I really like # 7's answer, because it suggests that utilitarianism is not necessarily a crude form of ethical philosophy but rather can be one that can take seriously all the possible complexities involved in a given situation. I agree with everyone else that, all things being equal, the utilitarian would choose to kill the one person rather than the five. Here's an interesting wrinkle: what if the train driver recognized that the one person was a world-famous doctor known to be on the verge of discovering the definitive cure for cancer?
Since we are not debating whether utilitarianism is correct or incorrect and since we are not debating what would happen in real life, the answer, all things being equal, is a no-brainer. As difficult as it is to say, you take the one life and save the others. If things are not equal and that one person is a scientist with the only vaccination for a pandemic, then things can change.
The utilitarian, before trying to make the split-second decision of how many people to kill, would make every effort to kill no one. He would blow the train's horn in an effort to wake the people up. He would engage the brakes. He would pull the throttle back. After all those efforts have failed -- and the hypothetical here is an absolute: he will kill the five or the one -- he would make the decision that the other posters have already agreed on; switch to the track with one person on it. With no other information available -- the guy is driving a train! He can't go out and ask the five if they are murderers! -- the utilitarian would sacrifice the one for the five, every time, but would also try to avoid the situation if possible.
I have an issue with the nature of the hypothetical situation. People react emotionally in situations like that, and most likely the driver would be unable to decide between either track in that small amount of time and would merely continue on whatever track he was already on. I understand this is just an academic discussion about the definition of utilitarianism, and some good points have been made here. But understanding the definition has little purpose if there is no practical application, or if we ignore human nature in our expectations of how utilitarianism will function in our society.
Answer number 2 is the correct one- it would depend on the people on the track. Everything being equal, he would choose to run over the single person, but in order to really answer the question, a utilitarian would want to know about the relative usefulness to society (i.e. the utility) of the people on the track. It would not really be a moral decision though, a utilitarian would weigh the psychological impact of killing five people against killing just one, and then factor in their utility.
I agree with pohnpei. Utilitarianism looks at the the greatest amount of unity. Therefore, the driver would switch to the track which would kill only one person. Killing only one person would result in the least amount of sorrow.
Pohnpei makes another wonderful point when noting the driver's knowledge. Who is on the track? One or five murderers? One or five upstanding citizens? Depending upon this, the driver's choice would fluctuate greatly.
Utilitarianism says that you do what will cause the greatest total amount of happiness/utility for the community as a whole. So you have to sort of know how much the driver knows.
The most likely answer is that you switch to kill the one person. Killing one brings less of a negative impact than killing five and therefore is the right thing to do. If the driver had more time and information, he might want to know who the people are. What if the five are escaped felons and the one is a respected member of the community? Then, killing the five might well be better.
So you have to know (or at least stipulate for the purpose of your answer) what the driver knows. Then, using whatever information he has, determine which course of action creates the most possible happiness/benefit for the community as a whole.