Based on chance rather being planned or based on reason. (Cambridge Dictionary)
Subject to individual will or judgement without restriction; contingent solely upon one’s discretion: (Dictionary.com)
Decided by a judge or arbiter rather than by a law or statute. (Dictionary.com)
Having unlimited power; uncontrolled or unrestricted by law; despotic; tyrannical: (Dictionary.com)
Based on random choice or personal whim, rather than any reason or system. (Oxford Dictionaries)
(of power or a ruling body) unrestrained and autocratic in the use of authority. (Oxford Dictionaries)
If you describe an action, rule, or decision as arbitrary, you think that it is not based on any principle, plan, or system. It often seems unfair because of this.
Why Women Are Arbitrary and Capricious.
Age is arbitrary. – Discussion paper on setting minimum wages.
Voice Conversion Across Arbitrary Speakers based on a Single Target-Speaker Utterance.