arbitrate
Verb

arbitrate (arbitrates, present participle arbitrating; past and past participle arbitrated)

  1. To make a judgment (on a dispute) as an arbitrator or arbiter
    to arbitrate a disputed case
    • 1595 December 9 (first known performance)​, William Shakespeare, “The life and death of King Richard the Second”, in Mr. William Shakespeares Comedies, Histories, & Tragedies: Published According to the True Originall Copies (First Folio), London: Printed by Isaac Iaggard, and Ed[ward] Blount, published 1623, OCLC 606515358 ↗, [Act I, scene i]:
      There shall your swords and lances arbitrate / The swelling difference of your settled hate.
  2. To submit (a dispute) to such judgment
  3. (mathematics, rare) To assign an arbitrary value to, or otherwise determine arbitrarily.
    We wish to show f is continuous. Arbitrate epsilon greater than zero...
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