The word "arbitrary" has several meanings, but for each instance of its use, there is only one meaning, and the context determines which one it is. In the definition of "whim", the meaning of "arbitrary" is not one you mentioned, but this one: "Determined by chance, whim, or impulse, and not by necessity, reason, or principle". Unfortunately, that makes it a bit circular. Let's try another dictionary. Webster gives "existing or coming about seemingly at random or by chance or as a capricious and unreasonable act of will", which I think is suitable in that context.
Of course, your judgment of what is suitable in the context may be different from mine, but there is at least one thing that speaks in my favor: your very own claim that your version "would provoke stronger visceral response". Why would it, if its meaning was the same?
You're unsuccessfully trying to argue an academic point while ignoring the basic gist of the decision, which is de facto one of considerable extrapolation. There simply isn't enough data in many cases to make a decision based on reason; that leaves whim. Even in cases where the data is obvious, whim comes into play, which is why Cisco had to go to 70 or 80 venture capitalists despite doing hundreds of thousands a month in business already without outside investment. Other VCs' stories of "the one that got away" involve a long-haired Steve Jobs.
This is merely human nature. It's no particular indictment of YC, everyone does it. I'm advocating for not leaving your decision of what to do with your life up to any single investor, or indeed, a series of 70 or 80 of them.
Of course, your judgment of what is suitable in the context may be different from mine, but there is at least one thing that speaks in my favor: your very own claim that your version "would provoke stronger visceral response". Why would it, if its meaning was the same?