Liberal Values and Independence

Abstract

A. K. Sen argues in [5] and [6] that the Pareto principle is inconsistent with liberal values, the latter taking the form that for each individual there is a pair of alternatives regarding which his own preference is adopted socially. This liberal assumption is justified when the difference between the two alternatives concerns only the individual. The context of the discussion is very similar to that of an Arrow social welfare function, from which it differs in that the social preference pattern is not required to be an ordering but only to be free of cyclic preferences. Thus the inconsistency is the more impressive. Sen claims not to have imposed Arrow's condition of the independence of irrelevant alternatives . This is undoubtedly true, in the sense that the condition contains a large number of assertions, of which only a few are invoked. I shall suggest, however, that the condition was used in a significant way, and that this is at the heart of the paradox. I then argue that the independence component of Sen's liberalism is unjustifiably strong in terms of its rationale, and I offer weaker versions, with discussions of their consistency or inconsistency with the Pareto principle. One of the results will show, incidentally, the critical need for an unrestricted domain. The main theme of this paper is the role of independence. This powerful condition, used fully or sparely, together with any non-trivial restriction on the social preference pattern, forces connections between different pairwise decisions. The technique was invented by Arrow [1]. These remarks do not detract from the interest of Sen's striking theorem, but they perhaps soften the suggested conflict between liberalism and the Pareto principle.