An interview with Paul Samuelson: welfare economics, “old” and “new”, and social choice theory

Those who are interested in Herbert Foxwell’s life, work and his relationship with Alfred Marshall are referred to Foxwell (1939); Groenewegen (1995, pp.622–627& pp. 670–679) and Keynes (1936).

[Paul Samuelson’s footnote] Long before these writers, J. S. Mill had recognized that the winners from free trade had (transferable) gains larger than the losings of the losers. Implicit in what today we call “Pareto optimality” is a parallel theme, and two decades before Pareto Edgeworth’s 1881 “contract curve” construction shows that he understood when deadweight loss did or did not negate the ability to “make compensation.” Already prior to 1930, my teacher Jacob Viner had anticipated the Kaldor–Scitovsky notions.

In an early response to Chipman (1976); Samuelson (1977b, p.177) made an almost sarcastic remark on Chipman’s assertion to the following effect: “This, I believe, involves an act of sympathetic charity since Pareto’s many writings are often obscure on what we now call Pareto optimality, and since expressions such as θ ₁(δU ¹)+θ ₂(δU ²)+ ··· are sometimes used by Pareto as positivistic-politics constructs and sometimes as vague Lagrange multiplier expressions relevant to the first-order conditions for being on the (“Pareto-optimal” points of the) utility-possibility frontier”. Subsequently, Bergson (1983, p.44) basically concurred with this verdict when he concluded that “it still seems difficult to quarrel with Samuelson’s ··· assessment of Chipman’s perception.”

For the sake of setting the record straight, two lengthy remarks on the literature may be in order at this juncture. In the first place, it seems fair to cite two of Arrow’s actual writings on the concept of a social welfare function. On the one hand, in “Notes on the Theory of Social Choice, 1963”, which Arrow appended to the second edition of Social Choice and Individual Values, he wrote as follows: “It would perhaps have been better for me to use a different term from ‘social welfare function’ for the process of determining a social ordering or choice function from individual orderings, although the difference between Bergson’s definition and my own was pretty carefully spelled out... . I will therefore now use the term ‘constitution,’ as suggested by Kemp and Asimakoplos. The difference, however, is largely terminological; to have a social welfare function in Bergson’s sense, there must be a constitution (Arrow (1963, pp.104–105)).” On the other hand, in his contribution to the book edited in honour of Samuelson, Paul Samuelson and Modern Economic Theory, Arrow referred to a passage from Samuelson’s 1981 Bergson Festschrift article, “Bergsonian Welfare Economics,” and firmly asserted as follows: “If there are ‘rumors that Kenneth Arrow’s Impossibility Theorem rendered Bergson’s “social welfare function” somehow non-existent or self-contradictory,’ they are indeed ‘quite confused’ (Arrow (1983, p.21)).” To substantiate this statement, Arrow observed that the Pareto quasi-ordering corresponding to each and every profile of individual preference orderings can be extended into a complete ordering by virtue of Szpilrajn’s classical extension theorem. Thus, it seems fair to say that the conceptual difference and interrelationship between the Bergson social welfare function and the Arrow social welfare function are by now well recognized by Arrow and whole profession. It may also be asserted that a wide recognition exists by now that Arrow’s general impossibility theorem does not disprove the existence of the Bergson social welfare function; it is a theorem on the non-existence of the Arrow social welfare function, or constitution, and not on the non-existence of the Bergson social welfare function. In the second place, although Bergson and Samuelson are in complete agreement on the conceptual distinction between the Bergson–Samuelson social welfare function and the Arrow social welfare function, as well as on the irrelevance of the Arrow impossibility theorem to welfare economics, there are at least two junctures where they seem to have chosen somewhat different directions. On the one hand, there is no room for compromise whatsoever in Samuelson’s purge of the Arrow impossibility theorem from the territory of welfare economics. In contrast, Bergson seems to have taken a somewhat more flexible stance in this arena. It is true that Bergson (1954, p.240) began his examination of “Arrow’s Theorem in Relation to Welfare Economics” by declaring that “[i]n my opinion, Arrow’s theorem is unrelated to welfare economics.” However, he was careful enough to note that there is a conception of the concern of welfare economics which allows a different interpretation of the Arrow impossibility theorem: “According to this view, the problem is to counsel not citizens generally but public officials. Furthermore, the values to be taken as data are not those which might guide the official if he were a private citizen. The official is envisaged instead as more or less neutral ethically. His one aim in life is to implement the values of other citizens as given by some rule of collective decision-making. Arrow’s theorem apparently contributes to this sort of welfare economics... (Bergson (1954, p.242)).” It is worthwhile to point out that Arrow (1963, p.107) fully endorsed this view of welfare economics which Bergson aptly identified. On the other hand, Samuelson (1947, p.221) admits no reason whatsoever to be concerned with the origin and/or nature of the values captured by the social welfare function: “Without inquiring into its origins, we take as a starting point for our discussion a function of all the economic magnitudes of a system which is supposed to characterize some ethical belief—that of a benevolent despot, or a complete egoist, or ‘all men of good will,’ a misanthrope, the state, race, or group mind, God, etc. Any possible opinion is admissible, including my own, although it is best in the first instance, in view of human frailty where one’s own beliefs are involved, to omit the latter. We only require that the belief be such as to admit of an unequivocal answer as to whether one configuration of the economic system is ‘better’ or ‘worse’ than any other or ‘indifferent,’ and that these relationships are transitive....” In contrast, Bergson (1976, p.186) is ready to be concerned with the nature of the values to be captured by the social welfare function: “The practitioner of welfare economics is in principle free to take any values as a point of departure, but the resulting counsel as to economic policy is not apt to be too relevant unless the values in question are held by, or can plausibly be imputed to, one or more officials concerned with the policies in question. Should the practitioner for any reason disapprove of those values, he may, of course, refrain from offering the officials any counsel at all.”

When I had corresponded with Professor Ian Little about this interview, he kindly made the relevant passages of Professor Samuelson’s letter available to me. Since it is of some interest, I am hereby citing it after receiving permission to do so from Professors Samuelson and Little:

Little to Suzumura: 29 March 2005

Dear Suzumura,

The relevant part of Paul Samuelson’s letter of 3 November 1999 is as follows:

‘Belatedly I have learned about the existence of your Collection and Recollections. Now that i have got as far as page 18, I wish to present you with a gift. On page 18, in your first complete sentence you seem to be lowring your flag— which is also my flag. This is because of the Kemp and Ng 1976 Economica paper.

I suggest you rewrite that sentence in all the subsequent editions of your Memoirs to read as follows: “I was quite right in my original position, even though Kemp and Ng in a 1976 Economica article purposed to prove the opposite. Professor Samuelson in a pre-homous letter has supplied me with a reprint of his cogent 1977 Economica refutation of the kemp-Ng contention, which serves as a confirmation of my critique of Arrow.”

Take care of yourself. They are not making many of our kind any more.’

I had regrettably not read Samuelson’s 1977 Economica article. If I had, I would not have ‘lowered our flag’. I promised him I would include his ammendent in any future edition of Collection and Recollections. However, I fear that the probability of there being another edition is extremely close to zero. Do with this what you like. I am very happy to know that Paul is still pre-humous. With best wishes.

Yours sincerly,

Ian Little

Let us recapitulate Samuelson’s criticism on Axiom 3 of Kemp and Ng more in detail.

Suppose society has a fixed total number of chocolates that could be partitioned between two specified selfish hedonists: say, 80 and 20, 50 and 50, 20 and 80, or more generally as any of two non-negative real variables (X chocolates to Person 1 or x chocolates to Person 2), where X+x=100 and neither is negative.... What is the meaning of the new Axiom 3 in this context? It says, “If it is ethically better to take something (say one chocolate or, alternatively, say 50 chocolates) from Person 1 who had all the chocolates in order to give to Person 2 who had none, then it must be ethically preferable to give all the chocolates to Person 2.” One need not be a doctrinaire egalitarian to be speechless at this requirement. Is it “reasonable” to put on an ethical system such a straightjacket? Few will agree that it is [Samuelson (1977a, p.83)].

It seems to me that the forcefulness of this criticism originates in the fact that we are informed of the material background of the following preference orderings of Person 1 and Person 2: where ε is a small positive number. If the informational basis of social welfare judgements is limited only to the profile of (ordinal) individual utilities and we are deprived of whatever non-welfare information about the social alternatives, the Kemp–Ng Axiom 3 may not be that easy to shoot down. It is in this sense that the Kemp–Ng Axiom 3 is said to be a counterpart in their single-profile framework of Arrow’s Axiom of “Independence of Irrelevant Alternatives” in his multiple-profile framework. Therefore, what is to blame may not be the Kemp–Ng Axiom 3 per se, but the narrow informational basis of ordinal welfarism.

There is a debate in the literature concerning the legitimate articulation of individual rights in the conceptual framework of social choice theory. As this debate has very little to do with the present issue of the ubiquitous applicability of the Pareto principle, we have only to refer those who are interested in this debate to Gaertner, Pattanaik and Suzumura (1992); (Gärdenfors 1981); Sen (1992); Sugden (1985) and Suzumura (1996).

According to Sen (1979, p.538), welfarism just represents an informational constraint to the following effect: “Social welfare is a function of personal utility levels, so that any two social states must be ranked entirely on the basis of personal utilities in the respective states (irrespective of the non-utility features of the states).”

Likewise, we find a passage in Bergson (1948, p.418), which reads as follows:

If the decision is in favour of consumers’ sovereignty, the welfare function may be expressed in the form, (1)W=F(U ¹, U ², U ³, ....). Here U ¹, U ², U ³, etc., represent the utilities of the individual households as they see them and W, the welfare of the community, is understood to be an increasing function of these utilities. The welfare of the community, then, is constant, increases or decreases, according to whether the utilities of the individual households are constant, increase or decrease.

If U ¹ has arguments about corn² in it, the weak separability is spurious (Added by P. Samuelson).

Among many post-Marshallian literature on the concept of consumer’s surplus, those who are interested should start their reading with Willig (1976) and Hausman (1981), which present rather contrasting messages with each other.

It was Joseph’s (1933) pioneering work that showed how U-shaped cost curves, belonging to replicable plants or to replicable firms under free entry, leads asymptotically to a horizontal unit cost curve for the industry and multiplant firms. Capitalizing on this seminal result, Samuelson (1967b) showed that the possibility of replication leads to “asymptotic-first-degree homogeneity” of the production function.