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subject to individual will or judgment without restriction; contingent solely upon one’s discretion:
an arbitrary decision.
decided by a judge or arbiter rather than by a law or statute.
having unlimited power; uncontrolled or unrestricted by law; despotic; tyrannical:
an arbitrary government.
capricious; unreasonable; unsupported:
an arbitrary demand for payment.
Mathematics. undetermined; not assigned a specific value:
an arbitrary constant.
arbitraries, Printing. (in Britain) (def 9).
Contemporary Examples

In reality, the Iraqi borders had been arbitrarily drawn and disregarded 2,000 years of tribal, sectarian, and nomadic occupation.
Gertrude of Arabia, the Woman Who Invented Iraq Clive Irving June 16, 2014

Many of the others were arbitrarily sentenced under similar charges of “acting” or “conspiring” against national security.
Forget About a Kindler Gentler Iran Nina Strochlic August 18, 2014

(Note the arbitrarily rough edges on two sides of this drawing, versus the clean cuts of the others).
The Maximal Minimalist Blake Gopnik March 28, 2012

If the IRS can target and discriminate against one group of Americans, it can arbitrarily do it to anyone.
The IRS Will Come for You Next, Unless Congress Acts Now Matt Kibbe May 16, 2013

Who wants to leave their cash in an institution that unilaterally and arbitrarily reduces its deposit insurance commitment?
Cyprus on Fire? Blame the German Bullies. Daniel Gross March 18, 2013

Historical Examples

They were arbitrarily thrust into prison, where they were at last completely at the mercy of their enemies.
A New Witness for God (Volume 1 of 3) B. H. Roberts

A mistake; they lack only the right of arbitrarily dismissing the insubordinate.
Freeland Theodor Hertzka

But they did not arbitrarily do that which it seemed to them they might have done.
The Rise of Canada, from Barbarism to Wealth and Civilisation Charles Roger

He had arisen to his feet as if arbitrarily to end the argument.
The Plunderer Roy Norton

If not, then how vaguely and arbitrarily these occult powers work!
A Spring Walk in Provence Archibald Marshall

adjective
founded on or subject to personal whims, prejudices, etc; capricious
having only relative application or relevance; not absolute
(of a government, ruler, etc) despotic or dictatorial
(maths) not representing any specific value: an arbitrary constant
(law) (esp of a penalty or punishment) not laid down by statute; within the court’s discretion
adj.

early 15c., “deciding by one’s own discretion,” from Old French arbitraire (14c.) or directly from Latin arbitrarius “depending on the will, uncertain,” from arbiter (see arbiter). The original meaning gradually descended to “capricious” and “despotic” (1640s). Related: Arbitrarily; arbitrariness.