George is 20 years old and Jake is 50. Neither has friends, or is very likely to make a significant contribution to the pleasure of others, in George's case because of anti-social tendencies, and in Jake's because of severe disability. George hates Jake and pushes him overboard. As Jake flies overboard, George loses his balance and falls in, too. Both call to us for help. We can only pull out one. What should be done?
Here is a hedonist utilitarian answer (it makes a lot of assumptions, but the assumptions are not crazy). We should pull out George, and have him tried and convicted of murder. Then we should publicly sentence him to a lifetime of pain. We then need to hook him to electrodes in a cell, for the rest of his life. But unbeknownst to the public, the electrodes will deliver intense pleasure for the rest of his life. George will never tell anyone this, because he will be enjoying the pleasure too much. We need to tell George about this before he is sentenced to the lifetime of pain, so that he doesn't get too scared of the sentence.
On hedonist utilitarian grounds shouldn't pull out Jake, because (a) Jake is probably not going to agree to being hooked up to the pleasure-machine, and (b) even if he did, he wouldn't have as long left to live, and hence as much pleasure to experience, as George would, since George is younger. To satisfy the public, we might need to lie that we couldn't pull out Jake. George will support us in that lie. Since contortions of pleasure don't look too different from contortions of pain, we can exhibit George to the public, and this will have a significant deterrent effect on murder.
Yes, I know that hedonist utilitarians will cavil at this and at that in the story. But of course the real reason the story is all wrong is that it is surely wrong to save the life of the murderer while letting his victim drown (unless maybe the victim requests that we save the life of the murderer instead—for instance, if the victim is the murderer's parent).