Hyper-advanced trolley problems


In the annals of philosophical thought experiments, it is written:
There is a runaway trolley barreling down the railway tracks. Ahead, on the tracks, there are five people tied up and unable to move. The trolley is headed straight for them. You are standing some distance off in the train yard, next to a lever. If you pull this lever, the trolley will switch to a different set of tracks. However, you notice that there is one person on the side track. You have two options: (1) Do nothing, and the trolley kills the five people on the main track. (2) Pull the lever, diverting the trolley onto the side track where it will kill one person. Which is the correct choice?
And lo, there were many variations:

Fat Man Trolley

As before, a trolley is hurtling down a track towards five people. You are on a bridge under which it will pass, and you can stop it by putting something very heavy in front of it. As it happens, there is a very fat man next to you – your only way to stop the trolley is to push him over the bridge and onto the track, killing him to save five. Should you proceed?

 Hammock Trolley

As before, a trolley is hurtling down a track towards five people. You can divert its path by colliding another trolley into it, but if you do, both will be derailed and go down a hill, and into a yard where a man is sleeping in a hammock. He would be killed. Should you proceed?
And so on. That experimental subjects often varied significantly in their endorsement of one option over the other across different scenarios (sacrificing one to save five in the original, but not pushing the fat man) doesn't concern us here. I just want to work towards exhausting the space of trolley problems.

Godwin's Trolley

As before, a trolley is hurtling down a track towards five people. Suppose though that these are Himmler, Goebbels, Hess, Eichmann, and Goering—top Nazi Party officials, hard to pick just five—and the man on the other track is Adolf Hitler. Do you throw the switch?

Stormfront Trolley

As in the Godwin's Trolley scenario, except that Hitler did nothing wrong.

Monty Trolley

A trolley is hurtling down a track that splits into three branches. Each branch enters a very dark tunnel. You know that two of the tunnels house only one man each, while the third houses five men. A sadistic signalman named Monty asks you to throw the switch for a random branch, then shines a light into a that tunnel, revealing a single man. Do you throw the switch again?

Hilbert's Grand Central Station

A trolley is hurtling down a track that splits into countably infinite branches, and on each of these branches there is a person tied up and helpless. And yet you can still save everyone by directing each person (via megaphone) to roll one track to their right (e.g., the person tied up on track branch #5 moves to branch #6) and send the trolley down branch #1. Wait, what...?

Newcomb's Trolley

Two train cars are each hurtling down separate, unfinished tracks—if you do nothing, they will derail. One car carries a standard cargo container; the other has sides made of transparent plexiglass and is ostensibly empty. You can remotely trigger the brakes only on the cargo car. An omniscient and malevolent being, Omega, has foreseen your choice and stocked the cargo car accordingly: if Omega predicted that you would only save the cargo car, then the cargo car contains nothing and the plexiglass car actually contains aerosolized Andromeda Strain microbes. On the other hand, if Omega predicted that you would do nothing, then the plexiglass car actually does contain nothing but the cargo car contains five men. Do you trigger the brakes?

Yudkowsky's Trolley

An omnipotent machine intelligence sometime in the future is capable of perfectly simulating past events and copies of past minds. It determines that it will subject 3^^^3 virtual copies of your mind to the indignity of a dust speck in the eye, unless you develop a robust and coherent decision theory to tackle any well-posed trolley problem. How much money will you donate to MIRI to ensure this happens?

I encourage both solutions and new variations!