How do you apply the Doctrine of Double Effect to the trolley problem?

Answer: Throwing someone into the tracks of an out of control trolley to stop it from running over five people would be wrong because it would require intentionally harming one person to save five. On the other hand, diverting the runaway trolley onto a path where one person will be killed, instead of five, would be admissible, as we may foresee that one death as an unintantional side effect.

Explanation:

The Doctrine of Double Effect, developed by St. Thomas Aquinas, allows us to better understand why we find it unacceptable to push a man onto the tracks: the good result must be a consequence of the action taken, not of the bad effect, so pulling the switch is better than pushing the man onto the tracks.