Against the no-difference argument

There are 1,000 of us and one victim. We each increase the level at which a ‘discomfort machine’ operates on the victim – leading to great discomfort. Suppose that consecutive levels of the machine are so similar that the victim cannot distinguish them. Have we acted permissibly? According to the ‘no-difference argument’ the answer is ‘yes’ because each of our actions was guaranteed to make the victim no worse off. This argument is of interest because, if it is sound, similar arguments threaten intuitive moral verdicts about many cases in which a large number of individual choices cumulatively make a great difference, while each choice seems to make no difference on its own. But the argument is not sound, as is shown by a simple objection based on a plausible dominance principle – an objection that avoids challenges that have been brought against previous criticisms of the no-difference argument.