For what it's worth, etymology of the word "arbitrary": late Middle English (in the sense ‘dependent on one's will or pleasure, discretionary’): from Latin arb

For what it's worth, etymology of the word "arbitrary": 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 . Literally comes from the Latin word for a judge!