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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 civilians 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 others 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 distinction 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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