Like Larry, I'm more used to hearing the word mean something like "It could be otherwise without making a difference to the point I'm trying to get across".

I'd say that's close, but too specific. A better definition would be "there are no rational reasons to select this position rather than any of the alternatives" or "there are no rational restrictions on the possibility space from which the selection is chosen randomly".

An arbitrary decision is one not founded in objective, shared principles and rules of logic that permit derivations to be made from them.