The trolley problem is a family of thought experiments, not a single dilemma, and its purpose is diagnostic rather than a request for your answer.

The cases

Switch. A runaway trolley will kill five people. You can pull a lever diverting it to a side track where it will kill one. Most people say pull.

Footbridge. The same trolley, the same five. You are on a bridge beside a large stranger, and pushing them onto the track would stop it, killing them. Most people say do not push.

The arithmetic is identical. Something other than the numbers is doing the work, and identifying what is the entire point.

What the cases isolate

Doing and allowing. In both you act, so this does not separate them.

Intending and foreseeing. In Switch the death is a side effect; if the one person vanished, your plan still works. In Footbridge the death is the means; without it the plan fails. This is the doctrine of double effect, and it maps the intuitions closely.

Using a person. Footbridge treats someone as an instrument, which is Kant's prohibition on using a person merely as a means.

Why philosophers built it

Philippa Foot introduced the case in 1967 and Judith Jarvis Thomson developed the variants. They are not asking what you would do. They are testing whether consequentialist and deontological principles can account for stable, widely shared intuitions — and a strict utilitarian view struggles, because it has to call the two cases equivalent when almost nobody does.

The standing criticism

The cases are artificial: certain outcomes, no time, no consequences, no relationships. Critics argue that intuitions produced under those conditions are poor evidence about real moral judgment, and that the literature has spent decades on a scenario nobody faces.

The reply is that isolation is the method. You remove every variable except one to find out which variable matters, and the artificiality is what makes the test clean. See ethics and deontology.