Appiah, MIll, and Liberalism

Appiah uses Mill's concept of Liberalism in the first chapter of Ethics of Identity.  Mill attempts to fuse utilitarianism and romanticism through his concept of Liberalism.  This is not Liberalism in the sense of right/left politics; its is a liberalism in a sense of a split between public and private spheres.  The private sphere is what individuals do in their private spaces(i.e. Home).  The public sphere can be recognized as government action, or even being in the class room.  Certain constraints are imposed on individuals in the public sphere that are not imposed in the private sphere.  Mill uses his 'harm principle' as a tool for the public sphere to distinguish when intervening on individuals private spheres is warranted.  Appiah points out that Mill's harm principle is vague is what constitutes as a harm, but goes something like this: Harm can be distinguished when one individual prevents another individual from pursuing their own projects.  The problem I see, and Appiah, with this principle is that one person's project may directly prevent/oppose another persons project.  An example of this could be an employee for amedical marijuana club having a project to help people in pain, and  DEA agent having a project to shut down marijuana clubs. The 'harm principle' works with simple situations, but not with complexities(such as the complex issue of federal vs state power within our own country).  Even though in parts of Chapter 1, Appiah appears to be criticizing Mill's conception of liberalism, he seems to rely on it.