A Measure Of The Trade-Off Between Responsiveness and Nondictatorship for Arrovian Social Welfare Functions


  • Donald E. Campbell, Department of Economics, The College of William and Mary (decamp@wm.edu). Jerry S. Kelly, Department of Economics, Syracuse University.

  • We are grateful for the input of our referees and associate editor. The paper has benefitted substantially from their assistance.


If individuals are never indifferent between distinct alternatives then for any transitive-valued social welfare function satisfying IIA, and any fraction t, either the set of pairs of alternatives that are socially ordered without consulting more than one individual's preferences comprises at least the fraction t of all pairs, or else the fraction of pairs that have their social ordering determined independently of everyone's s preferences exceeds, or is very close to, 1 −t. The Pareto criterion is not imposed. (There is also a version of this result for the domain of preferences that admit indifference.)