This is most likely a stupid question, but it has been on my mind for a really long time now.
We think of utilitarianism as saying "action X is right if it promotes happiness and wrong if if it promotes unhappiness". This is the so-called principle of utility.
I understand that libertarianism (basically) says that A government should only impose its power on its citizens (e.g. arrest someone) in order to prevent harm to others. (the so-called harm principle).
Could someone familiar with this sort of philosophy explain the relationship between the principle of utility and the harm principle? Or are they "orthogonal" principles? Does Mill "prove" the harm-principle using the principle of utility? If so then that's a very serious project... Anyway, what is his argument if he does indeed do this? If he doesn't do this then do any philosophers take this position? Or should one regard liberty as "irreducible" just like happiness is, and not try to relate the two concepts?