The Collaborative International Dictionary of English v.0.48:

Arbitrate \Ar"bi*trate\, v. t. [imp. & p. p. Arbitrated; p.
   pr. & vb. n. Arbitrating.] [L. arbitratus, p. p. of
   arbitrari to be a hearer or beholder of something, to make a
   decision, to give judgment, fr. arbiter. See Arbiter.]
   1. To hear and decide, as arbitrators; as, to choose to
      arbitrate a disputed case.
      [1913 Webster]

   2. To decide, or determine generally. --South.
      [1913 Webster]

            There shall your swords and lances arbitrate
            The swelling difference of your settled hate.
                                                  --Shak.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Arbitrate \Ar"bi*trate\, v. i.
   1. To decide; to determine. --Shak.
      [1913 Webster]

   2. To act as arbitrator or judge; as, to arbitrate upon
      several reports; to arbitrate in disputes among neighbors;
      to arbitrate between parties to a suit.
      [1913 Webster]

WordNet (r) 3.0 (2006):

arbitrate
    v 1: act between parties with a view to reconciling differences;
         "He interceded in the family dispute"; "He mediated a
         settlement" [syn: intercede, mediate, intermediate,
         liaise, arbitrate]

Moby Thesaurus II by Grady Ward, 1.0:

29 Moby Thesaurus words for "arbitrate":
   act between, adjudge, adjudicate, appease, bargain, go between,
   hear, hold court, hold the scales, intercede, intermediate,
   interpose, intervene, judge, make terms, mediate, meet halfway,
   moderate, negotiate, officiate, placate, referee, represent,
   sit in judgment, soothe, step in, treat with, try, umpire