Social Choice Theory: A Case of Moral Blindness
By Bryan Caplan
Steven Brams of NYU presented his latest paper on approval voting at GMU Wednesday. While it was better than most papers in the field of social choice theory, its main effect was to help me realize what’s wrong with the whole field.
What exactly is social choice theory? Back in the 50’s, it was closely tied to public choice theory, but it quickly split off and became a nearly separate field. The main focus of social choice theory is to start with normatively appealling axioms for group decision-making, and then try to logically derive decision-making rules that satisfy those axioms. The most famous example is Arrow’s Impossibility Theorem, which shows that there is no voting rule that satisfies all of the following axioms:
unrestricted domain or universality: the social welfare function should create a deterministic, complete societal preference order from every possible set of individual preference orders… non-imposition or citizen sovereignty: every possible societal preference order should be achievable by some set of individual preference orders… non-dictatorship: the social welfare function should not simply follow the preference order of a special individual while ignoring all others… positive association of social and individual values or monotonicity: if an individual modifies his or her preference order by promoting a certain option, then the societal preference order should respond only by promoting that same option or not changing, never by placing it lower than before… independence of irrelevant alternatives: if we restrict attention to a subset of options, and apply the social welfare function only to those, then the result should be compatible with the outcome for the whole set of options…
So how can I furrow my brow in annoyance at this whole field? Simple: Social choice theorists want to morally rank choices without mentioning what the choices are. For example, suppose a group can do A, B, or C, and A is everyone’s first choice. Surely they should do A, right?
A=”Murder everyone who isn’t in our group”
B=”Murder everyone over 6 feet tall who isn’t in our group”
C=”Don’t murder anyone.”
Then it’s morally obvious that the group should choose C, and any rule that gives a different result is wrong. For Arrow’s Theorem buffs, my claim is that the non-imposition axiom is not only not obviously right; it is obviously wrong.
Of course, you could respond that social choice theory isn’t moral at all. It merely states what axioms are consistent with what; that’s it. Well, if that’s so, then it looks like a giant waste of brain power. If it isn’t supposed to give us moral guidance, what’s the point?
My colleague Alex Tabarrok suggests that social choice theory, rightly understood, is trying to come up with a way to choose between morally acceptable choices. We first remove A and B from the previous list; then we consider different voting rules for deciding between the remaining options. There’s nothing wrong with that either, though there may not be many options left after we delete everything that isn’t morally acceptable.
But in any case, this interpretation demotes social choice theorists from moral architects to moral interior decorators. The people who do the heavy lifting in moral philosophy are not and never have been math gurus like Ken Arrow, but traditional humanities-type philosophers like Robert Nozick.