In his recent book,Rational Behaviour and Bargaining Equilibrium In Games and Social Situations, John C. Harsanyi devotes a chapter to his new theory of morality, which he calls ‘Critical Rule Utilitarianism’, and which contains his solution to the problem of the interpersonal comparison of utility. After a detailed exposition of his theory, arguments will be presented to show that: (i) there are certain formal difficulties in the solution that he offers which leads to a rejection of the axiom that there is to be agreement between an individualj’s personal preferences and individuali’s (i ≠j) extended utility function out of which the social welfare function is to be constructed; and (ii) Harsanyi’s theory of critical rule utilitarianism cannot be accepted as a theory of morality because it presupposes a more fundamental theory in its actual construction.