Democracy and Social Choice: A Response to Saari

In my paper "Arrow's Theorem, Indeterminacy, and Multiplicity Reconsidered" (published in "Ethics" in 2001) I argue that, contrary to many skeptics, majoritarian democracy is indeed conceptually coherent. I do so by submitting a majoritarian method of decision making that is not disqualified from being such a method by Arrow's theorem and has various other significant merits (in particular it solves the so-called "indeterminacy problem", the problem that majority rule sometimes leaves a group without a recommendation). I also argue for the multiplicity thesis, the claim that, under the same circumstances, there are different reasonable decision methods. However, this fact does not undermine common justifcations of democracy. In a recent response to my paper, the distinguished mathematician and voting theorist Donald Saari argues that my claims vary between questionable and wrong. This paper is a reply to Saari. It turns out that the multiplicity thesis emerges strengthened, and that majoritarian democracy is indeed conceptually sound. Saari's reasoning displays some widespread fallacies, not mathematical fallacies, but fallacies in the reasoning about mathematical insights. His arguments fail, but in ways that teach lessons about the philosophy of social choice and the insights social choice theory offers to democratic theory and that thus are instructive far beyond the limits of our disagreement.