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 arbitrarius arranged through arbitration, uncertain)
English Collins Dictionary - English Definition & Thesaurus
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"Collins English Dictionary 5th Edition first published in 2000 © HarperCollins Publishers 1979, 1986, 1991, 1994, 1998, 2000 and Collins A-Z Thesaurus 1st edition first published in 1995 © HarperCollins Publishers 1995"