Ordain vs Arbitrate - What's the difference?

As verbs the difference between ordain and arbitrate

is that ordain is to prearrange unalterably while arbitrate is to make a judgment (on a dispute) as an arbitrator or arbiter.

to prearrange unalterably

to decree

to admit into the ministry of a religion, for example as a priest, bishop, minister or Buddhist monk.

to authorize as a rabbi

to predestine

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To make a judgment (on a dispute) as an arbitrator or arbiter

to arbitrate a disputed case

* Shakespeare

There shall your swords and lances arbitrate / The swelling difference of your settled hate.

To submit (a dispute) to such judgment

(mathematics, rare) To assign an object an arbitrary value, or otherwise arbitrarily determine it

We wish to show f is continuous. Arbitrate epsilon greater than zero...

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