For example (from memory, so it may come out a little different than his version):
You are raiding on a railcar when you come to a switch in the track. Down the branch you are riding there are four workers standing on the track who are unaware they are in danger and will die if the railcar keeps going. On the right branch there is another worker who is in the same situation. You can flick a switch to change over from the left to the right track: do you?
On the other hand: You are standing next to some tracks when a railcar comes down the track and is about to hit four workers farther down. There is a heavyset person next to you who, if you push into the path of the car, will (obviously) die but slow the railcar down enough so as to not hit the workers. Do you push?
Now, the 'paradox' here is (as he claims) that many people are perfectly willing to switch the track, but not willing to push even though the results are the same. This supposedly reveals something interesting in terms of our philosophical outlook on ethics.
(Specifically, I think he was going after Mill [individual happiness matters, so don't push] vs. Kant [the overall good matters most, so push] but even that doesn't map out neatly so I won't dwell here.)
I have issue on two points: 1. the physics of the second situation. As phrased, I find it bizarre that one would *know* that pushing will work to save the workers, and it will be the only way. Even if one is told the statement as absolutely, the real-world creeps in somewhat to taint the situation. In addition, 2. the first action is clearly legal, while the second is clearly not.
Now, let's say we remove both these points -- it's firmly established that you know for absolute certain pushing will work, *and* it is the only way to save the workers. In addition, it will be considered legal to do so because all information about cause and effect is known and the legal system will somehow be aware of all that. In this case, the 'paradox' loses a lot of the power, and I find myself considering them equally -- but admittedly with all real-world context stripped out.
I'd almost consider the answers to the original version of this paradox to be more indicative of how much we trust authority rather than how we view life -- how much do you take the researcher abstractly at their word on the second situation, and how much is tinged by what things would be like in real life?