Several recent papers have developed partial or complete characterization of classes of social decision functions in terms of constructs based upon the associated collections of decisive sets. Hansson (1976) interpreted Arrow’s impossibility theorem in terms of the associated ultrafilter of decisive sets. Brown (1973) extended this correspondence to the case of acyclic choice functions and prefilters. To deal with the multiplicity of social decision functions having the same collection of decisive sets, Brown restricted the class of social decision functions while Ferejohn and Fishburn (1979) and Blau and Brown (1980) added structure to the collections of decisive sets, and thereby obtained a characterization of certain social decision functions.

John A. Ferejohn, David M. Grether, Steven A. Matthews, Edward W. Packel; Continuous-Valued Binary Decision Procedures, The Review of Economic Studies, Vol