I told my Advanced Micro students the other day that economists don't really believe in good and evil. There's just good or bad incentives. They protests: what about rapists and murders? This lead me to the following (working) definition of evil:
A person is evil if the derivative of his/her utility function with respect to actions with negative externalities is positive because such actions have negative externalities.
-A utility function is a mathematical formula that describes how different variables affect how happy someone is.
-Taking the derivative of the function with respect to a variable tells us if this person is happier (result is positive) or sadder (result is negative) if they get more of something.
-A negative externality is something that makes others' worse off.
So if someone enjoys playing loud annoying music because he enjoys the fact that he is annoying people, he is evil by this definition. If someone enjoys killing someone because the victim doesn't want to be killed, this person is evil. If someone enjoys torturing someone, but only if the victim doesn't enjoy being torture, then that person is evil.
Note that the victim would have her own utility function with a negative derivative with respect to the activity. The louder your music, the greater the torture, the sadder she is.
We can further qualify levels of evil by either (a) how much the person enjoys making others miserable (the size of the derivative) and/or (b) how much the negative externality hurts other (the size of the derivative of victim with respect to that same activity).
You can quibble--how much do we control our own utility functions?--but I think this is mathematically close to what most people imagine "evil" to be.