Nitpick: I've seen a distinction between affective empathy (automatically feeling what other people feel) and cognitive empathy (understanding what other people feel), where the former is what psychopaths are assumed to lack. In practice, caring without affective empathy isn't intuitive and does take effort, but that's how I view the whole effective altruism/"separating warm fuzzies from utilons" notion. You don't get any warm empathic fuzzy feelings from helping people you can't see, but some of us do it anyway.