Computational Criteria for Voting Systems

Condorcet's paradox of voting and Arrow's impossibility theorem are by now well known. Inspired by Arrow's treatment of social choice, others have presented alternative proofs of his theorem and different impossibility results. Professor Fishburn has recently treated us to some interesting new voting paradoxes. It is important to have the area of inconsistency among the various treatments explored and clearly mapped out. It is equally important to come to terms with the known inconsistencies in order to construct a solid social choice edifice on safe ground. Coming to terms with the inconsistencies must surely mean deciding between alternative normative conditions when all of them cannot be satisfied simultaneously. This paper attempts to do just that by adding some computational criteria to the standard list of normative criteria and then singling out a subset as being more important (to the author at least) than the rest. Since the ‘important’ criteria are mutually consistent they can be used to derive some properties of democratic decision processes. Simple majority rule, applied in sequential elimination, is distinguished as the best collective decision method. It fails to satisfy the Pareto, or unanimity, criterion – one often regarded as a sine qua non of social choice – but when this condition is added to the author's list an impossibility result obtains. An argument is proposed to counter the suggestion that Pareto optimality be added to the list and some other condition removed.