A new answer to the trolley problem, plus follow-up on likely outcomes

The problem: A train is going down some tracks, as trains do. I am standing many yards away. I can see the train, but I cannot get any nearer to it. The track the train is on will soon have it run over and kill five people, because they are tied to the tracks. But! I have a lever that will make the train go down a different track. However, that track has one person tied to it. What am I, a moral agent, to do?

The solution: I close my eyes and rapidly pull the lever back and forth. This takes my agency out of the question and leaves it to God. Since God is perfectly good, they will make the morally best decision.

The follow-up: My friend who knows a bit more about track-based transportation than I do pointed out to me that this answer leads to multi-track drifting. The front of the train will go down one set of tracks. The rear will go down another. Thus, this solution kills all six people.

If the tracks are too far apart, then the train will derail. Then the surrounding environment will determine what happens. If the tracks are in a secluded area, then nothing of further note will happen. If there are things on the train’s new, freer path, then the train will hit them.

Regardless, the train is unlikely to be usable again, thereby solving the problem once and for all.

The Collatz Trolley Problem

I enjoy a good trolley problem (meme). I came across this one and it presents an odd problem:

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All initial values of n thus far tested end up looping with 4, 2, 1, so if it’s any of those, I’m not sure how many people are sucked into the black hole. (Though it’s fewer than 5, so if the goal is minimization of deaths, pulling the lever is ideal regardless.)

This one is a bit odd to think about. On the one hand, at least 5×2^60 initial values have been shown to result in that loop. But many, many more have not (infinitely many, if you believe in infinities).

And if you look at the odd numbers in any sequence the geometric mean of the ratios of outcomes is 3/4, though this only means no divergence. Maybe there’s some cycle involving numbers bigger than 5×2^60.

Also it’s apparently been shown that for any m, the number of option for n between 1 and m is at least proportional to m^.84.

So on the one hand my gut says pull because that evidence sounds kinda compelling. But then some part of me recognizes that m^.84 isn’t even half of m for most m, and 2^61 is relatively small. But then there seems to be some sort of abductive principle allowing the practical inference that pulling is probably right, but I can’t tell what it is.