Bentham is not unaware of this tension. He addresses part of theproblem in the political context in other writings, notably hisPlan for Parliamentary Reform (1817). In the politicalcontext, the problem is how we can get self-interested rulers to rulein the interest of the governed, as utilitarianism implies that theyshould. Bentham's answer invokes his commitment to representativedemocracy. We can reconcile self-interested motivation and promotion ofthe common good if we make rulers democratically accountable to (all)those whom they govern, for this tends to make the interest of thegoverned and the interest of the governors coincide. Bentham'sargument, elaborated by James Mill in his Essay on Government,is something like this.
John Stuart Mill’s book Utilitarianism is one of the most influential and widely-read philosophical defenses of utilitarianism in ethics. The essay first appeared as a series of three articles published in Fraser’s Magazine in 1861; the articles were collected and reprinted as a single book in 1863. It went through four editions during Mill’s lifetime with minor additions and revisions.
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So Mill rejects the substantive doctrines of psychological egoismand hedonism that Bentham and his father sometimes defended orsuggested. This is really part of a larger criticism of the conceptionof psychology and human nature underlying Benthamite utilitarianism,which Mill elaborates in his essays on Bentham. Mill's desire todistance himself from Benthamite assumptions about human nature andpsychology are also reflected in his conception of happiness and hisdoctrine of higher pleasures.