The trolley problem exposes the limits of pure cost-benefit morality
Sandel opens with the classic trolley dilemma: a runaway trolley will kill five people unless you divert it onto a track where it kills one instead. Most people say diverting is right, matching a utilitarian logic of minimizing harm. But Sandel complicates the case: if the only way to save the five is pushing one bystander off a bridge into the trolley's path, most recoil, even though the math is identical.
Sandel uses this contradiction to argue that pure cost-benefit reasoning, treating all outcomes as interchangeable units to maximize or minimize, doesn't actually capture how people reason morally, and arguably shouldn't. Physically using a person as an instrument feels different from redirecting an already-moving threat, even with the same numerical outcome.
He doesn't resolve which intuition is "correct" — that's the point. Most people aren't consistent utilitarians, however naturally they reach for aggregate outcomes when a dilemma is framed abstractly.
Takeaway: if identical outcomes can feel morally opposite depending on how they're produced, then outcomes alone can't be the whole story of ethics.