Suchergebnisse

This paper is concerned with the "General Possibility Theorem" of Dr. K. J. Arrow. Since the theorem is certainly elegant and probably important, it is proper as well as convenient to refer to it from this point on as Arrow's theorem. The theorem deals with the problem of discovering a rule by which social preferences can be constructed from individual preferences. Such a rule, or social welfare function, gives a social ordering of alternatives of any kind for every possible arrangement of the corresponding individual orderings. Arrow's theorem declares that no social welfare function exists that satisfies those conditions that most of us would consider essential to a satisfactory rule. The outcome is something of a shock to preconceptions.In what follows two aspects of Arrow's theorem are considered. In the early part of the paper the theorem as such is examined. A brief and informal statement of Arrow's argument is followed by a formal statement of the conditions on which the argument depends. A proof of the theorem is offered that seems to be rather more naturally constructed than the original. A set of conditions is proposed (derived from Arrow's proof) that is weaker than the original set, that seems to be at least as plausible, and that leads to the same conclusion by a short and direct route. In the later part of the paper, methods of circumventing the theorem (there seems to be no way of removing it) are explored.