'arbitrarily-applied' originates from the word 'arbitrary', which comes from the Latin word 'arbitrarius', where 'arbitr-' meant 'judge or witness'.

'arbitrarius' transformed into the Old French word 'arbitraire', and eventually became the modern English word 'arbitrary'.

Initially, it meant 'dependent on the will or judgment of an arbiter', but over time it evolved into its current meaning of 'based on random choice or personal whim'.