 Suppose you decide to save the lone swimmer on the second rock. Intuitively, this seems wrong. Surely you should have saved five people instead of one. The challenge for contractualism is to explain why what you did is wrong. Utilitarians have a straightforward answer, based on aggregation. You should save the five people instead of the one simply because five deaths is a worse result than one death. This case is tricky for contractualism because it rejects aggregation. The five people will each want to reject the principle that allows you to save the one, by appealing to the fact that such a principle leaves them to die. But the lone person on the second rock will want to reject any principle that allows you to save the five. And the reason for objecting to the principle is exactly the same in each case—this principle leaves that person to die. The five people cannot appeal to the fact that there are more of them—because this is not an individual reason. (Suppose you are one of the five. The fact that four other people will die is not something you can object to, as it is not something that happens to you.) It therefore looks as if we have reached a stalemate—and perhaps the best solution (the principle that no-one can reasonably reject) is to toss a coin. That way, each of the six people gets a fifty-fifty chance of survival. No-one can reasonably reject this principle on the grounds that it only gives them a fifty-fifty chance of survival, because any alternative gives someone even less chance. Tossing a coin is the only principle that guarantees everyone at least a fifty-fifty chance. So it is the only principle that no-one can reasonably reject.