arbitrate

verb

Etymology: From Latin arbitratus, past participle of arbitrari (“to be a witness, act as umpire”), from arbiter (“umpire”); see arbiter.

1. To make a judgment (on a dispute) as an arbitrator or arbiter

   “to arbitrate a disputed case”

   “There shall your swords and lances arbitrate / The swelling difference of your settled hate.”

2. To submit (a dispute) to such judgment
3. To assign an arbitrary value to, or otherwise determine arbitrarily.

   “We wish to show f is continuous. Arbitrate epsilon greater than zero...”