(of an independent person or body) reach an authoritative judgement or settlement.
Mid 16th century: from Latin arbitrat- ‘judged’, from arbitrari, from arbiter ‘judge, supreme ruler’.
“The whole dilemma will need us to arbitrate!”
With regard to, or at the level of, orders in a taxonomic system; according to an ordinal number, system, etc.; on an ordinal scale; with regard to order.
Mid 19th century; earliest use found in The Edinburgh Review. From ordinal + -ly.