arbiter / arbitrator / mediator
Three roles in a dispute.
An arbiter is anyone with the power to decide: the market is the final arbiter. An arbitrator is a person appointed to hear both sides and issue a decision, usually binding. A mediator helps the parties reach their own agreement and does not impose one. Do not call a mediator an arbitrator, or an informal judge an arbitrator, unless that office is real.
Examples
Use Taste is a poor arbiter of fact.
Use The contract names an arbitrator.
Use A mediator sat with both families.
Avoid A mediator issued a binding award.