arbiter \AR-buh-tuhr\ (noun) - 1 : A person appointed or chosen to judge or decide a dispute. 2 : Any person who has the power of judging and determining.
"If he was superior to the dog, the arbiter of its fate, wasn't God in like measure the arbiter of human fate?" -- Czesław Miłosz, 'The Issa Valley'
Arbiter is from Latin arbiter, "a witness, a spectator," hence "a judge of any matter."