Consistency of decision processes

If a statistical or a voting decision procedure is used by several subpopulations and if each reaches an identical conclusion, then one might expect this conclusion to be the outcome for the full group. It is shown that this property fails to hold for large classes of decision procedures. The geometric reasons why the consistency does not hold are described. A general theorem is given to characterize the procedures that satisfy this property of weak consistency.This research was supported in part by NSF Grant IRI-8803505 and a Guggenheim Fellowship. Also, the author thanks a referee for some comments that stimulated certain revisions.