Seeing people talk about the Trolley Problem on here is always... interesting. Because the Trolley Problem isn't meant to be a narrative trope, and it's not meant to have a "right" answer, and it's not meant to be an immediately realistic scenario that you can argue your way out of, it's not meant to make you feel proud that you picked the "right answer". It's an ethics thought experiment. "Somebody has to die and you can't save everyone" needs to be taken as a given premise in order to get at what the Trolley Problem is making you consider, which is how you allocate value of people's lives, something that it's very, very hard to get people to address in any circumstances but extremely contrived ones.
Because the way I was taught it, the Trolley Problem isn't a one-and-done thing in isolation - its classic form is there to set up the variations and test where your values change.
The classic form is: a runaway trolley is careening down the tracks. The brakes are broken, it can't be stopped. In its path, five people are tied to the tracks, and if it's left to its own devices, the trolley will run over them and kill them. BUT you have the option to pull a lever and send the trolley down a different track. On that track, one person is tied to the tracks. As it stands Right Now, if you do nothing, the five people will die, and the one person will live. But you can pull the lever and switch the trolley's track so that the one person will die, and the five will live. The trolley is approaching and you don't have time to untie anyone from the tracks. Would you pull the lever?
In its base form, the question is fairly simple, and it's about if the capacity to intervene makes you morally obligated to intervene, and if doing nothing and letting more people die is better or worse than personally intervening to make it so that fewer people die, but one person will die who without your intervention would otherwise have lived.
But that's even one iteration of the problem, because most people say yes - saving five people and sacrificing one is, overall, better than saving one person and sacrificing five.
And the real value of the Trolley Problem comes after you've said, yes, I'd pull the lever.
You've established that you believe intervening to save five people even if that means sacrificing one person is the more morally correct option. Then the question-asker hits you with,
... what if the five people were strangers, and the one person was your mom/your spouse/your sister/your best friend? Would you pull the lever then?
... what if the five people were adults, and the one was a child? Would you pull the lever then?
... what if the five people were convicted felons, and the one was not? Would you pull the lever then?
... what if the five people were disabled, and the one person was an Olympic athlete? Would you pull the lever then?
... what if instead of one person, it was four people? Would you pull the lever then?
... what if instead of five people, it was a critically endangered bird, whose death might doom its species to extinction? Would you pull the lever then?
The one that sticks in my head is, let's go back to the baseline version - a trolley is careening out of control towards five people, and you can intervene to shift it to the track where it will kill one person. Did you say yes to that?
Now imagine there are five terminally ill people who need a heart transplant, a liver transplant, a lung transplant, and two kidney transplants, or they'll die. Meanwhile, there is a perfectly healthy adult in front of you with fully functional organs that are a perfect match for these five people. Would you kill that healthy adult and distribute their organs to the five sick people, saving their lives?
If you said no to that, but yes to pulling the trolley lever... why? The logic is the same: kill one person who would otherwise have lived, in order to save five people who would otherwise have died. But it feels different, doesn't it? Why?
That's what the Trolley Problem is for. It's a deliberately contrived ethical thought experiment to draw out our values, our feelings, and how we apply our values about people's lives when we make decisions - and maybe make us face the realization that we have some gut feelings about the value of some lives over others, and make us ask ourselves why we feel that way.
It's applied to hospital triage situations about who to treat first, and to decisions when programming self-driving cars in a crash scenario of whether to prioritize the safety of a pedestrian or the driver.
And it exists so that once you realize the way you're thinking about this, you then have to turn the question to the trade-offs we actually make in society.
... what if instead of five people, it was seven million people, and on the other track, instead of one person, it was The Economy?
... what if instead of five people, it was 7,500 people, and on the other track, instead of one person, it's letting car companies do what they want forever?
... what if instead of five people, it was 1,000 people, and on the other track, instead of one person, it was police budgets and police immunity?
... what if instead of five people, it was a ground invasion of Japan, and on the other track, instead of one person, it was 140,000 people in Hiroshima and Nagasaki?
... what if instead of five people, it was 251 hostages, and on the other track, instead of one person, it was the entire population of Gaza?
These are treated as acceptable tradeoffs, as things that are acceptable sacrifices for the other. And it's up to us to ask. Is this an acceptable trade-off. And is it really a Trolley Problem the way that the people in power want us to believe it is, with no other options.