Samuelson’s social welfare function and Buchanan’s critique: the struggle with normative science

Abstract

A history of the transformation of public finance into public economics necessarily involves an understanding of the tension between positive and normative statements, that is a history of how public economists dealt with Robbins’s requirements that economists should not make normative statements. In this paper, we propose to contribute to this history by discussing and comparing the works of two major economists of the 20th century, Paul Samuelson and James Buchanan. We show that they both use the same strategy to deal with the positive/normative tension: they adopt a reduced scale of analysis to escape normative judgements – the family for Samuelson and small groups (clubs) for Buchanan. What they do manage at this level is to create examples or models which remove that normative response from the theorist, and ascribe it to the participants. The normative views of the theorist are not involved. Yet, when one shifts back to a larger scale, the positive element of the analysis is less clear, at least in Samuelson’s work.

Keywords:

• Samuelson
• Buchanan
• Robbins
• Arrow
• public economics
• positive
• normative
• science
• idealism
• utilitarianism
• scale issues

JEL codes:

• B21
• B22
• B31
• B4

Acknowledgements

A preliminary version of the paper was presented at the workshop From Public Finance to Public Economics, Graz, 5–6 September 2022. We wish to thank the participants and also two referees for very insightful comments. We also thank Roger Backhouse, Maxime Desmarais-Tremblay, J. Daniel Hammond, and Marianne Johnson for their equally relevant and extremely useful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The use of Robbins as a point of reference is simply the result of his being referenced by Samuelson and Buchanan at critical points in their discussions. It is not to downplay the importance of other thinkers developing similar lines of argument, even those on whom Robbins himself may have relied, such as Weber.

2 For the sake of concision, we are ignoring elements that complicate this simple overview. They will be addressed in the body of the paper.

3 “It is impossible to form any concept of 'social efficiency' in the absence of some general measure of value” (Knight 1923, 580–581).

4 Samuelson “cherished the image of the economist as a theoretician that we encountered… in looking at Lionel Robbins” (Maas 2014, 100). More specifically, Samuelson recalled Robbins as “not only important for my own thinking, but was important for the whole profession” (in Suzumura 2005, 331).

5 The "bad element" would be Robbins's Austrian leanings, which Samuelson considered in many ways more extreme than the views of the Austrians themselves.

6 The point is put forward with great clarity by Roger Backhouse who insists on the importance of ethics in Samuelson’s work. Backhouse (2017, 226) quotes Samuelson who wrote that “welfare economics implied making ethical judgments.” (1938, 261) See also Backhouse 2021.

7 In a 1949 book review we find, "freed from the obscurities of geometry and Paretian French, the new welfare economics stands revealed as being merely a set of incomplete necessary conditions whose whole raison d'être disappears if the additional ethical conditions are not adjoined." (Samuelson 1949, 372)

8 The social transition implication is reinforced here, “What we have been calling a family is after all but a disguised version of society itself – i.e., a collection of more than one person.” (Samuelson 1956, 12)

9 As evidence of Samuelson's preoccupation with Arrow's critique, there is this in the (1956) paper. When discussing whether the titular head of the family might be dictatorial – whether the family’s demands would only reflect "his or her consistent indifference curves" – Samuelson argues that this notion isn't a reasonable view of family life. There is, instead, a "family consensus". But then he notes "Perhaps Arrow will produce a proof that such a consensus is impossible." (1956, 9)

10 For an excellent exploration of the Samuelson/Arrow tension over this issue, see Igersheim (2019) "The Death of Welfare Economics: History of a Controversy". For a pre-Arrow assessment of Samuelson's welfare ideas, see Backhouse (2021).

11 He dates it from roughly the beginning of the century.

12 “Democratic moralists have inveighed against the pretensions of experts for more than a century. The converse problem has been less noticed, though it is even more consequential: that what is not mainly technical is often understood as outside the proper domain of science and therefore as not amenable to empirical enquiry or reasoned argument.” (Porter 2009, 293)

13 Backhouse (2017, 23) explains that Samuelson “made the decision to become an economist and to approach the subject using mathematics” when he “was as an undergraduate” at Chicago. To Mirowski, Samuelson can be said to have “set the tone for the 'appropriate' demeanor to be displayed vis-a-vis Science in the twentieth century, and this involved the construction of an elaborate rapprochement with the developments in twentieth century physics. However much the average economist cited Milton Friedman’s 1953 essay on 'method', it was Samuelson, and not Friedman, who by both word and deed was responsible for the twentieth century self-image of the neoclassical economist as 'scientist'." (1989, 182) For a detailed look at Samuelson's graduate education and the influence of physics on his economics, see Carvajalino 2018.

14 Indeed, Arrow’s 1951 mathematics were different from Samuelson’s. Thus, here was an economist who was challenging Samuelson on two grounds, economics and mathematics. And the contrasting (incommensurate?) mathematical approaches may have contributed to the enduring debate this critique has generated (we thank M. Desmarais-Tremblay for his comment, who led us to write this note).

15 In his 1956 article, Samuelson does imagine Arrow making an objection within the essay, and the whole model of the family directly avoids Arrow's critique. See note 8 above.

16 Samuelson here is leading to imposition from above, or decisions made by elites for the population at-large. We can complete this comparison by seeing that Buchanan objects to both these (Bergson’s and Samuelson’s) scenarios. Buchanan sides with Samuelson in seeing individuals as inherently self-interested (Economic Man), but disagrees with his solution of elites. The reason is that elites are not an exception to the charge of being economic men. Neither will individuals maintain Bergson’s disinterested view (Social Man) – from their current vantage point. This vantage-point issues is solved, however, or greatly attenuated at least, through Buchanan's introduction of the constitutional perspective.

17 "In most of the cultures actually studied by modern economists the fundamental unit on the demand side is clearly the 'family'…." (1956, 9). For the family as a parallel to a full economy, see the development of this idea in Desmarais-Tremblay (2021). He traces the idea back to Aristotle: "Hence an economy, generally speaking, corresponded to the early modern counterpart of the Aristotelian authoritative model of the family." (188)

18 It is unclear whether Samuelson recognizes that a key dimension of his argument – altruism – is also a vital component of utilitarianism. "If, however, the parties are conceived as perfect altruists, that is, as persons whose desires conform to the approvals of such [an impartial] spectator], then the classical principle would, of course, be adopted. The greater net balance of happiness with which to sympathize, the more a perfect altruist achieves his desire. Thus we arrive at the unexpected conclusion that while the average principle of utility is the ethic of a single rational individual (with no aversion to risk) who tries to maximize his own prospects, the classical [utilitarian] doctrine is the ethic of perfect altruists." (Rawls 1971, 188–9) Smart also affirms that one of the "ultimate attitudes" to which a utilitarian must appeal, and which he holds in common with others, is "generalized benevolence." (Smart and Williams 1973, 7) Samuelson (and Bergson), however, sharply disassociated their analysis from utilitarianism. (Bergson/Burk 1936, 42, note 1; Samuelson 1937, 161)

19 And the reference to Arrow (quoted above) occurs at the end of this paragraph.

20 Another example: "This faces us squarely with what has been called the 'Dr. Jekyll and Mrs. Jekyll' problem." (1956, 9) Samuelson is here repeating a joke from an earlier paper: "… what is a man? Or a consumer? I am not so much concerned with the problem of Dr. Jekyll and Mr. Hyde, but with the problem of Dr. Jekyll and Mrs. Jekyll" (1950, 374).

21 Samuelson is here referring to an idea elucidated in his 1950 paper: "Much consumption behaviour is family rather than individual behaviour. Now a family must be quite sophisticated indeed to end up with a consistent set of collective preferences: e.g., if they set up the rule that the wife will always spend 99 per cent (or 50 per cent) of the income on her needs and the husband 1 per cent (or 50 per cent) on his quite different needs, this will not be consistent with an integrable set of price-ratio elements. Only if the family acts in terms of a Bergson Social Welfare Function will this condition result" (1950, 374–375).

22 The change in scale of course does not go completely smoothly. Commenting on Samuelson, Hammond (2015, 162) remarked: "The quantitative difference between the size of a family and that of a nation becomes a qualitative difference as one moves from the small group that is the family to the large group that is the nation." The above quote from the Suzumura interview does indicate, however, that Samuelson envisions elites in society as having a decision-dynamic similar to that of the family. The "different powers" of those elites would thus meld and be internally reconciled. If such elites would then "decide for others" or "impose" their decisions, this would appear – despite Arrow's critique – not to greatly concern Samuelson. As he indicates elsewhere in the interview, ethical concerns are not properly determined through democratic means.

23 Buchanan took notes that, at this date, are gathered in a folder in the archives titled ‘The theory of fiscal socialism’ (“The Theory and Practice of Fiscal Socialism", 1951–1952” is in Box 213, Folder 12).

24 See Fleury and Marciano, 2018, 516, 519 or Desmarais-Tremblay, 2014, 284.

25 Buchanan will come back later on this point (2012). We thank a referee for having suggested us to add these references.

26 Box: 176. Folder: 9. James M. Buchanan papers, C0246. George Mason University. Libraries. Special Collections Research Center.

27 They indicate, in other words, what Adam Smith’s self-interest leading to cooperation in the market indicates.

28 The deemphasis of process in Samuelson is noted by Hammond (2015), "Ultimately, Samuelson concluded that economic theory had little to contribute to discussions of the appropriate role of government." (148)

29 Notice that Musgrave is omitted in Buchanan's recapitulation of post-WWII transitions.