ADJECTIVE (1)

1. based on or subject to individual discretion or preference or sometimes impulse or caprice;
- Example: "an arbitrary decision"
- Example: "the arbitrary rule of a dictator"
- Example: "an arbitrary penalty"
- Example: "of arbitrary size and shape"
- Example: "an arbitrary choice"
- Example: "arbitrary division of the group into halves"

The Collaborative International Dictionary of English v.0.48:

Arbitrary \Ar"bi*tra*ry\, a. [L. arbitrarius, fr. arbiter: cf.
   F. arbitraire. See Arbiter.]
   1. Depending on will or discretion; not governed by any fixed
      rules; as, an arbitrary decision; an arbitrary punishment.
      [1913 Webster]

            It was wholly arbitrary in them to do so. --Jer.
                                                  Taylor.
      [1913 Webster]

            Rank pretends to fix the value of every one, and is
            the most arbitrary of all things.     --Landor.
      [1913 Webster]

   2. Exercised according to one's own will or caprice, and
      therefore conveying a notion of a tendency to abuse the
      possession of power.
      [1913 Webster]

            Arbitrary power is most easily established on the
            ruins of liberty abused licentiousness.
                                                  --Washington.
      [1913 Webster]

   3. Despotic; absolute in power; bound by no law; harsh and
      unforbearing; tyrannical; as, an arbitrary prince or
      government.                                 --Dryden.
      [1913 Webster]

   Arbitrary constant, Arbitrary function (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.

   Arbitrary quantity (Math.), one to which any value can be
      assigned at pleasure.
      [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

133 Moby Thesaurus words for "arbitrary":
   absolute, absolutist, absolutistic, aristocratic, arrogant,
   autarchic, authoritarian, authoritative, autocratic, autonomous,
   bossy, capricious, careless, chance, chancy, cranky, crotchety,
   despotic, dictatorial, discretional, discretionary, dogmatic,
   domineering, doubtful, elective, erratic, fanciful, fantasied,
   fantastic, feudal, flaky, freakish, free, free will, gratuitous,
   grinding, harebrained, heedless, high-handed, humorsome, iffy,
   imperative, imperial, imperious, impetuous, inadvertent,
   inconsiderate, inconsistent, independent, indiscreet, irrational,
   kinky, kooky, lordly, maggoty, magisterial, magistral, masterful,
   monocratic, moody, motiveless, nonmandatory, notional, offered,
   oppressive, optional, oracular, overbearing, overruling,
   peremptory, petulant, precipitate, proffered, quirky, random, rash,
   reasonless, repressive, screwball, self-acting, self-active,
   self-determined, self-determining, severe, spontaneous, strict,
   subjective, summary, suppressive, temperamental, thoughtless,
   tyrannical, tyrannous, unasked, unbesought, unbidden,
   uncalculating, uncalled-for, uncertain, uncoerced, uncompelled,
   uncompromising, unconstrained, undisciplined, unforced, unguarded,
   uninfluenced, uninvited, unpredictable, unpressured, unprompted,
   unreasonable, unreasoning, unreflecting, unrequested, unrequired,
   unrestrained, unruly, unsolicited, unsought, unthinking,
   unthoughtful, vagarious, vagrant, varying, voluntary, volunteer,
   wanton, wayward, whimsical, wild, willful, zany