Arbitrary, a.
Etymology: [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. It was wholly arbitrary in them to do so. Jer. Taylor. Rank pretends to fix the value of every one, and is the most arbitrary of all things. Landor.
2. Exercised according to one's own will or caprice, and therefore conveying a notion of a tendency to abuse the possession of power. Arbitrary power is most easily established on the ruins of liberty abused licentiousness. Washington.
3. Despotic; absolute in power; bound by no law; harsh and unforbearing; tyrannical; as, an arbitrary prince or government. Dryden. 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.
Shades of meaning
Fernald has no entry of its own for arbitrary; he lists it under absolute.
Where he writes about it:
Autocratic power knows no limits outside the ruler's self; arbitrary power, none outside the ruler's will or judgment, arbitrary carrying the implication of wilfulness and capriciousness. — from absolute
Arbitrary may be used in a good sense; as, the pronunciation of proper names is arbitrary; but the bad sense is the prevailing one; as, an arbitrary proceeding. — from absolute
An imperious demand or requirement may have in it nothing offensive; it is simply one that resolutely insists upon compliance, and will not brook refusal; an arrogant demand is offensive by its tone of superiority, an arbitrary demand by its unreasonableness; an imperious disposition is liable to become arbitrary and arrogant. — from absolute