Directly derived:
* Arbitrate: To act as a judge in a dispute.
* Arbitrator: A person appointed to settle a dispute.
* Arbitration: The process of settling a dispute by an impartial third party.
* Arbitrary: Based on random choice or personal whim, rather than any reason or system.
Less directly derived:
* Arbiter of taste: A person whose opinions on matters of taste are respected.
* Arbiter of fashion: A person whose opinions on fashion are highly influential.
* Arbitrament: A decision or judgment, especially one made by an arbitrator.
These are just a few examples. The root "arbiter" can be found in a variety of words related to decision-making, judgment, and authority.