based on or subject to individual discretion or preference or sometimes impulse or caprice
"an arbitrary decision"; "the arbitrary rule of a dictator"; "an arbitrary penalty"; "of arbitrary size and shape"; "an arbitrary choice"; "arbitrary division of the group into halves"
is similar to
not limited by law
"an absolute monarch"
is similar to
determined by chance or impulse or whim rather than by necessity or reason
"a capricious refusal"; "authoritarian rulers are frequently capricious"; "the victim of whimsical persecutions"
is similar to
having or using the ability to act or decide according to your own discretion or judgment
"The commission has discretionary power to award extra funds"