based on random choice or personal whim, rather than any reason or system:

任意の; 恣意的な, 独断的な; 気まぐれな

e.g. his mealtimes were entirely arbitrary.

(of power or a ruling body) unrestrained and autocratic in the use of authority:

〈政府などが〉専制的な, 独裁的な

e.g. arbitrary rule by King and bishops has been made impossible.

Mathematics (of a constant or other quantity) of unspecified value.

late Middle English (in the sense ‘dependent on one's will or pleasure, discretionary’): from Latin arbitrarius, from arbiter ‘judge, supreme ruler’, perhaps influenced by French arbitraire.