Journal Article Algorithms for Social Choice Functions Get access Donald E. Campbell Donald E. Campbell Ontario Economic Council and University of Toronto Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 3, April 1980, Pages 617–627, https://doi.org/10.2307/2297312 Published: 01 April 1980 Article history Received: 01 June 1977 Accepted: 01 April 1979 Published: 01 April 1980

[A choice function C on X identifies, for each subset Y of X, a set C(Y) of "best" alternatives in Y. A. computationally viable choice function is one for which a member of the choice set C(Y) can be located by a computational procedure which does not waste time, generates reasonably satisfactory intermediate alternatives, and adjusts easily as new alternatives become available. Computational viability is defined precisely and the class of computationally viable choice functions is neatly characterized. In addition, the various types of binary choice functions are distinguished in terms of computational criteria.]

A social welfare function f is Arrowian if it has transitive values and satisfies Arrow's independence axiom. For any fraction t and any Arrowian f, either there will be some individual who dictates on a subset containing at least the fraction t of outcomes, or at least the fraction 1 minus t of the pairs of outcomes have their social ranking fixed independently of individual preference. And for any Arrowian f, there is a set containing a large fraction of the citizens whose preferences are never consulted in determining the social ranking of a large fraction of the pairs of alternatives.