Bryan Caplan  

Social Choice Theory: A Case of Moral Blindness

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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?

    Wrong! Suppose:

    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.


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    COMMENTS (9 to date)
    Dan Landau writes:

    This is one of the many openings for “behavioral economics” that neo-classical economics creates. Society deals in part with problems of morality by teaching the young and impressionable non-decision rules. For example, “

    You should not kill or rob because it is morally wrong. You should not weigh the pluses and minuses of doing things that are morally wrong. You just should not do them.”

    Adam writes:

    This seems to me to be entirely besides the point. I always thought it obvious that voting systems are for deciding among choices that are not otherwise set off limits by morality, the constitution, or the by-laws. (So obvious that I had not considered it before.) What kind of a voting system, other than a dictatorship (with you deciding, I suppose, but how do we know that you won't make immoral decisions?) do you propose that will exclude all immoral choices?

    I mean to ask that rhetorically, but it would be extremely interesting if some idea about such a system could be formed, but my inclination is to be extremely skeptical. Could it be formalized to any degree?

    George Paci writes:

    Well, one way math impinges on morality is this: if it's impossible to do something, you're not morally obligated to do it (in most moral systems; your mileage may vary).

    In the present case, we all think we should have a voting system and a system of government that is as fair as is practically possible, which is the same thing as saying we're morally obligated to try to achieve it. So it's useful for us to know how much we can hope for even in the theoretical limit, and how much special situations can frustrate our efforts (e.g. third-party spoilers in Presidential elections).

    Hegel, for another example, expends a lot of verbiage on "the will of the German people". Well, if you mull over Arrow's Theorem a while, it becomes very unclear that there is a single will of the German people in regard to most interesting (e.g. multiple-choice) questions, and that in fact there may be an enormous number of multiple wills of the German people, in which case an awful lot of Hegel's ethics is clearly not applicable. (I can't believe I used "clearly" and "Hegel" in the same sentence; that can't be right....)

    So, yeah, it sounds like the social choice guys are trying to reason without the complications of morality, and then some of them sneak it in at the end (wittingly or unwittingly). The Naturalistic Fallacy strikes again.

    drtaxsacto writes:

    I think your analysis of social choice theory is correct. I also think, however, at times that public choice theory falls into the same trap. Hayek argued that you should not let math get in the way - that was an is a fundamentally sound comment. When I first encountered Arrow, I thought OK, but what are the elements of a decision process that could allow most people to circumvent the problem? The goal here should not be to construct the model but to improve understanding - which your posts frequently do - and did again today!

    John Thacker writes:

    Social choice theorists want to morally rank choices without mentioning what the choices are.

    Social choice theorists want to have a method which would be accepted as fair as a voting system even if we were under a "Rawlsian veil of ignorance" as to what the choices would be. Surely that's a reasonable problem to attempt to discuss, since no moral philosophy is going to be able to convince everyone of the rightness of its position. There will be disputes to be rectified, and having fair ground rules that are agreed as fair beforehand is reasonable.

    (In addition, there are certainly decisions which do not really qualify as moral ones, such as what to eat, or what movie to watch.)

    It's not moral philosophy, precisely, but to some people it is a form of meta-morality. So long as we live in a world where people disagree, there will be different options proposed. I don't see how you can avoid the question of how best to decide what options to choose. Even if you want to limit to the most moral option, how do you decide what that is?

    John Thacker writes:

    Your post seems to me to be roughly the same thing as someone complaining about "economists having moral pretenses because they boil everything down to money and materialism, and focus on maximizing utility without mentioning what the utility is for and whether it is moral."

    After all, economists often argue for the morality of letting market solutions and utility maximizing solutions function without mentioning what the choices are, and what sort of utility is being maximized. Of course, as you point out, in reality economists may be influenced by moral philosophers ranging from Benthamite utilitarians to Nozick when they argue for it. Well then so too do the social choice theorists have philosophers to draw on when the cite the importance of having a decision making system which can be agreed on as fair a priori by participants without knowing the choices. In both cases the practitioner may have a moral system without explicit recourse to a philosopher, of course.

    Does this mean that economists too, are mere "moral interior decorators," while those like Nozick do the real heavy lifting? Perhaps, but that interior decorating you seem to sneer at is serious work in both cases. Even if it is technical, it is work worth doing.

    Econblogger writes:

    Bryan,

    You said:

    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.

    And then you said:

    Social choice theorists want to morally rank choices without mentioning what the choices are

    The first is accurate; the second is entirely a non sequitur.

    R A Leeper writes:

    The *point* is [presumably] to define rationality in the context of group decision-making. Morality has nothing to do with *that*.

    Barkley Rosser writes:

    Gosh, there you guys go again knocking math. I would agree that Arrow is more mathy than Nozick was, and Nozick did not do much math in his most famous books. However, he was very much a part of the western analytic philosophy tradition and certainly dealt with many questions in many papers that involved formal logic and math. Check out his stuff on Newcomb's paradox.

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