Basic Trolley Case: There is a run away trolley car careening down some railway tracks towards two tunnels. If it stays on the track it is on, it will kill five people working in the eastern tunnel. If you pull a switch it will move onto a side track, go through the western tunnel and kill the person working in it. Assume you can’t do anything to stop the car or change its path except pull this switch. You pull the switch, saving the five and leading to the one’s death.Fatman: Same runaway car, but without the switch. This time, you’re standing on a cliff looking over the track the car is about to careen down. If unchecked it will kill the five people in the tunnel. Fortunately, there is a very fat man standing beside you fat enough that if somehow he were to fall onto the track his sheer mass would stop the trolley. You give him a little shove, he falls off the cliff onto the train tracks is killed by the trolley (if not the fall) and the five are saved.
A significant number of people think your action in the first case is permissible, perhaps even mandatory, but the action in the second case is impermissible.
Levitt appears to take the utilitarian argument (push the fat man to save the five) without justifying the calculation. Andrew Gelman refutes Levitt here.