Professor Kenneth Arrow died on February 21, 2017, at the age of 95. He was widely regarded (along with Paul Samuelson, John Hicks and possibly --- depending on tastes --- John Maynard Keynes, Milton Friedman and Gary Becker) as one of the greatest economists of the 20th century. He also happened to be my favorite economist of all time.
Professor Dipak Banerjee, my teacher, introduced me to Kenneth Arrow in 1974, who appeared (much in the manner of Hindu god[esses]s for whom my mother had special reverence) in the form of a small yellow paperback. I acquired Social Choice and Individual Values from Dasgupta and Co. of College Street, and still have it. I was a first year undergraduate. That little book was a repository of the most profound logical thought. I had never seen anyone distill what appeared to be an abstract question in political economy into a theoretical device that cut sharply, and cut deep.
What was the question? Briefly, it was well known from the so-called Condorcet paradox that majority voting could produce nasty cycles in choices, even when the individual preferences involved in that voting process were perfectly reasonable. That led to the question: was there any political system that could “reasonably” aggregate individual preferences? Now think about the question for a second: we know what majority voting is, but there is in principle an infinity of other systems. How could one ever formulate such a problem, let alone attempt to answer it? The very formulation — as axioms placed on an abstract mapping that connected individual preferences to their social counterpart — was sheer genius. But the apparatus was not only beautiful: it could also speak. It argued that under the minimal desiderata placed on the aggregator, there was no way of putting together individual preferences into a satisfactory social ordering; one that was cycle-free.
Arrow had received the Nobel Prize just two years before this encounter with him. He was just 51 years old, by far the youngest Laureate then (or since) in Economics. I ran off to the National Library in Calcutta to dig out the Nobel citation, excitedly anticipating a homage to my beloved Impossibility Theorem. Yet oddly, the The Nobel citation mentions Arrow’s monumental theorem only at the very end, and almost in passing. It focused instead on Arrow’s (and Hicks’s) contributions to general equilibrium theory:
“[Arrow] provided the basis for a radical reformulation of the traditional equilibrium theory. Through this reformulation, which was based on the mathematical theory of convex sets, the general equilibrium theory gained both in generality and in simplicity… The model presented in this paper became the starting point for the major part of further research in this field. Among Arrow's many important contributions should also be mentioned his development of the theory of uncertainty and its incorporation within the frame of general equilibrium theory and, furthermore, his analysis of the possibilities for decentralized decisions in a society where the price system is fixed by the central authority… As perhaps the most important of Arrow's many contributions to welfare theory appears his ‘possibility theorem,’ according to which it is impossible to construct a social welfare function out of individual preference functions.”
This was disappointing as far as my current passion was concerned. But it was also exhilarating: because there was more! (Later, I realized just how much more.) Back I went to Professor Banerjee. I wanted to know why general equilibrium was not just a question of several equations in the same number of unknowns, and what all this was about “the mathematical theory of convex sets.” In response, Dipak-babu helpfully produced another small tome by Gerard Debreu. This was based on the work with Arrow. Though certainly more mainstream this time in its questions, the techniques went way over my 17-year old head....
As a graduate student, reading all this in late 70s and early 80s, I viewed Arrow as a thinker who could both ask the deepest questions in economic and political philosophy, and at the same time use mathematical arguments with ease and utility to answer them to a substantive degree. This was someone who could put past accomplishments into perspective, leave them behind, and seek to look beyond to newer and more difficult concerns. Such were the nature of his forays into questions of incomplete information, pervasive externalities, increasing returns and interpersonal equity. There was just one word for it: inspirational. The inevitable reaction was not long in coming: I wanted to be like Ken Arrow. Surprise surprise, that was not destined to happen. But something else did: I had the immense good fortune to become his colleague at Stanford.
I was at Stanford on a job flyout, at the very beginning of 1982. I had been warned about the meeting with Arrow. Apparently, all I had to do was tell him the assumptions of my model and then, before I could get any further, he would proceed to tell me all the results that could conceivably be proved from those assumptions. This was unnerving news. But nothing of the sort happened.
I walked into his office. It was small and cluttered, full of books that went up high. It had a vertical rather than horizontal feel. Arrow himself gave the opposite impression. He was shorter than I had expected, strong, rooted to the ground. The man seemed to be in constant motion. He was both brisk and welcoming. He was wearing brightly colored suspenders, and there was an immense bicycle helmet on his desk. (I did not then realize that these, along with the perennially flipped pencil at seminars, would be an intrinsic part of my later memory of him.) I began talking about my work. It was a bit of an out-of-body experience; I could see myself talking to him. Arrow listened very closely. There was an intensity of gaze that never wavered, except when he would start speculating, during which he would look up at the ceiling and back to me. He asked questions non-stop. He talked very fast, the words tripping over one another, the tone uneven, the sentences clearly struggling to keep up with the flow of thoughts. He didn’t exactly anticipate my results. But after 15 minutes, I had a second eerie sensation: that I was talking to someone who had thought about my problem for a very long time. This was a weird feeling that I came to associate with Arrow over the next few years.
Less enthusiasm was shown [by Arrow] towards the neo-Ricardians. Once I had mustered up enough courage, I would talk with Arrow with complete freedom, and before long I had told him that I had once spent an entire day with Piero Sraffa at Cambridge, and that he had given me a signed copy of his book ...I told [Arrow] that I admired the book for its apparent demonstration that the distribution of income across labor income and profit could not be fully pinned down by economics — that some reference to the political system was needed. Arrow looked at me with a mix of irritation and pity: “I’ll get you out of that soon enough.” And of course he did convince me that Production of Commodities By Means of Commodities had an extra degree of freedom in it that generated a fake indeterminacy, though I still harbor a sneaking suspicion that Sraffa was on to something.--Debraj Ray "Kenneth Arrow, 1921-2017"
Of the quick, first round of obituaries of Arrow, the one by Ray, himself a leading economist (recall that I have remarked on his criticism of Piketty), stands out for its excellence mixing intellectual, psychological, and sociological observations on the significance and nature of Arrow's scholarly life as seen by professional economists today. It's worth reading in full (including the stuff on the scale and content of some of Arrow's many contributions to economics as well as Arrow's relationship to socialism) not the least for acquiring a flavor of the anecdotes that circulate around Arrow's life. One other reason why I quote so much of it -- despite some names and issues being obscure to philosophers -- is that Ray's manner of evaluation is so familiar to us professional philosophers (genius; deepest questions; out-of-body experience; intensity of gaze; talking to someone who had thought about my problem for a very long time, etc.) They reminded me of the tenor of the recent remarks about Derek Parfit (who, to be sure, published much less than Arrow and was probably slightly less central to the disciplinary formation in philosophy than Arrow was in economics).
In the final sentence of the quoted paragraph (which is not the end of the obituary), Ray allows himself one very modest reservation: "I still harbor a sneaking suspicion that Sraffa was on to something." Now, in context, Ray is remarking on the fact that Arrow (then already very famous) "was teaching History of Economic Thought" and that among the history covered Arrow favored Cournot.* Ray is reporting on a series of exchanges with Arrow some time in the early 1980s (so more than thirty years ago). Even then Sraffa's work was not setting the agenda and conceptual framework for professional economics (in the way that Samuelson and Arrow did and to some extent still do). Even if we allow historical distortion, Arrow's irritation at the interest of his younger, talented colleague in a by then discarded project is notable.+
As an aside, as it happens in 1991,** Arrow published (inter alia) about Sraffa's role in the (Marxist leaning) reception of Ricardo, which influenced the way Keynes was assimilated, especially at Cambridge (and especially by Joan Robinson). In the paper, "Ricardo's Work as Viewed by Later Economists," Arrow self-describes himself as "a practicing theorist, not a scholar in the history of economic thought." Yet, Arrow shows great command over the historical material and the history of Ricardo reception.** One criticism of Sraffa by Arrow is that Sraffa is "indifferent to [Ricardo's] the full employment hypothesis, though one would have thought a position on this question to be basic to the formulation of a coherent model." Another (more implicit) criticism of Sraffa is that "the possibility of diminishing returns was dropped by Marx and equally by Sraffa and Joan Robinson."
To return to my main point. Ray reports his own "sneaking suspicion that Sraffa was on to something" despite being exposed to (presumably conclusive) proof that Sraffa's attempted formal "demonstration that the distribution of income across labor income and profit could not be fully pinned down by economics" was incoherent or unsupported. Lurking in the background is not just the question of the role of politics in determining economic outcomes, but also the question of disciplinary autonomy and closure. One would have liked to hear more about Ray's suspicions here -- Ray is the editor of the American Economic Review so he plays a non-trivial role (among many others) as gate-keeper and standard setter in the profession.++
But leaving aside the question of Arrow's criticism of Sraffa, I think the phenomena that Ray puts his finger on is more widespread (and also prevalent in philosophy): often the technically superior person will refute a theory Y -- and let's stipulate these are not straw-man versions of Y --, and [this matters] will do so in ways such that new recruits will not drift toward Y or variants of Y, and yet the insight (u) that gave rise to Y may not have been adequately handled.*** This is due to the fact that the relationship between (u) and Y is not a tight mapping. Much formalization in economics (recall my piece on the criticism of Harberger by MA. Khan) and all explication (recall my post on Leitgeb, Carnap, and Tarski) have some degrees of freedom and judgment about the way in which a would be Y captures (u), especially if (u) is interesting. After the refutation of Y, the partisan of (u) is often told to keep quiet until she can offer a successor to Y that is not prone to the fatal flaws exposed of Y (by technically superior person). [This is even so in circumstances where Y could handle stuff in ways that no other present theory does, as in cases of Kuhn loss (recall).]
If (u) is something non-trivial, even important, it can be problematic that a discipline avoids working on developing successors or replacements of Y. And so, ideally, one would wish that the refutation of Y would be accompanied by some theoretical articulation that does justice to the significance of (u). [Notice that this is true of formal and non-formal theories of Y.] But currently the incentives and norms of many disciplines work against this and we are not encouraged to reflect on how this might be improved.