Arbitrary 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: