An official was assigned to arbitrate which runner crossed the finish line first.2. Etymology: from Latin arbitrat-, "judged"; from arbitrari, "to judge" from arbiter, "judge, supreme ruler".
2. To settle an argument or a disagreement in which the people or groups on both sides present their opinions and ideas to a third person or group for settlement: The teachers' union agreed to arbitrate its pay differences with the school board.
To mediate a dispute is to try to find a middle ground or compromise on which both sides may agree.
At first Rex thought there would be a need to arbitrate an end to the disagreement; however, once all of the parties sat down together, they realized that it was possible to mediate an agreement without difficulties.