Tag Archives: Arrow

Bleeding-Heart Social Moral Anti-Realism?

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Like many of you, I have been enjoying recent posts on Cato Unbound about “bleeding-heart libertarianism,” as well as on the similarly-named blog. What follows are some half-formed thoughts they prompted. This post is not meant as an explicit critique of anybody; everyone involved knows way more about philosophy than I do.

Most philosophers (and virtually all ordinary people) accept or lean toward moral realism, the idea that moral claims purport to report facts, and that these facts are sometimes true. But it seems to me that we can distinguish between “individual moral realism” and “social moral realism” (my terms; real philosophers might have other ones). For the purposes of this post, let me accept individual moral realism; there is such a thing as the good life, and moral claims about individuals sometimes correctly report facts about it.

The acceptance of individual moral realism does not necessarily obligate me to accept social moral realism. There is at least one possible reason to think that social moral realism is unnecessary, and one for rejecting it. First, social moral realism is unnecessary if all true claims about the good society follow directly from facts about the good life. If this were true, then there would be no independently true claims about the good society. True claims about social justice, for instance, would be mere restatements of true claims about ordinary justice.

Second, we should reject social moral realism if insofar as the good life for some people is in tension with the good life for others, it is impossible to coherently rank different conceptions of the good society. Think of it like Arrow’s impossibility theorem. Arrow proves that even if there are such things as facts about individual rationality, there are not necessarily facts about collective rationality (under particular assumptions). Why would something similar not hold for morality?

I read both Rawlsians and utilitarians as attempting to assert facts about the correct way to adjudicate tensions between individual pursuits of the good life. These assertions are similar to those about different methods of collective decision-making: “Simple majority voting is the best decision-making system!” “No, instant run-off voting is the best!” “Have you forgotten about the Borda count?” If something like Arrow’s theorem holds for morality, we should reject Rawlsian and utilitarian claims. Further, we might be suspicious of them as attempts to wield power over people (not very libertarian, huh?).

What does this mean for bleeding-heart libertarianism? To my mind, it means that the strongest grounds for BHL is simply individual morality. It is wrong, inconsistent with the good life, to seek to dominate other people for the sake of domination; this plus some reasonable positive claims about the world implies quite a bit of libertarianism, does it not? It is good for people—it cultivates gratitude and compassion, which are good—to be concerned about those who are marginalized. These, to me, are far more persuasive than top-down approaches to BHL.

I know the above is sloppy. I’m happy to be corrected or constructively criticized, so go ahead, real philosophers: shoot holes in my argument.

A Difficulty in the Concept of Social Welfare

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Welcome to the third installment in our series of discussions of the Most Insightful Articles in economics. Today we are discussing Ken Arrows’s 1950 article A Difficulty in the Concept of Social Welfare.

If you’re interested in politics, you may have done the following thought experiment. Suppose there are three voters—1, 2, and 3—and three alternatives—A, B, and C. Voter 1 prefers A to B to C. Voter 2 prefers B to C to A. Voter 3 prefers C to A to B. By a vote of 2-1, “society” prefers A to B. It also prefers B to C. If a rational person prefers A to B and B to C, then that person prefers A to C. But in this example, “society” prefers C to A! Is society irrational? Is this just a problem with majority rule? To cut to the chase, in this paper Arrow shows that it is a general problem. Any method of aggregating individual preferences is either irrational or has some other properties that are arguably undesirable.

One can envision collective decision-making as selecting a social welfare function and then using it to compare states of the world. Arrow defines five conditions to which a social welfare function ought to hold:

  1. The function is universally defined. There are not certain preferences that people can have that cause the function to be indeterminate (though the function is allowed to express indifference).
  2. If someone decides that X is more desirable than he initially thought, and nothing else changes, the social welfare function cannot penalize X.
  3. The function should provide the same ranking for a subset of options as it would for that subset within a complete set of options. Adding or removing an option should not affect the ranking of other options.
  4. No preferences are taboo. Any social preference ordering is possible if people have the right individual preferences.
  5. The function must be collective in the sense that it does not simply mimic one person’s preferences.

Seems reasonable, no? Arrow’s proof proceeds by contradiction. He assumes that there are two individuals, three alternatives, and a social welfare function that satisfies the above conditions. These assumptions lead to three consequences:

  1. If both individuals prefer one outcome to another, then the social welfare function prefers it as well.
  2. “[I]f in a given choice, the will of individual 1 prevails against the will of individual 2, then individual 1′s views will certainly prevail if 2 is indifferent or if he agrees with 1.”
  3. If individual 1 prefers X to Y and individual 2 prefers Y to X, then the social welfare function must be indifferent between X and Y.

Now, suppose that individual 1 prefers X to Y to Z and individual 2 prefers Z to X to Y. By consequence 1, the social welfare function prefers X to Y. By consequence 3, the function is indifferent between Y and Z. Since the function prefers X to Y and is indifferent between Y and Z, the function must prefer X to Z. However, also by consequence 3, the function must be indifferent between X and Z. This is a contradiction, which means that one of our assumptions cannot hold. In Arrow’s words:

If we exclude the possibility of interpersonal comparisons of utility, then the only methods of passing from individual tastes to social preferences which will be satisfactory and which will be defined for a wide range of sets of individual orderings are either imposed or dictatorial.

What does this mean? There is no “will of the people,” at least not if that phrase is to encompass what we normally think of as rationality. Rousseau is incoherent. Democracy can be manipulated by agenda control, as Levine and Plott show in a hilarious article in Virginia Law Review.

How can we get around this conclusion? One way is if preferences are unidimensional and single-peaked. If all voters think in terms of a single liberal-to-conservative spectrum and prefer candidates that are closer to some optimum point, then you can no longer demonstrate the contradiction. Another way is if you allow some way of expressing intensity of values (interpersonal comparisons of utility), such as by bidding with dollars, though this may undermine some of Arrow’s conditions.

For discussion: Voter preferences are shockingly unidimensional, are they not? People who favor high taxes tend also to be pro-choice on abortion. What do these have to do with each other? Does this correspondence save democracy from the charge of irrationality? Or is it further evidence of it? Does Arrow’s result explain why everyone is so dissatisfied with the government basically all of the time? In light of Arrow’s result, are some voting systems better than others? Does the fact that collective choice is incoherent mean that collective morality is also incoherent?

Next time, we will discuss Ronald Coase’s 1960 paper The Problem of Social Cost. If Arrow had read Coase, he would not have made the errors that he made on p. 334. See you in the comments!

The Use of Knowledge in Society

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Welcome to the second installment in our series of discussions of the Most Insightful Articles in economics. This post is going up a little later than I had planned, but hopefully you have stuck around. Today we are discussing Friedrich Hayek’s 1945 article The Use of Knowledge in Society.

Whereas Coase invites us to consider (and dismiss) a world without transaction costs, Hayek invites us to consider (and dismiss) a world in which all information is known to a single mind. In this world, Hayek points out, allocating resources in the most rational or efficient way is strictly a math problem, a more complicated version of some of the problems I make my Intermediate Micro students do. “This, however, is emphatically not the economic problem which society faces.” In the real world, information is dispersed, incomplete, and frequently contradictory. How can we use all this dispersed, incomplete, and contradictory information to make the best use of the resources we have?

When we engage in decision-making about resource allocation—whether collectively or individually—we are engaging in what Hayek calls “planning.” This raises two questions. First, how can those who possess some fragments of information communicate them in a useful way to the planner? Second, who should do the planning—one person or many people—and should it be centralized or decentralized? Under what arrangement can we make the best use of all the knowledge that is dispersed in society?

Most of the knowledge that exists in society is not universal, like F=ma. Instead, it is local; in Hayek’s words, “the knowledge of the particular circumstances of time and place.” Everyone knows at least something that no one else knows. For instance, I need a new holder for my EZ Pass because my old one melted in the sun. How likely is it that anyone else would know that? For society to make the best use of its resources, it must develop a method to collect and exploit local knowledge, not just universal knowledge.

It is essential that this method be robust in the sense of being able to withstand constant change. The world is not static. Statistical aggregates hide the innumerable small changes that occur. For instance, if my demand for eggs rises and my neighbor’s demand for eggs decreases by the same amount, my neighborhood’s demand for eggs has not changed. Nevertheless, the optimal allocation of eggs has changed; this suggests that statistical aggregates are not an appropriate basis for allocating resources.

“[T]he economic problem of society is mainly one of rapid adaptation to changes in the particular circumstances of time and place.” To solve the problem, we need some form of decentralization. Decentralized actors need to be able to 1) exploit their local knowledge while 2) making use of some sort of summary of the local knowledge possessed by others that is relevant to their decisions. This summary can strip out a lot of “why” questions. The actor does not need to know why some resource is more or less scarce than before, but he does need to know if it becomes more or less scarce.

The problem is solved by the price system. “[P]rices can act to coördinate the separate actions of different people in the same way as subjective values help the individual to coördinate the parts of his plan.” If there is some new and valuable use for tin, the price of tin will rise and people will economize on tin without even knowing why they are doing it. “The whole acts as one market, not because any of its members survey the whole field, but because their limited individual fields of vision sufficiently overlap so that through many intermediaries the relevant information is communicated to all.”

“We must look at the price system as such a mechanism for communicating information if we want to understand its real function…The most significant fact about this system is the economy of knowledge with which it operates, or how little the individual participants need to know in order to be able to take the right action.” This is not to say that the system operates with 100% efficiency. But it is nevertheless a marvel that changes occur and tens of thousands of people adapt by moving in the right direction, without any orders being issued. “I have deliberately used the word ‘marvel’ to shock the reader out of the complacency with which we often take the working of this mechanism for granted. I am convinced that if it were the result of deliberate human design…this mechanism would have been acclaimed as one of the greatest triumphs of the human mind.”

Hayek was more aware than most intellectuals of the extent and significance of our ignorance, and of the importance of extending the range of human cooperation beyond that which could be imagined by a single mind. The idea of a spontaneous order, that some phenomenon could be the product of human action, but not of human design, has been around since at least Adam Ferguson of the Scottish Enlightenment. It is striking that so many people persist in attributing both omniscience and deliberate design to society. We will discuss something else that people erroneously attribute to society next time when we review Ken Arrow’s 1950 paper, A Difficulty in the Concept of Social Welfare.

Suggestions for discussion: I have quoted extensively from this paper because it is very quotable. What are the best quotations that I have left out? Approximately how many bytes of local knowledge are there? Is it conceivable that a very powerful computer could solve the economic problem society faces? Are there other difficulties beyond the sheer quantity of information? What is it about undesigned phenomena that makes people uneasy? What is the greatest deliberately-designed triumph of the human mind and how does it compare in importance to the discovery of the price system? Is there any value at all to the math problems I make my Intermediate Micro students do? Does Hayek’s way of thinking about prices yield any insight into what happens when relative prices are distorted by taxes and subsidies? I look forward to your comments!