Arrow’s Theorem holds that no constitution can satisfy certain properties. In annex to that theorem, Arrow claims that those properties are reasonable and morally desirable. In Arrow’s view there thus is the difficulty that people desire a constitution that cannot exist. While the Theorem stands as a mathematical result, the additional claims concern some other matters, namely the domains of reasonableness and morality. It are these claims that have caused much confusion in the literature. It is shown here that the claims are unwarranted, since inconsistent properties are neither reasonable nor morally desirable. It is shown too that Arrow’s axiom of Pairwise Decision Making (formerly known as the Independence of Irrelevant Alternatives) is not realistic, and thus unattractive. We show the existence of some constitutions without that axiom that are consistent and might be optimal to many. The major error made by Arrow and his students is to mix up the context of scientific discovery and learning with the context of application to the real world by educated people.
Introduction
Arrow (1950, 1951, 1963) showed that if certain properties are postulated for a constitution, then such a constitution would not exist. This result has been checked by numerous scholars, is accepted by this author, and thus stands as a mathematical theorem. In fact, we will give a short proof below.
Arrow also claimed, annex to the theorem, and this will be at issue here, that those properties would be reasonable and morally desirable. He recently repeated that claim in the Palgrave (1988:125). He writes:
“(...) conditions to be imposed on constitutions (...)”
“(...) there is no social choice mechanism which satisfies a number of reasonable conditions”.
For clarity it is useful to introduce the following abbreviations for the theorem and its companion claims, and their conjunction:
AT = the Arrow Theorem
ARC = the Arrow Reasonableness Claim = the properties are reasonable
AMC = the Arrow Moral Claim = that they are to be imposed