Harming a group without harming an individual

Imagine that a dart with a perfectly defined tip is going to be thrown by a monster at a circular target, with the impact position uniformly distributed over the target and every point equally likely. There are uncountably many people, and there is a one-to-one assignment of points on the target to people, with every point and every person assigned. There is a monster who will throw a dart with a perfectly defined tip, in such a way that its impact point is uniformly distributed over the target with each point equally likely. The monster will then eat anyone whose point is hit by the dart.

People come in two kinds. There are pointy-eared and round-eared people. The pointy-ears are assigned the left half of the target and the round-ears are assigned the right half, and the dividing line is divided as fairly as can be, too. But along comes a racist who changes all the assignments, moving the pointy-ears to a tiny circle in the middle of the middle of the target containing 1% of the target, and spreading the round-ears over the remaining 99% of the target, but ensuring still that each point is assigned to one person and each person to one point.

The racist harmed the round-ear group. For increasing the chance of harm to a group or individual is a form of harm to the group or individual. (Endangerment is not a victimless crime, even if the danger does not actually befall anyone.) But the racist harmed no individual. No round-ear had her probability of being eaten go up. After all, every point on the target had equal probability of being hit. John, a man with round ears, was first assigned, let's say, to a point right by the middle. Later he was reassigned to a point near the rim. That does nothing to affect the chances of John being eaten.

Thus, it is possible to harm a group without harming any individual from the group.

But perhaps this doesn't give group-rights proponents quite as much as might at first sight seem. Certainly our racist harmed the round-ear group. But she also benefited many other groups of people, each group of the same size as the round-ears. For we can subdivide the benefited pointy-ear group into infinitely many groups, each with the same number as the round-ears, and many of these groups will have been benefited. In fact, there need be no difference between how many groups of that cardinality were benefited and how many groups were harmed. So how can we blame our racist rearranger? She harmed infinitely many groups and she benefited infinitely many groups.

Well, you might say: But the round-ears are a non-arbitrary (maybe more natural in the David Lewis sense) grouping of people, while most of the benefited groups are completely arbitrary groupings.

That may be. If so, then the argument supports the idea that it makes sense to talk of group harm in the case of non-arbitrary groups.