This is the second of two posts I am writing in reaction to Adam Martin, who wrote two responses to my essay about ways in which James Buchanan may be leading free market economists astray with his ideas. This post will focus on social welfare functions and debt.
To start, I am a perplexed that Martin claims social welfare functions are a “zombie” idea that was “buried” long ago by Kenneth Arrow and James M. Buchanan. 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.
With regard to Arrow’s “impossibility” theorem, Martin supports the unpopular Independence of Irrelevant Alternatives (IIA) condition. IIA is indefensible for at least two reasons. The first is that it requires pairwise comparisons. That is, it requires the decision maker to choose between alternatives in pairs, rather than in groups of three, four, or some other number. There is no basis for this assumption. It certainly doesn’t conform with reality, where people routinely choose amongst many options simultaneously. For this reason alone, we can disregard Arrow’s theorem.
Even if we assume the pairwise comparison restriction is reasonable, IIA has other problems. For example, it rules out the possibility of contingencies. In a previous essay, I used the example of how if the option to go to college becomes available, this could change a preference ordering I have with respect to how I spend my evenings (studying or partying). By excluding information from this alternative as “irrelevant,” it’s as if consequences are removed from consideration.
If Martin doesn’t like my college example, a common example found in the academic literature is third party candidates running in a political race, which can result in strategic voting. Some Florida voters in 2000 preferred Nader over Gore, but in a matchup between Nader, Gore, and Bush, they voted for Gore in hopes of preventing Bush from winning the election. They did this because they care about the outcome of the election. According to IIA, Bush running against Nader and Gore shouldn’t result in strategic voting of this kind. Again, consequences seem not to matter.

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.
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.
On the other hand, we can assign normative claims to such equations, labelling them “good” or “bad” or something else. To claim that following the decision-making apparatus of the market leads to good outcomes is simply another way of expressing the invisible hand of Adam Smith. I see value in both the positive and the normative enterprises.
Finally, with regard to debt, Martin compares my critique of Buchanan to a similar critique from the market socialist, Abba Lerner. I have no problem with this comparison. My criticisms here are not original, as others before me have pointed out the errors in this line of thinking. It may be worth noting that Ludwig von Mises agreed with me that government deficits are financed with real resources today and not through future taxpayers magically transferring resources to the present.
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.
To suggest I have a simple “state bad, market good” perspective or am somehow a market socialist-MMT sympathizer (which is it, by the way?) is not helpful. I acknowledge James Buchanan has made positive contributions to economics and that those contributions are sometimes undervalued by the mainstream of the profession. At the same time, in at least three areas: cost, social welfare functions, and debt, Buchanan’s theories are either logically invalid or missing pertinent information that would lead to alternative conclusions. The purpose of my original essay was to point out that for some reason Buchanan seems to be influential in these areas amongst the libertarian/Austrian/free market community of economists. This community’s attachment to these ideas could help explain the lack of progress observed in the Austrian economics research program in recent decades.
I proposed James Buchanan may be one important part of this story, but I am open to alternative explanations. It was in hopes of furthering this kind dialogue that my original essay was written. I still hope that discussion takes place.
James Broughel is a Senior Fellow at the Competitive Enterprise Institute with a focus on innovation and dynamism.
READER COMMENTS
Jon Leonard
Oct 12 2023 at 9:53am
If you really want to avoid Arrow’s theorem, probably better to object to the ordinal preferences part. One way of interpreting the theorem is along the lines of “If you discard the information about how much people care about their rankings, you’ve discarded vital information.” Sort of like how I can ask my wife “What’s your first choice?”, and also “How much do you care about it?” The answer to the second question sometimes matters, and the preconditions to Arrow’s Theorem discard that. So from a math formalism perspective, you don’t have to discard aggregating utility functions for that reason; though there are certainly theoretical and practical problems remaining, such as getting people to honestly report their preferences (either in the sense of tactical voting, or revealed preferences). IIA is certainly the easiest condition to discard philosophically, but it does still matter: “Spoiler candidates” occasionally have real impact, and the statement “I would prefer that adding or subtracting candidates that can’t win not change the outcome” is still plausible.
vince
Oct 12 2023 at 11:57pm
If you have a bad voting system, like most of the United States. Approval voting or ranked choice voting resolves the spoiler problem. Of course, the two-party system wouldn’t dare support it.
Jon Leonard
Oct 13 2023 at 10:33am
Ranked choice voting isn’t sufficiently specific: It also matters how the votes are aggregated. If aggregated using “Instant Runoff Voting”, which eliminates the candidate with the lowest number of fist-place votes until one candidate remains, then IIA still happens. Not only that, it can even under realistic conditions violate monotonicity: The candidate you voted for lost, but would have won if you hadn’t voted for them. Approval voting is indeed outside the domain of Arrow’s Theorem, but has its own quirks. In can elect a Condorcet loser, a candidate who would lose to every other candidate in pairwise elections. More frustratingly, it makes it hard to express your voting preferences in reasonable circumstances. If I think all candidates are at least decent, or all terrible, then my vote doesn’t count unless I lie, and sometimes theory means I need to randomize my vote. Range voting (like ranked, but you can have gaps and ties) would be my choice where a vote is called for; but non-voting mechanisms (like markets) are often better anyway.
clay shentrup
Oct 13 2023 at 11:05pm
approval voting is excellent. see voter satisfaction efficiency metrics from harvard stats phd jameson quinn to prove it.
https://electionscience.github.io/vse-sim/VSEbasic/
someone where mistakenly believed condorcet efficiency was a good metric. no.
vince
Oct 14 2023 at 1:51pm
Perfection is the enemy of the good. With IRV, you can support a third party candidate without throwing away your vote. Unless we replace our system, third parties play little role other than as spoilers.
Jon Murphy
Oct 13 2023 at 6:59pm
As a point of fact, at least one state does have ranked choice: Maine.
James Broughel
Oct 13 2023 at 9:42am
A common criticism of IIA is it rules out cardinality, i.e., intensity of preferences. So if you don’t like the ordinal preference assumption in Arrow’s theorem, dispensing with IIA is the place to start.
Pierre Lemieux
Oct 13 2023 at 3:23pm
James: We must not confuse the intensity of preferences of the electorate (or whatever rule maps individual preferences into the “social welfare function,” which is the thing challenged here) and the intensity of preferences of an individual. (An ordinal individual utility function has built into it any intensity of preferences one wants: just change the coefficient or the exponent of a given good.)
Pierre Lemieux
Oct 12 2023 at 3:42pm
James: I am very puzzled by your defense of the “social welfare function,” but it is not impossible that I am missing something. For example, you write:
Please do write the equation of the American “social welfare function.” I assume it is in utility space, not in goods space, because the latter would require a continuous and costless redistribution of income. One way or another, then, redistribution is presupposed and it requires a value judgment. See Paul A. Samuelson, “Social Indifference Curves,” Quarterly Journal of Economics, Vol. 70, No. 1 (February 1956).
If it is a social welfare function, it incorporates, by definition, the value judgments of all members of society (notwithstanding Arrow’s Impossibility Theorem). If it doesn’t incorporate the value judgments of all members of society–say, I think the weight given to my utility is too low–the “social” welfare function just represents the value judgment of Joe or Mossadegh, as Francis Bator would say (see “The Simple Analytics of Welfare Maximization,” American Economic Review, vol. 47, No. 1 [March 1957]).
This is a way to see why the “social welfare function” has basically disappeared from economic analysis.
James Broughel
Oct 13 2023 at 9:57am
The social welfare function that guides market activity is essentially a dual test that says for projects to improve social welfare, they have to benefit people in the aggregate (which for practical purposes means people in the future) as well as benefit certain specific individual(s) today. It’s a combination of the utilitarian social welfare function and the discounted utilitarian individual utility function from neoclassical economics. Some refinements may be in order, but that’s basically it.
It’s similar to a joint test you could apply to regulations, which I describe in a recent paper. That joint test says: To proceed, regulations must pass a regulatory budget test and a cost-benefit test.
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4235287
Matthias
Oct 24 2023 at 10:17pm
Also keep in mind that Arrow’s famous theorem only applies to deterministic procedures.
A little bit of randomness is a powerful tool. We can see that in eg statistical sampling.
Sortition is the traditional way to implement similar ideas in politics. You could eg fill up your parliament with 600 randomly selected volunteers, instead of having people vote for them. (If you want to fill a single position like a president or pick a single policy, I would suggest slightly more complicated procedures to danpen the variance of the process.)
Keep in mind that randomness is no panacea. There are generalisations of Arrow’s Theorem that put limits on what randomised selection processes can achieve too.
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