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302 M. Hoffman et al.
So even when a witness knows that the perpetrator anticipated the harm, the witness
believes other witnesses will not be aware of this and will presume the harm was not
anticipated by the perpetrators. For instance, suppose we observe Israel killing civil-
ians as a by-product of a strategic raid on Hamas militants. Even if we knew Israel
had intelligence that confirmed the presence of civilians, we might not be sure oth-
ers were privy to this information. On the other hand, when the harm is done as a
means, the harm must be anticipated, since otherwise the perpetrator would have no
motive to commit the act. Why would Hamas fire rockets at civilian towns with no
military presence if Hamas does not anticipate a chance of civilian casualties?
Consequently, it is Nash equilibrium to punish harm done as a means but not harm
done as a by-product.
Similar arguments can be made for why we find direct physical transgressions
worse than indirect ones, a moral distinction relevant to, for instance, the United
States’ current drone policy. Cushman et al. (2006) found that subjects condemn
pushing a man off a bridge (to stop a train heading toward five others) more harshly
than flipping a switch that leads the man to fall through a trap door. Pushing the
victim with a stick is viewed as intermediate in terms of moral wrongness. Such
moral wrongness judgments are consistent with considerations of higher-order
beliefs: When a man is physically pushed, any witness knows the pushing was
intended, but when a man is pushed with a stick some might not realize this, and
even those who realize it might suspect others will not. Even more so when a button
is pressed that releases a trap door.
It is worth noting that the above argument does not depend on a specific model
of punishment, as in DeScioli and Kurzban’s (2009) Side-Taking Game. The above
model also makes the two novel predictions enumerated above, but nevertheless
captures the same basic insight. It is also worth noting the contrast between the
above argument and that of Cushman et al. (2006) and Greene et al. (2009), whose
models rest on ease of learning or ease of mentally simulating a situation. It is not
obvious to us how those models would explain that the omission-commission and
means—by-product distinctions seem to depend on priors or be unique to settings of
coordinated punishment.
Why Morality Depends on Categorical Distinctions
We explain why our moral intuitions depends so much more strongly on whether a
transgression occurred than on how much damage was caused. Our argument again
uses coordinated punishment and higher-order beliefs: When a categorical distinc-
tion is violated, you know others know it was violated, but this is not always true for
continuous variables.
Consider the longstanding norm against the use of chemical weapons. This norm
recently made headlines when Bashar al-Assad was alleged to have used chemical
weapons to kill about a thousand Syrian civilians, outraging world leaders who had
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