As Stentor pointed out, this problem is structurally very similar to the 'fat man' case in the trolley problem literature:
a trolley is hurtling down a track towards five people. You are on a bridge under which it will pass, and you can stop it by dropping a heavy weight in front of it. As it happens, there is a very fat man next to you - your only way to stop the trolley is to push him over the bridge and onto the track, killing him to save five. Should you proceed?According to Marc Hauser's data, only 10% of people are willing to push the fat man.
It seems to me that people will always imagine the death of the fat man in the above scenario more vividly than they'll imagine the deaths of the five people on the track. There are a couple reasons for this. For one thing, there's direct physical contact with the fat man in that case (though apparently Hauser has gotten similar results from cases involving less direct contact). There's also the way that deciding to push the fat man forces us to imagine all the intermediate steps between our action and its intended goal, raising lots of negative emotions. When we contemplate doing nothing in the fat man case, however, we aren't forced by the nature of deliberation to imagine anything in particular. So the same violent negative emotions don't arise.
Sort of like matt w said in comments, my example tried to correct for this by thrusting the (gruesome) deaths of the five workmen in your face, so you couldn't escape vividly imagining their predicament. At the same time, it put the guy whose body would block the train at a distance and out of view. Judging from the responses in comments, a majority of the people would push the button to make the guy on the scaffolding fall down. Even if this is a somewhat weirdly collected sample in some respects, this is a lot more than Hauser's 10%.
The larger point I'm hoping to make with this example is that many of the factors that drive people towards deontology may arise from how the structure of deliberation forces us to imagine different harms with different vividness, rather than from genuine moral convictions in support of deontology. This plays into an argument against deontology. Differentially vivid imagination is implicated in lots of irrational behavior -- for example, I think it explains why people fail to delay gratification, choosing smaller pleasures presented vividly before them at great long-term cost. Insofar as I can explain the appeal of deontology in terms of how the structure of deliberation keeps us from imagining all outcomes with equal vividness, I can argue that deontological constraints are based on something irrational, and that we should accordingly diminish their significance in moral theory.
Anyway, the deadline for submitting papers to December's American Philosophical Association meeting is Feb. 15, so it's time for me to cram out a short paper on this stuff. Thanks again to all who helped.