[roenxi]

The mugger, through no coercion of Bentham, chooses to go down a finger. It is obvious that the mugger has an insane utility function, but it isn't obvious that Bentham letting him act it out is causing a drop in overall utility.

If the mugger doesn't want his own finger, it is Bentham can choose to trust him that 9 fingers are better than 10. Maybe the mugger is even behaving rationally, maybe the 10th finger has cancer, who knows. As the story illustrates, giving him $10 didn't stop him from losing his finger. There are many factors here that make the situation unclear.