Justice: A Beginner's Guide (2017) by Raymond Wacks. p. 79.
Some find his refutation of utilitarianism unfounded. H.L.A. Hart describes it as paradoxical, because it yields an outcome that is indistinguishable from one of the least satisfactory implications of an absolute maximizing utilitarianism, in that 'given certain conditions there is nothing to choose between a society where few enjoy great happiness and very many very little and a society where happiness is more equally spread'. A utilitarian would regard the aggregate or average welfare in both societies as the same; Nozick treats the situation as historical. Neither, Hart seems to be claiming, is likely to to disrupt the existing the pattern of distribution, however unequal.
Secondly, Nozick's assault on utilitarianism is, as Hart shows, paradoxical:
[l]t yields a result identical with one of the least acceptable conclusions of an unqualified maximising utilitarianism, namely that given certain conditions there is nothing to choose between a society where few enjoy great happiness and very many very little, and a society where happiness is more equally spread.64
A utilitarian would regard the aggregate or average welfare in both societies as the same. Nozick, of course, treats the condition as a historical one. But neither, Hart seems to be suggesting, is willing to disturb the existing pattern of distribution, how-ever unequal.
64 'Between Utility and Rights' in Essays in Jurisprudence and Philosophy, 205.
I understand that the emboldened sentences are true, as "an absolute maximizing utilitarianism" doesn't care about the distribution of happiness. But what exactly is paradoxical about Nozick's refutation of utilitarianism? What paradox stems from the idea of "an absolute maximizing utilitarianism"?
I linked to, but don't replicate, the primary source (Hart's writing).