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.
noun, plural arbitraries.
arbitraries, Printing. (in Britain) peculiar ( def 9 ).

1400–50; late Middle English < Latin arbitrārius uncertain (i.e., depending on an arbiter's decision). See arbiter, -ary

arbitrarily [ahr-bi-trer-uh-lee, ahr-bi-trair-] , adverb
arbitrariness, noun
nonarbitrarily, adverb
nonarbitrariness, noun
nonarbitrary, adjective
unarbitrarily, adverb
unarbitrary, adjective Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
arbitrary (ˈɑːbɪtrərɪ)
1.  founded on or subject to personal whims, prejudices, etc; capricious
2.  having only relative application or relevance; not absolute
3.  (of a government, ruler, etc) despotic or dictatorial
4.  maths not representing any specific value: an arbitrary constant
5.  law (esp of a penalty or punishment) not laid down by statute; within the court's discretion
[C15: from Latin arbitrārius arranged through arbitration, uncertain]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

early 15c., "deciding by one's own discretion," from L. arbitrarius "depending on the will, uncertain," from arbiter (see arbiter). The original meaning gradually descended to "capricious" and "despotic" (1640s).
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
It would reveal an underlying order to the seeming arbitrariness of nature.
And this arbitrariness also relates to our testing of intelligence.
The process is fraught with arbitrariness, internecine politics, etcetera.
But as the desperate reach for some larger meaning begins, the sheer
  arbitrariness of his approach is laid bare.
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