Journal Article Liberal Values and Independence Get access Julian H. Blau Julian H. Blau Antioch College Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 42, Issue 3, July 1975, Pages 395–401, https://doi.org/10.2307/2296852 Published: 01 July 1975

The problem of aggregating individual preference orderings to form a social ordering took a new turn when Arrow organized the subject abstractly. We study here his celebrated theorem that five plausible conditions on the method of aggregation are inconsistent. This theorem is in fact false in general, as a counterexample shows. When we increase the amount of disagreement which is allowed to occur, then the inconsistency is restored. The modified result preserves much of the impact of the original theorem.

[A social decision function operates on individual weak orderings to produce acyclic social preference. The structure of a general neutral monotonic SDF is studied. It is shown to be characterized by the veto, if individual indifference is banned. With such indifference present, the characterization is by a veto structure, a hierarchy embracing all individuals. The reason for the interest in acyclicity [21, 22] is that it averts the voting paradox, permitting a choicefrom each subset of alternatives. This is for the finite case. When that assumption is dropped, an infinite ascending sequence of preferences prevents a choice. It is shown that this last phenomenon need not be prohibited along with cycles; the absence of such social sequences is implied by their absence from individual preferences.]