Lame Pareto Optimality :
Ideally, you'd derail the train prior to it reaching its destination. Conductor seats have some (minimal) safety measures to mitigate damage to the conductor, and as such you'd save all parties involved. Everyone walks away free to live with none of their right to live violated (except maybe the conductor, who has insurance and a union to support his family thereafter).
Minimin Principle :
Suppose that in the normal operating day of a train, incidents like these occur often enough to expect regular lawsuits (albeit, frivolous, as the train company is not responsible for tying people to the tracks / having fat men shoved in the way). Assuming that the railroad companies and stations have had all their safety measures bypassed, would it be optimal to maximize casualties and seek the worst possible outcome?
Maybe, if we assume that :
- every death results in a litigation
- in the event of a class action, every claimant joins together in the same "class" and expects to divide the reward by the end
- payments to litigation are written off as an expense and thus contribute to tax benefits
As the operation of the railroad is not made for the expressed purpose of making sausage fillings out of people, our railroad stands to lose money over events they have no control (and yet are still liable) over. To minimize the amount of compensation per claimant, killing as many people as possible at one time would add more individuals to the overall class, at which point the reward for each claimant could be diminished (if the rate at which the reward is divided is greater than the rate of settlement costs per death). This reduces the incentive to sue the railroad company, and if we're lucky, charges may be dropped due to the lack of proportional reward to the effort put into the lawsuit. The capability of the litigating lawyers does not increase in spite of the greater amount of people affected.
You should, in this case, time the derailment to maximize casualties and create a large write-off for the tax year.
Moral Desert:
If the fat man is on the track but you have to switch the track to kill the fat man, abstain from doing so and let natural events run their course. The five fucks on the track deserved to die for simply being on the tracks.
Likewise, if he's standing at the platform, don't push him; he has done no such thing to warrant getting pushed, and as such does not deserve to die.
Utilitarianism:
There's two interpretations :
1. The fat man dies because society overall benefits from having more bodies, even if it's five skinny guys who survive. After all, five skinny guys can experience more pleasure (and therefore utility) than any single individual can.
2. The five skinny people die because their adverse living conditions has caused them to be skinny; they would have never expected to experience much pleasure compared to the one fat man anyway, so you could cut the losses then and there.