I think the topic divides in two : the relationship between empathy and evil can involve (1) the empathic understanding of evil (from the outside, as it were) and (2) the connexion between evil and empathy within the 'evil' agent. But first, what is evil and what is empathy ?
▻ WHAT IS EVIL ?
'Evil' can be taken axiologically to refer to things, states of affairs, situations, natural catastrophes, which have severe disvalue. One might see death as an evil, or the animal liability to pain. Nothing moral need be involved here : evils are occurrences that are adverse to human life or well-being.
By contrast, and relevant to your question, 'evil' can be taken morally. Many attempts have been made to define the nature of moral evil. All I can offer is 'intensified wrong' : an action is evil if it is so wrong as to be beyond the pale of mere moral wrongness. Stealing from a supermarket is merely morally wrong (in most cases); the Shoah was evil. (Paul Formosa, 'Understanding Evil Acts', Human Studies, Vol. 30, No. 2 (Jun., 2007), p.58.)
▻ WHAT IS EMPATHY ?
Well, it's not sympathy. If you break your leg and are prevented from doing work that is very important to you, then in sympathy I feel for you. I am sorry that this has happened to you. In empathy I project myself into your situation, trying to work out how you think or feel about the circumstances you are in. I may have no sympathy for you at all. (Formosa, 62, note 6.)
▻ EMPATHIC UNDERSTANDING OF EVIL
Empathy involves a certain kind of understanding - understanding why the evil-doer did what s/he did. There are two kinds of answer to this 'why' question. (1) We can look for the reason the evil-doer had for acting. Or (2) we can explain the action in terms of a state of mind, say extreme anger or depression, in which the evil-doer reacts in a certain way for which s/he has no particular reason to do that specific action. So, for instance, X may do an evil action because it is part of a calculated policy; or X may do the action in a mood of great frustration s/he must 'take it out' on someone or something. Depressed, I hit out viciously at a passing child but I could equally have stabbed a dog or caused a massive road accident. In either case I do something evil.
I will fix on (1)-type situations. Empathy is often defeated in (2)-type situations since the evil-doer's state of mind and why it found expression in the particular evil action s/he did is likely to be unclear even to themselves.
Formosa suggests that we can understand empathically the evil-doer's state of mind under two conditions : (a) we can give a reason explanation and (b) we can see how that reason could lead the agent to act as they do. Formosa, 61.)
Take one of the most notorious examples of evil-doing, that of Adolf Eichmann. Here is Formosa's attempt at empathic understanding :
In order to reach a basic understanding of Eichmann's acts we need to appreciate the evil-encouraging nature of the situation he acted in, the beliefs he held, and the lack of character he possessed. The bureaucratic situation Eichmann operated in was one where it was 'easier' to just follow orders. Someone 'above' always made the hard decisions. However, unlike the obedient teachers in the Milgram experiment, Eichmann did not seem deeply conflicted. His duties did not seem to weigh too heavily upon him. Part of the reason for this was that ... Eichmann was not directly fed back the results of his handiwork. He
heard no screams of pain. The evil consequences of his actions were belated and
distant. Further, he worked within a competitive bureaucratic system where his
deeds were officially approved and rewarded. This system encouraged efficiency
and a detached and compartmentalising approach to work.15 Not only that, but
Eichmann held beliefs under which he could see his acts as justified ones, done in the pursuit of what he was told was his duty. He also lacked character, making him the sort of petty and selfish person who thoughtlessly did what he was told (Formosa 2006, p. 514). All of these things were deeply evil-encouraging. In short, in that situation, with those beliefs and with that lack of character, it does not seem overly surprising or puzzling that Eichmann should come to perpetrate evil acts.
This analysis, though simplistic by necessity, is enough to illustrate how we This analysis, though simplistic by necessity, is enough to illustrate how we can achieve a basic understanding of why Eichmann acted as he did. Of course, this analysis remains but a sketch. Thankfully, in this case I can point towards a work that provides a more complete basic understanding?namely, Arendt's Eichmann in Jerusalem (1965). (Formosa, 67-8.)
It may be added that simulation theory, closely related to the kind of analysis Formosa offers, is an approach that should be examined though there is not the space to go into it here. See R.M. Gordon, R. M. (2000), 'Simulation and the explanation of action', H. H. Kogler, & K. R. Stueber (Eds.), Empathy and agency: The problem of understanding in the human sciences (pp. 62-82). Boulder, CO: Westview Press.
▻ EVIL AND EMPATHY IN THE AGENT
We can now look at how the evil-doer might him- or herself stand in relation to empathy. One explanation of evil-doers' actions is that that they 'do not have an adequate pathway to other people's minds'. If we, here the evil-doers :
... do not have an adequate pathway to other people's minds we shall be unable to think in terms of their interests, or to understand why their interests matter. The ability to think in this way seems fundamental to the development of moral agency, so a defect here is a very grave moral disability. John Deigh suggests that psychopaths, being at least minimally socialized, possess knowledge of conventional moral standards, but fail to acquire the more sophisticated knowledge 'that comes from understanding the reasons for the conventions and the ideals that give them meaning'. But the knowledge required for mature moral agency cannot be simply a more sophisticated understanding of the conventions, since one can imagine an intelligent psychopath who could give the reasons why other people take certain actions to be wrong, and list the ideals which the conventions serve, much as an anthropologist might, but who still fails to be moved by moral concerns. (Jeanette Kennett, 'Autism, Empathy and Moral Agency', The Philosophical Quarterly (1950-), Vol. 52, No. 208 (Jul., 2002), p. 342.)
We need to be clear here. Kennett is not characterising autistic persons as evil. Emphatically not. But what she is valuably doing is to pick a thread from the discussion of autism, pluck it out and apply it elsewhere - to the evil-doer. The evil-doer may be 'unable to think in terms of [other people's] interests, or to understand why their interests matter', and this would explain why 'intensified wrong' does not appear to them as such or to matter even if it does.
▻ MORAL RESPONSIBILITY
An evil-doer may or may not be a moral agent open to responsibility, blame or punishment. This will depend at least in part on whether they have any responsibility for being in a condition in which they are 'unable to think in terms of [other people's] interests, or to understand why their interests matter'. At least in some cases they won't. But I say no more about this since the Question focuses purely on the relation of empathy and evil.
Paul Formosa, 'Understanding Evil Acts', Human Studies, Vol. 30, No. 2 (Jun., 2007), pp. 57-77.
P. Formosa (2007) 'Is radical evil Banal?', Philosophy and Social Criticism.
P. Formosa (2006) 'Moral responsibility for Banal evil', Journal of Social Philosophy, 37(4), 501-520.
Jeanette Kennett (2002) 'Autism, Empathy and Moral Agency', The Philosophical Quarterly (1950-), Vol. 52, No. 208, pp.340-57.
E. Garrard(2002) 'Evil as an explanatory concept', The Monist, 85(2), 320-336.
E. Garrard (1998) 'The nature of Evil', Philosophical Explorations, 1(1), 46-60.
H. Arendt, (1965) Eichmann in Jerusalem: A report on the banality of evil. New York: Penguin Books.