Arrow’s impossibility result stems chiefly from a combination of two requirements: independence and fixity. Independence says that the social choice is independent of individual preferences involving unavailable alternatives. Fixity says that the social choice is fixed by a social preference relation that is independent of what is available. Arrow found that requiring, further, that this relation be transitive yields impossibility. Here it is shown that allowing intransitive social indifference still permits only a vastly unsatisfactory system, a liberum veto oligarchy. Arrow’s (...) argument for independence, though, undermines any rationale for fixity. (shrink)

I conclude that Gibbard fails to solve several of the traditional problems for expressivism. He solves some of these problems, but his solutions to them in effect give up expressivism. Of course, one might respond that it does not really matter whether his theory is expressivist. In some ways, I agree. Gibbard says many fascinating things about morality which have at most indirect connections to his expressivist analysis. I am thinking especially of his later discussions of hyperscepticism, parochialism, and indirect (...) pragmatism. These views could still be developed even if he gave up expressivism. All I have tried to show here is that he does need to give up expressivism unless he can solve the problems that I have raised. (shrink)

Rawls' Difference Principle asserts that a basic economic structure is just if it makes the worst off people as well off as is feasible. How well off someone is is to be measured by an ‘index’ of ‘primary social goods’. It is this index that gives content to the principle, and Rawls gives no adequate directions for constructing it. In this essay a version of the difference principle is proposed that fits much of what Rawls says, but that makes use (...) of no index. Instead of invoking an index of primary social goods, the principle formulated here invokes a partial ordering of prospects for opportunities. (shrink)

Arrow's Theorem, in its social choice function formulation, assumes that all nonempty finite subsets of the universal set of alternatives is potentially a feasible set. We demonstrate that the axioms in Arrow's Theorem, with weak Pareto strengthened to strong Pareto, are consistent if it is assumed that there is a prespecified alternative which is in every feasible set. We further show that if the collection of feasible sets consists of all subsets of alternatives containing a prespecified list of alternatives and (...) if there are at least three additional alternatives not on this list, replacing nondictatorship by anonymity results in an impossibility theorem. (shrink)