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wobster109 comments on Human errors, human values - Less Wrong
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The problem of whether or not to push the person onto the tracks resembles the following problem.
The most popular way I have seen utilitarians respond to this is to espouse what they call rule utilitarianism. They claim that according to rule utilitarianism, the healthy man should not be sacrificed to harvest his organs to save the five. (Rule utilitarianism is explained and the argument is briefly sketched at the same link.)
This causes me to wonder whether rule utilitarianism would tell us not to push the person in front of the trolley.
Another similar problem that I've encountered runs thus: suppose we're in a scenario where it's one person's life against a million, or a billion, or all the people in the world. Suppose aliens are invading and will leave Earth be if we were to kill an arbitrarily-determined innocent bystander. Otherwise, they will choose an arbitrary person, take him to safety, and destroy Earth, along with everyone else. In that case, consensus seems to be that the lives of everyone on Earth far outweigh a healthy innocent's rights.
The largest difference between the two cases is numbers: five people becomes six billion. If there is another difference, I have yet to find it. But if it is simply a difference in numbers, then whatever justification people use to choose the healthy man over five patients ought to apply here as well.
Within the thought experiment, the difference is simply numbers and people are giving the wrong answer, as long as you specify that this would increase the total number of years lived (many organ recipients are old and will die soon anyway). Outside the experiment in the realm of public policy, it is wrong to kill the "donor" in this one case because of the precedent it would set: people would be afraid to go to the hospital for fear of being killed for their organs. And if this was implemented by law, there would be civil unrest that would more than undo the good done.
At a practical level, there's another significant difference between the two cases: confidence in the probabilities.
As has been pointed out above, the thought experiment with the donors has a lot of utilitarian implications that are farther out than just the lives of the five people in the doctor's room. Changing the behavior of doctors will change the behavior of others, since they will anticipate different things happening when they interact with doctors.
On the other hand, we haven't got much basis for predicting how choosing one of the two scenarios will influence the aliens, or even thinking that they'll come back.