't the same as random. You may as well have tried to suggest that I intended 2; ruling by absolute authority, if you want to be equally daft.
M-W lists synonyms for arbitrary as:
1) dictatorial, high-handed, imperious, peremptory, willful (or wilful)
2) aimless, arbitrary, catch-as-catch-can, desultory, erratic, haphazard, helter-skelter, hit-or-miss, scattered, slapdash, stray
3) arbitrary, autocratic (also autocratical), czarist (also tsarist or tzarist), despotic, dictatorial, monocratic, tyrannical (also tyrannic), tyrannous
Some of those synonyms apply to my intended meaning, some do not. Synonyms often don't apply to a word except under a specific usage.
Random doesn't show as a synonym or even a related word, although it probably ought to be listed as a related word for 3b.
Even if it did, it wouldn't matter. Words are often synonyms in one defined meaning and not another. The usage I intended, which is clearly spelled out, does not include randomness as a component.
Nice sidestepping the example of how something can be arbitrary and not random.