The basic trolley problem is under-specified. In the basic case (no one will ever know what you did or did not do, a transfer saves N people and dooms M other statistically identical people) I hold that the answer is clearly switch if and only if N>M.
But sometimes it gets more complicated than that. And hilarious. I was thinking, since absurd situations are quite useful in clarifying philosophical positions, it might be worth taking these situations seriously (without taking ourselves too seriously, but then I try never to do that.)
The Time Traveler
This one seems easy at first glance, since it seems cannot possibly get it wrong. If you fail to save the man now then the man cannot be on the other track from ten minutes from now, and since you have already observed him there, not saving him creates a paradox, so you save him. This, however, is a trap caused by poor decision theory and that answer costs you a million points.
Using correct decision theory, you would realize that if you would in this situation switch the track and cause the older version to die, then this means that the person on the tracks will die. However, if you do not switch the track, then this creates a paradox, which means that the situation on the tracks will never come to exist, since it cannot be self-consistent. Therefore, by being a person who would not close the time loop, you prevent the situation from ever happening, and chances seem much better that the result would be either there being no one on at least one of the tracks, there being different people on the tracks (which results in a possible choice that can only improve matters), or not being the one caught in a no-win ethical dilemma if one even exists at all, all of which seem like a clear win.
Do not be the type of person that would, when given the opportunity to close a time loop, fails to close a loop they would prefer did not exist! Or, of course, be the one who fails to close a loop that is doing good work.
The Cancer Caper
Math on this one is pretty easy. Both sides have one brilliant cancer researcher, and a brilliant cancer researcher’s positive impact is far bigger than the negative impact of a serial killer. A serial killer that only kills lesser cancer researchers is probably doing more harm than a normal serial killer, so that is a win. If 14% of cancer researchers are Nazi sympathizers, and Hitler is alive but dying of cancer, then Hitler is probably getting a lot of sympathy via his condition, but even considering that, it seems unlikely that cancer researchers are unusually likely to be Nazis, especially given how many of them are Jewish, so it is likely that at least 14% of everyone is also a Nazi sympathizer, so that should at least cancel out. The turn signal thing is annoying, but I respect it, because they have places to be.
As a final note, Hitler would be old enough that even if you cured his cancer, he would die of something else soon anyway.
The Suicide Note
Knowing all this information, there are two questions. One is, which worker is more likely to actually want to be hit by a trolley? Second, is either of them too stupid and/or annoying to live, regardless of their intentions? The second question is tough, since the first worker owns a stupid t-shirt and loaned it to the second worker about to work on train tracks, but the second worker wore it when working on train tracks, so that seems like a wash. Owning the shirt as a railroad worker seems more intentional than wearing it (probably ironically or unknowingly), so I would give the edge to worker one there. On the suicide note, given it is written in the second workers’ handwriting, it seems more likely the second worker wrote it than that the first one wrote it – and I would not put it past him to have put it in his pocket and then tied him to the railroad tracks, or the first worker being here to try and save him. Killing the second worker seems right.
The Ethics Teacher
If the teacher pulls the levy, that will make the ethics class late. This is obviously a very good result, so they should stop and pull it.
Stick to your story. It is too late to change it now.
Relative size is key here. Is the one dick a bigger dick than the sum of two smaller dicks? We do not know. A good rule of thumb is that dickishness has quite a long tail (among other things), and is capable of growing quite large, so the largest dick dominates. Switch the trolley.
The Business Ethics Version
Teenagers are known to be jerks and no one likes rich people much these days, whereas workers are much more sympathetic, plus one case is easier to settle than three cases – you only have to worry about one rogue agent rather than three. This one seems pretty easy.
The Real Stinker
My mom is working? No, I definitely didn’t see that coming.
The Surrealist Version
Keep your head on your shoulders!
The Meta-Ethical Problem
If you rescue Kant, any further work Kent does is likely to move people towards better ethical theories, and you save the only copy of the right book. If you rescue Bentham, relatively few people would even notice, and moving from Bentham’s previous stances in a random direction is much less likely to be an improvement than moving Kant, and given the book he is holding, chances are he will not choose a good direction, whereas Kant is likely about to make some substantial improvements. Some of the incentive effects on future philosophers are unfortunate. But Bentham would understand, and if recent changes mean he wouldn’t, then that Kant be helped.