My own moral intuition is that these two versions of the trolley problem are not equivalent. I would pull the lever, but I would not push the fat man. More interestingly, if I were the fat man, I would be indignant at being pushed. But when I think of being the lone man on the tracks, and having the train redirected at me, I don’t feel the same indignation.
The difference between the two situations — the chief difference, anyway — is psychological rather than ethical. In his book On Killing, military psychologist Dave Grossman argues that distance enables killing by soldiers in battle: the greater the distance, the easier it is to kill. This distance can be physical — it is easier to shoot at someone from a distance than to stab them up close. But it can also be cultural (if the victim is a member of a different racial or ethnic group), moral (if the killer believes that the victim is evil), and even mechanical (if the killer is looking at the victim through a television monitor, for example). Even just not being able to see the victim’s face makes it easier to kill them.
In the classic version of the trolley problem, there is a great distance between you and the people involved. This distance is partly physical (“You are standing some distance off in the train yard”) and partly mechanical (your intervention takes the form of pulling a lever). In the alternative version, by contrast, the fat man is “next to you” and you have to push him “over the bridge and onto the track.” And it goes without saying that if YOU are the fat man, there is zero distance between you and the person who will be sacrificed to save the others.
And yet, at the same time, I can’t shake the intuition that there’s more to this than just distance — that there is a real ethical difference between the two scenarios. Pulling the lever seems like mitigating a disaster, and reducing the death toll from five to one, rather than sacrificing one to save five. If I was at the wheel of a car, and the brakes failed, and I had to choose between running over one pedestrian or five, I would consider it a moral duty to steer for the one.