defined

arbitrary (ar·bi·trar·y)
adjective

1. subject to individual will or judgment without restriction; contingent solely upon one's discretion: an arbitrary decision.
2. decided by a judge or arbiter rather than by a law or statute.
3. having unlimited power; uncontrolled or unrestricted by law; despotic; tyrannical: an arbitrary government.
4. capricious; unreasonable; unsupported: an arbitrary demand for payment.
5. Mathematics. undetermined; not assigned a specific value: an arbitrary constant.

Origin:

late Middle English (in the sense 'dependent on one's will or pleasure, discretionary'): from Latin arbitrarius, from arbiter 'judge, supreme ruler', perhaps influenced by French arbitraire