I came up with, a decision or belief is arbitrary if it is not caused by the factors that would be expected to cause that sort of decision or belief. This reduction has the nice quality that it also explains arbitrary variable choices in mathematics—for example if you are trying to show that your compression algorithm gets good results on arbitrary data (heh), then it is data that was not, as might be otherwise expected, chosen to play well with your compression algorithm.
I came up with, a decision or belief is arbitrary if it is not caused by the factors that would be expected to cause that sort of decision or belief. This reduction has the nice quality that it also explains arbitrary variable choices in mathematics—for example if you are trying to show that your compression algorithm gets good results on arbitrary data (heh), then it is data that was not, as might be otherwise expected, chosen to play well with your compression algorithm.