In his most recent post, James Broughel was perplexed with my claim that social welfare functions are a “zombie idea.” He writes: 

Maybe this is true amongst libertarians, but social welfare functions are alive and well in numerous areas of modern economics, including climate change economics, optimal tax theory, and macroeconomic growth theory, just to name a few. Neither Arrow nor Buchanan buried them, and it may be a sign of an insulated culture amongst Austrian economists that Martin incorrectly thinks they did.

When I said that social welfare functions are a zombie idea, I did not mean that economists did not still use them. The labor theory of value is a zombie idea, and yet Marxists still publish as if it were not. I am well aware that various subfields of public economics / welfare economics make use of the idea. But all good economists are as free to ignore them as they are to ignore the astrology section in their local newspaper.

Broughel can of course have a different judgment. But saying that Austrians’ rejection of social welfare functions is what is holding them back is a big empirical claim. Perhaps he should look over the articles and books that the Society for the Development of Austrian Economics has recognized over the past decade before pronouncing that Austrian economics has stagnated. I doubt economics would be in better shape if those scholars had spent the past decade churning out social welfare functions.


Broughel’s Broken Arrow Problem

Broughel has misinterpreted my critique of his argument as a defense of the relevance of the “Independence of Irrelevant Alternatives” condition. This is not correct. As explicitly stated, I agree with Buchanan that it was wrong of Kenneth Arrow to think that transitivity would apply to collective actions. What I objected to was Broughel’s ineffectual objection to the condition.

Broughel’s objections all amount to saying: “what if the irrelevant alternative isn’t irrelevant?” He can multiply these thought experiments as much as he likes, but as long as the experiment posits the relevance of an alternative it fails to engage Arrow. I find myself in the odd position of defending Arrow, who was correct in his formal claims but incorrect in his judgment of their relevance, against this misunderstanding of his formal claims. If you’re going to beat up on Arrow, do it right.

Broughel’s next line of argument is a straightforward logical fallacy:

IIA is too rigid. Any new information contained in third options is ruled out as irrelevant by assumption. There can be no reaction in the form of a reordering of preferences based on new information contained in third alternatives. It’s as if time stands still. 

We should not be surprised therefore that Arrow’s theorem has had such considerable influence in areas like neoclassical equilibrium analysis and, yes, cost-benefit analysis, where analysis takes a fixed, static perspective constituted from the viewpoint of a single moment in time.

Let’s take the second paragraph before the first. Broughel argues that cost-benefit analysis is based on Arrow’s work because it “takes a fixed, static perspective.” I agree that standard cost-benefit analysis takes an equilibrium perspective. Broughel’s argument is then:

  1. Arrow’s theorem assumes time stands still.
  2. Cost-benefit analysis assumes time stands still.
  3. Therefore, cost-benefit analysis assumes Arrow’s theorem.

I am happy to grant that (a) and (b) are both true. But this argument is a straightforward instance of the fallacy of the undistributed middle. Consider another example:

  1. Adam is a GMU graduate.
  2. James is a GMU graduate.
  3. Therefore, James is Adam.

I suspect that James and I recoil from this prospect equally. There might be all sorts of problems with cost-benefit analysis, but they ain’t Arrow’s fault.

Moving back to the first paragraph: I applaud Broughel’s pseudo-Austrian emphasis on dynamics in these paragraphs. But dynamics don’t make constructing a social welfare function easier. Quite the opposite. They render even a coherent social welfare function—if it happened to exist at a moment in time—ephemeral.


Social Welfare Functions Just Are Normative

With regard to my claim that a social welfare function underpins market activity, there is both a positive and a normative side to this. On the one hand, we can write down the particular equation, or equations, that correspond with what we observe. In that sense, social welfare analysis is a form of positive analysis. There need not be any value judgments.

This claim is wrong.

Social welfare functions are one proposed method for aggregating preferences. Efficiency is another method for aggregating preferences. As noted in my previous response, the goal of mid-century welfare economists was to combine these two ways of aggregating preferences to identify social states that satisfied multiple normative criteria. The ideal was to base at least two distinct normative judgments on the same set of preferences.

Here’s the problem with individual preferences: you and I disagree. You think that Zack Snyder should be allowed to complete his vision for the DC cinematic universe while I am happy to see a competent filmmaker like James Gunn take the reins. What is the socially preferred choice?

There is no answer to this question that is not normative. How do we add up differing preferences? Any answer to this question involves criteria about which preferences count and how much they count. Willingness to pay is one criterion. Interpersonal comparisons of utility are another. Adam is right and you are wrong is a third. We can envision infinite options, all of which invoke value judgments.

Social welfare functions are normative criteria by which social states are judged. This is why Broughel’s Bush vs. Nader vs. Gore example is confusing. To say that voters won’t produce transitive results is not an indictment of a particular social welfare function but rather an indictment of said voters, if one takes that social welfare function seriously.


Deficit Financing Still Matters

Says Broughel, 

I also never suggested that the ability to roll over debt turns “government spending into a magic goodies creator.” However, rolling over debt can prevent the government from ever having to raise taxes in the future to pay debts. Faster economic growth can do the same. These facts in themselves contradict the assertion that deficits necessarily “reduce the present discounted value of assets held by individuals in the present.” There is no reason why, on net, this needs to be the case.

This is not to say our actions do not impose costs on future people. In fact, the costs we impose on the future generations are a paramount concern to me. But it’s not whether spending adds to the deficit that matters (within reason, course), but instead the composition of spending that is important. Buchanan turned economists’ attention toward little pieces of paper whilst simultaneously propping up the populist myth that deficits are paid for by future generations. This focus on deficits distracts us from the more important issue of how money is actually spent.

In the particulars, here, Broughel and I are verging on agreement.

Two points of clarification: in raising Abba Lerner, I was not trying to imply an affinity between market socialism and Broughel. As I tried to make clear, I think Lerner is partly right in his article. Lerner is a genius and not coincidentally a Hayek student. And by invoking MMT, I am simply pointing out the extreme version of Broughel’s view, which I don’t think he in fact holds, but is a useful point of reference for Econlib’s general readers.

I admit I was poking the bear when I used the phrase “magic goodies creator.” I used it twice on my macroeconomics comprehensive exam in graduate school and am proud to report that I only got a marginal pass. More than a marginal pass would indicate too much time studying macro. But let’s dig into why he is wrong to ignore deficits.

Let’s say that in period 1 the government decides to borrow instead of taxing. Then in period 2, the government confronts the choice again: tax to pay the debt off now or issue new debt to pay off the existing debt. This obviously just returns us to the same position as period 1. The government can either impose future taxes and thus alter the period 2 NPV of current assets or it can tax the period 2 generation to pay off the holders of debt. Either way some burden is imposed on period 2 citizens (unless they perfectly foresaw the future tax burden, in which case it was incurred in period 1). Scarcity is the ultimate binding constraint. Because of Ricardian equivalence, the ability to roll over the debt is irrelevant. 

Both the nature and the financing of government spending is relevant to the pros and cons of government spending. More importantly, the insight we get from Buchanan is that the possibility of deficit financing itself changes what government will spend money on and how much it will spend. The nature and quantity of spending is endogenous to the financing rule.


Once More on Cost

Does cost attach to actions like naps or things like widgets? The whole point of Buchanan’s Cost and Choice is that which one is correct depends on whether you are using cost in a predictive science or in a theory of choice. Hence the opening chapter about the deer-beaver model and the confusion resulting from conflating these distinct concepts of cost. 

What Broughel seems to want is a third concept of cost: a normative concept. Social cost. He might deny that his favored concept is normative, since he denies that social welfare functions are wholly normative. Since social cost necessarily involves aggregating preferences, it is necessarily normative.

So now we have three concepts of cost. But Buchanan is still right. The word simply means different things in different theoretical contexts. Insisting that cost is subjective or objective or normative misses the point. The point is not to conflate the different meanings.

Perhaps Broughel will be happy to know that I am more than willing to criticize Buchanan on this point. After a careful analysis of choice-influencing costs (cost in a theory of choice) he admits into the domain of subjective economics choice-influenced costs, or what I have called losses. His justification is that both losses and opportunity costs exist in “utility space.” 

I don’t doubt that Broughel has met dogmatic Austrians that say you can’t do cost-benefit analysis. I tell my own students that “BUT SUBJECTIVISM” is a bad argument because it conflates normative subjectivism with subjectivism in a theory of choice. Whether social cost is a valuable concept is simply a different question than whether costs are subjective at the moment of choice. 

Buchanan objected to social cost because he objected to utilitarianism. But one could easily be both a radical subjectivist about cost and a utilitarian. It is simply a matter of normatively picking out which costs and benefits count when aggregating preferences. I am a radical subjectivist in one sense but am happy to say that some preferences are just bad, such as preferences for listening to Nickelback or for using social welfare functions.


Adam Martin is Political Economy Research Fellow at the Free Market Institute and an assistant professor of agricultural and applied economics in the College of Agricultural Sciences and Natural Resources at Texas Tech University.

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