arbitrary

from The American Heritage® Dictionary of the English Language, 5th Edition.

• adjective Determined by chance, whim, or impulse, and not by necessity, reason, or principle.
• adjective Based on or subject to individual judgment or preference.
• adjective Law Relating to a decision made by a court or legislature that lacks a grounding in law or fact.
• adjective Not limited by law; despotic.

from The Century Dictionary.

• Not regulated by fixed rule or law; determinable as occasion arises; subject to individual will or judgment; discretionary.
• In law, properly determinable by the choice or pleasure of a tribunal, as distinguished from that which should be determined according to settled rules or the relative rights or equities of the parties.
• Uncontrolled by law; using or abusing unlimited power; despotic; tyrannical.
• Not characterized by or manifesting any overruling principle; fixed, determined, or performed at will; independent of rule or control.
• Ungoverned by reason; hence, capricious; uncertain; unreasonable; varying; changeful: as, an arbitrary character.

from the GNU version of the Collaborative International Dictionary of English.

• adjective Depending on will or discretion; not governed by any fixed rules
• adjective Exercised according to one's own will or caprice, and therefore conveying a notion of a tendency to abuse the possession of power.
• adjective Despotic; absolute in power; bound by no law; harsh and unforbearing; tyrannical.
• adjective (Math.) a quantity of function that is introduced into the solution of a problem, and to which any value or form may at will be given, so that the solution may be made to meet special requirements.
• adjective (Math.) one to which any value can be assigned at pleasure.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• adjective Based on individual discretion or judgment; not based on any objective distinction, perhaps even made at random.
• adjective Determined by impulse rather than reason; heavy-handed.
• adjective mathematics Any and all possible.
• adjective Determined by independent arbiter.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• adjective based on or subject to individual discretion or preference or sometimes impulse or caprice