Is a paretian liberal really impossible: A reply

TLDR: Bernholz as discussed by the authors does not dispute the correctness of the theorem of the impossibility of the Paretian Liberal (Sen (1970), but the difference would appear to lie in the interpretation of the result.

Abstract: Despite slightly ambiguous wording, Bernholz (1974) does not dispute the correctness of the theorem of the impossibility of the Paretian Liberal (Sen (1970)). So the difference would appear to lie in the interpretation of the result. (1) Bernholz says: "In my view Sen has not shown that there does not exist a wide range of issues, which should be decided according to the rule of liberalism, even if the actions of the deciding individuals imply some externalities to others" (typescript page 2). The same view is shared by me. Indeed, as was made clear in Sen (1970), the point of the theorem was to show that for some configurations of individual preference, liberalism conflicted with Pareto optimality; and not that this conflict arose for every configuration of individual preferences (or even for every configuration except for a narrow range). The bulk of Bernholz's paper is concerned with cases (Tables 1, 2, 3, and 4) in which this conflict does not arise, and in these cases there is not only no conflict between liberalism and the Pareto principle, but also none between Berhnolz and Sen. (2) Bernholz also says: "There is not much merit in showing that one decision rule, 'liberalism', does not in all cases lead to Pareto-superior social states, if this is true for any other decision rule" (typescript page 3). But the point is not that in itself liberalism does not "lead to" Pareto-superior social states, but that it rules out the choice of Pareto-superior states in some cases. A failure to grasp this distinctiohn causes some confusion in Bernholz's paper. Incidentally, as it happens it is also the