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

"his mealtimes were entirely arbitrary"

synonyms: capricious, whimsical, random, chance, unpredictable;

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

"arbitrary rule by King and bishops has been made impossible"

synonyms: autocratic, dictatorial, autarchic, undemocratic, despotic, tyrannical, authoritarian, high-handed;

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