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The Economics of Kenneth Arrow (annualreviews.org)
84 points by everbody on Aug 28, 2019 | hide | past | favorite | 33 comments

It's a testament to the sheer breadth of Arrow's work that he essentially created the field of health economics and it's only given a cursory mention in the intro.

The below (not excessively mathematical) paper was light years ahead of its time, and is well worth a read even now.


Of all the things that I thought I would never see on HN. However, this is a technical review, and needs an advanced formal economics education to appreciate.

As a physicist, I found it to be a very pleasant and self-contained read that required very little knowledge of economics to appreciate. It does require some familiarity with mathematical notation, but the logic of the exposition was easy to follow. I would encourage more people to read this review.

I can try to answer any questions you might have.

The article highlights two main contributions of Arrow.

One is a question of how a society can make collective decisions. A classical answer is "utilitarianism" -- if a collective decision makes me happy more than it makes you sad, then we should do it. This requires society to be able to be able to measure exactly how happy something makes me and how sad it makes you. What if we can't make those kinds of measurements? Arrow shows that (under reasonable assumptions) we're stuck. There is no good rule to decide.

His other contribution was to "general equilibrium". A set of markets are "in equilibrium" if we can find prices so that supply and demand are equal in every market simultaneously. Do such prices exist, even in theory? Arrow showed that the answer is yes.

I don't have the background to actually ask this question, but don't general equilibriums turn out to be NP-hard, meaning that the market can't always compute the solutions with a reasonable about of information exchange?

In Arrow's version the inputs are continuous rather than discrete, so I don't know if NP-hard is the right criterion. There is a discrete version that is NP-hard, but I'm not sure you even have existence for that case. The continuous version of general equilibrium is as hard as solving an arbitrary continuous system of equations, which is probably pretty hard.

There are a bunch of criticisms of general equilibrium. Some of these were begun by Arrow himself. If you have prices that are out of equilibrium, can you adjust them to be in equilibrium? If you see the whole demand curve, then you could. But imagine you just know that there is unfulfilled demand for some goods, and excess supply for other goods. If you just make small adjustments in prices to lower excess demand or supply, will you eventually converge on market-clearing prices? Arrow showed that the answer is: it depends.

I have a mathematics background and feel like I could muscle my way through most of this if I wanted to. Admittedly this is based on reading the third section and skimming a lot of the rest, but it's well-written and pretty self-contained. Seems like you just need familiarity with mathematical notation and concepts like convexity and equilibrium.

Eh. The mathematical discussions hardly involve any maths that a typical engineer or comp sci major may not be familiar with. I'd be surprised if more than a fifth-ish of HN readers (not necessarily commenters) were unable to understand most of it.

You (or anyone else) aware of an intro to his work for mere mortals?

For social choice this is often used as an introductory book:

Wulf Gaertner: A Primer in Social Choice Theory. Oxford UP 2009.

However, I personally found his proof of Arrow's Theorem cumbersome and not so accessible, and prefer the following books:

Christoph Börgers: Mathematics of Social Choice. Siam Publications 2010.

Alan D. Taylor: Social Choice and the Mathematics of Manipulation. Cambridge UP 2005.

They are both concise and easy to follow if you're familiar with this kind of mathematics (for example, if you have a CS background). As for "popular science" books on social choice, I don't know of any good one and unfortunately have heard a few colleagues in philosophy misinterpret Arrow's Theorem. In that respect it's quite similar to Gödel's Theorems.

Arrow's work is covered (at a high level) in "Licence to be Bad, How Economics Corrupted Us" by Jonathan Aldred:


Edit: A really good book - once I finished listening to the audiobook version I went right back to the start and listened to it again and I'm going to order a paper version.

Economics is an imperfect field, but a major source of criticism of it is that many people fundamentally object to the idea that you can ask "is" questions about the economy. The only proper questions are "ought" questions, and since economics is mostly about "is" questions, it's automatically suspect.

There really were a group of economists that fit the "license to be bad" stereotype, such as Milton Friedman. But Arrow was not one of them.

One of the themes of the book is that a lot of results from people like Arrow, Coase etc. are misrepresented by those belong to that group. From what I remember it is actually pretty complimentary about Arrow and his work - the criticisms being aimed at those who take such things out of context to further ideological arguments.

Edit: I wish I had a paper copy so I could refer to it more easily!

One of the main criticisms of classical political economy (including Quesnay...) and indeed of modern neoclassical economics is that they pretend not to have any normative content despite, for instance in the case of modern economists, a theory of value whose historical evolution was a direct response to the normative power of labour theories. It is a specific set of ideas in response to a social formation, and it's one reason so many economists are allergic to talking about medieval or ancient economies.

Modern economics doesn't really have a theory of value, which is a 19th century concern. (Arguably, Quesnay was the first person to have a theory of value.) Or, if you prefer, economics have a subjective theory of value. This has some normative content -- if you think the purpose of human existence is the greater glory of God you will find economics pretty disappointing -- but economists no longer try to explain what things are "really" worth.

Your argument is an example of what I mean, though. The labor theory of value lost out on "is" grounds -- there are too many things it can't explain. Now some of the people who made this argument were right-wingers, so if you think that only "ought" questions matter, the fact that people with the wrong notion of "ought" made a contribution proves that the whole thing is morally bankrupt.

There are economic historians, but economists don't talk about medieval or ancient economies just because they don't have much to say. Historians are better equipped to understand them. Though a recent paper applied a trade model (the gravity equation) to predict the locations of Assyrian ruins, so maybe there's more to be done.

A "subjective" theory of value grounded on concepts such as "utility" is still a theory of value, just as a theory of subjective morality is still a theory of morality.

> Now some of the people who made this argument were right-wingers, so if you think that only "ought" questions matter, the fact that people with the wrong notion of "ought" made a contribution proves that the whole thing is morally bankrupt.

I don't think that's the case; there is a distinct break in value theory after Marx, which totally pulls him out of the classical tradition, because he has a "truly social" (as Patrick Murray puts it) theory of value - it is the recognition of its historical specificity. And while it's true that not only neoclassicals objected to the labour theory of value, the current status quo was create through ideological objections veiled as a "revolution". Nevertheless, it is a mistake to view Marx and post-Marx value theory (and here I must emphasize not only value theory but the theory of the value-form) as merely a way to explain prices rather than to explain social dynamics. The subjective theory of value stops before that point, and by limiting its scope to analysis of capital's shadow forms it relies either on ahistorical thought experiments (Robinson Crusoe?) or atomistic views of society. By limiting its scope the theory becomes almost tautological and contentless. The Sraffian objection to the labour theory of value, which is that values are redundant, not only fetishises its claimed ability to explain price, but misses the whole point of the theory. As such, some philosophers who hold to the theory even go as far as to say that it does not hold on the level of the individual commodity, but only on aliquots representative of the lot. It is as if these commentators stopped reading Capital on section 2 of chapter 1.

My point about history is this: economics, in claiming to be scientific, should therefore be held to the same standards as any other science, to explain not only the what but also the why, and for its explanation to be full and complete regardless of time. Its object is intrinsically historical in nature, but either by the "limiting of scope" I talked about before or even projecting the laws of specific social formations on all of history, the task is relegated to economic historians.

The subjective theory of value is just that if people think something has value, then it has value. For a Marxist, telling people they are wrong about their subjective judgements is irresistable, so I can see why they strongly reject it.

Value theory was entombed by Marx' followers. Marx offered a theory that was a) a positive theory on how the economy functioned, b) a normative theory on why capitalism was immoral, and c) a mechanical explanation on why capitalism was doomed. In terms of a and c it has failed. I don't even think this is a damning criticism of Marx -- Smith and Ricardo were wrong about plenty as well. The neoclassicals moved on from Ricardo, but Marxists have refused to move on and instead of enveloped "the theory of value" in a cloud of words to insulate Marx from criticism. Mysteriously, while Smith and Ricardo can be criticized, critics of Marx are always "missing the whole point of the theory".

Economics is not all of social science. The core of economics is the study of markets, though it touches on history, or psychology, or sociology. Markets were pretty peripheral for most of human history, and historical, or psychological, or sociological explanations are more important. Maybe you can explain everything that has ever happened for all of human history, but I sure can't.

>The subjective theory of value is just that if people think something has value, then it has value. For a Marxist, telling people they are wrong about their subjective judgements is irresistable

Marxists do not, in fact, tell people that they are "wrong" about subjective judgements, but they do say that you are wrong to say that my house is $1 even if it is valued at $100k. You are free to value it at $1. Further, both Marx's and Ricardo's theory stipulate the value of commodities given that they are already objects of demand. For Marx, the theory of socially necessary labour time is the window into that observation.

Subjective value theory actually aims to do something more - to accumulate all these preferences in order to explain price. It reconciles objective facts about the world with the fact that people have preferences - and Smith, Ricardo and Marx are no different in that respect.

>In terms of a and c it has failed.

Plenty of Marxian economists and philosophers of economics would support, with various strength, both a and c. For instance, they argue that value comes to the forefront in explaining crises, and several empirical models (such as by Shaikh and Cockshott, although I have my reservations about their theories) confirm high correlation between the best measures of labour values we have and the prices actually observed in those sectors. That's not to say that the theory explains everything (e.g why a Nike shoe costs more than an Adidas) but it was never meant to - Marx stipulated that it ought to explain the value of commodities, not the price, and that the price-form, through such things as copyrights and patents, obscures the objective labour content. The key is that (1) it doesn't make sense to apply Marx's theory of value to individual commodities, (2) Marx's theory explicitly applies to freely reproducible commodities under capitalist modes of production. Thus, collector's items (like fine art) and items not freely reproducible (like Nike shoes) are not covered. There is, however, some work in incorporating those, in the notion of "general intelligence" and the prominence of financial labour.

>Mysteriously, while Smith and Ricardo can be criticized, critics of Marx are always "missing the whole point of the theory".

Not at all, but Marx can't be criticised on the same terms, because his theory is fundamentally different. If you want to criticise Marx then you can't do so on the terms of Smith and Ricardo - there is a reason, for instance, that despite his encyclopedic knowledge of political economy, Marx claimed that the tendency for the rate of profit to fall was one of his proudest achievements - despite it being in Ricardo.

>Markets were pretty peripheral for most of human history, and historical, or psychological, or sociological explanations are more important.

I disagree. The materialist perspective is that men make history, but they do not do so as they choose, only under circumstances transmitted from the past. The leap from commodity production to generalized commodity production in capitalism was decisive, and as Marx and Darwin agreed, the past is the key to the present.

"c" is as decisively refuted a claim as any in history. The Jehovah's Witnesses have a better case that their claim that the world would end in 1914 came true.

Value theory is an intellectual dead end, one that ultimately doomed Marxist economics. That's why it's necessary to say it's not about any of the things that people thought it was about for the first hundred years, but different things that suddenly became important post-Sraffa. That's why it's necessary to say that Sraffa was "missing the whole point of the theory" -- because Sraffa ultimately killed the theory.

The standards in philosophy and the social sciences are different. A philosopher can proclaim that the English Civil War or the Glorious Revolution were the result of class struggle. A historian has to actually get in there and study the evidence, and up close grand narratives tends to fall apart.

The fact that expected utility theory isn't nearly as scrutinized as the labor theory of value, whilst being at least as flawed, tells you something about the "value free" nature of modern econ.

Expected utility theory, if anything, is more scrutinized than the labor theory of value. They gave Kahneman the econ Nobel for (among other things) documenting empirical failings of expected utility.

It... is? The difference is that the labor theory has been thrown out as unsalvageable, whereas expected utility theory is useful enough in some theoretical applications to stick around.

The question is whether the grounds upon which it was thrown out (which relate to specific problems) are therefore sufficient for it to be "unsalvageable". Nonetheless, as I already mentioned, the pretension that economics lacks normative content gives the false impression that ideas must be discarded because they are not scientifically valid rather than for ideological reasons.

That's the thing, though -- the labor theory isn't just "not scientifically valid." It clearly doesn't describe what is -- it's not how people value things, and it doesn't make sense as a description of what ought to be.

The LTV was never intended as a description of what "ought to be" (in fact, Marx cautions against such use), and it was intended to describe how things are. The idea is that people do value things according to their socially necessary labour content, and that this mechanism works "behind the backs" of all members of society. I'm curious in what way it isn't scientifically valid.

The LTV wasn't thrown out because it fails to describe how things are, because soon enough marginalists realize that the same criticisms actually apply to their own theory. It was thrown out (mostly by Samuelson and his pals) of specific issues: the transformation problem, the generalized commodity exploitation theorem, and by extension the Okishio theorem, all of which have been addressed in the Marxian economic literature.

LTV is clearly normative, and it's why people still try to revive it. The idea that factory owners are exploiting their workers has a certain intuitive appeal as a moral proposition.

The LTV wasn't exactly thrown out -- there are situations where marginalism and the LTV exactly coincide -- but it was superseded because outside a narrow sphere it becomes incoherent. The classic example is technological substitution -- if you have two ways of making something, one that is capital-intensive and one that is labor-intensive, then you will probably pick the one that's cheaper. So you can't calculate the labor content of a good independently of prices.

The specific issues you enumerate are issues within Marxist economics in general. The LTV was superseded well before Samuelson's paper on the transformation problem.

Spoken like someone who truly doesn't know the history of the economic field.

The history of value theory is well explained in this paper by economist Alan Freeman: https://mpra.ub.uni-muenchen.de/48646/1/MPRA_paper_48646.pdf

It seems like an ok reading of the history on first glance but it is the Marxist perspective. I suppose necessary to understand the heterodox viewpoint.

> So central to capitalist reality is this motor of growth that it lies behind both imperialist conquest and the launching of those periodic prolonged booms of which the Belle Époque and the post-war Golden Age are the most recent examples.

This is a pretty ridiculous conclusion that is demonstrably false.

I don't know much about the examples myself. I'm interested in why the author is wrong.

Marxist value theory basically died out in the 70s, which Freeman basically concedes in the "The Marxists Divide" section. His TSSI is an attempt to resusitate the theory, but it has found few adherents.

It is worth noting that the TSSI isn't the only one around any more, though - nor is the strictly quantitative interpretation of value theory. The TSSI was constructed as an interpretation to solve the transformation problem, but there's Dumenil's New Interpretation now and Fred Moseley's Macro-Monetary Interpretation. It is not surprising that Freeman would make such a concession as an economist rather than as a philosopher, where Marxian value-form theory flourished in Germany and Japan during the 70s and 80s and still to this day.

When reading the section on social preference I couldn't help but think of Saaty's Analytic Hierarchy Process and its pairwise comparisons. Would that not satisfy Arrow's three requirements? It satisfies the first, since it functions regardless of the preferences themselves (though the consistency matrix may suffer); it satisfies the second on its face, since if everyone prefers A over B, then A will be ranked higher under AHP; and it satisfies the third, since only pairwise comparisons serve as inputs to the algorithm.

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