Arbitrary is a term given to choices an actions which are considered to be done not by means of any underlying principle or logic, but by whim or some decidedly illogical formula. For example, rearranging, for no reason, the letters of the alphabet so the letters appear in a staggered fashion (e.g. ab-cd-ef-gh). If there was a direct purpose in doing so, such as to make a better alphabet, then it would not be considered arbitrary.