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The Death of Welfare Economics: History of a Controversy A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Igersheim, Herrade Working Paper The death of welfare economics: History of a controversy CHOPE Working Paper, No. 2017-03 Provided in Cooperation with: Center for the History of Political Economy at Duke University Suggested Citation: Igersheim, Herrade (2017) : The death of welfare economics: History of a controversy, CHOPE Working Paper, No. 2017-03, Duke University, Center for the History of Political Economy (CHOPE), Durham, NC This Version is available at: http://hdl.handle.net/10419/155466 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. www.econstor.eu The death of welfare economics: History of a controversy by Herrade Igersheim CHOPE Working Paper No. 2017-03 January 2017 Electronic copy available at: https://ssrn.com/abstract=2901574 The death of welfare economics: history of a controversy Herrade Igersheim December 15, 2016 Abstract. The death of welfare economics has been declared several times. One of the reasons cited for these plural obituaries is that Kenneth Arrow’s impossibility theorem, as set out in his path-breaking Social Choice and Individual Values in 1951, has shown that the social welfare function – one of the main concepts of the new welfare economics as defined by Abram Bergson (Burk) in 1938 and clarified by Paul Samuelson in the Foundations of Economic Analysis (1947, ch. VIII) – does not exist under reasonable conditions. Indeed, from the very start, Arrow kept asserting that his famous impossibility result has direct and devastating consequences for the Bergson-Samuelson Social Welfare Function (1948, 1950, 1951a, 1963), though he seemed to soften his position in the early eighties. On his side, especially from the seventies on, Samuelson remained active on this issue and continued to defend the concept he had devised with Bergson, tooth and nail, against Arrow’s attacks (1967, 1977, 1981, 1987, 2005). The aim of this paper is precisely to examine this rather strange controversy, which is almost unknown in the scientific community, even though it lasted more than fifty years and saw a conflict between two economic giants, Arrow and Samuelson, and behind them two distinct communities–the fading welfare economics against the emerging social choice theory–, two conflicting ways of dealing with mathematical tools in welfare economics and, above all, two different conceptions of social welfare. By relying on different kinds of material, I attempt to grasp what the exchanges between Arrow, Samuelson and others, both overtly and behind the scenes, reveal regarding the motivations of my two main actors. Keywords. Social welfare function, Arrow, Samuelson, social choice theory, welfare economics JEL Codes. B21, B31, D60, D71 CNRS and BETA, University of Strasbourg (France). E-mail: [email protected] I am grateful to Jerry Kelly and Maurice Salles. I would like to thank also Roger E. Backhouse, Beatrice Cherrier, Kevin D. Hoover, Dorian Jullien, Steven G. Medema, Nicolaus Tideman, E. Roy Weintraub, as well as the participants in a seminar at the Center for the History of Political Economy at Duke University, and other conferences’ participants, for helpful comments on an earlier draft. 1 Electronic copy available at: https://ssrn.com/abstract=2901574 “My only point in writing is that I never find myself in disagreement with you on matters of logic. Sometimes my taste for, say, bounded utility, differs from yours; but I understand and respect your view. Your position on SWF baffles me.” (PASP, Samuelson to Arrow, April 30, 1976)1 I. Introduction: the stakes of the controversy As notably emphasized by Sen (1999: 351), in the speech he delivered in Stockholm for the reception of his Nobel Prize on December 8, 1998 “for his contributions to welfare economics,” the death of welfare economics has been declared several times. One of the reasons cited for these plural obituaries is that Kenneth Arrow’s impossibility theorem, as set out in his path-breaking Social Choice and Individual Values in 1951, has shown that the social welfare function – one of the main concepts of the new welfare economics as defined by Abram Bergson (Burk) in 1938 and clarified by Paul Samuelson in the Foundations of Economic Analysis (1947, ch. VIII) – does not exist under reasonable conditions. It is widely acknowledged that the project of the new welfare economics was called into question from that moment onwards.2 Enunciated this way, this statement does not appear very problematic, but the bite might come from the following claim made by Samuelson (PASP 1975, unpublished manuscript): During the first 13 years of its life a Bergson Social Welfare Function (or, by courtesy, a Bergson-Samuelson SWF) was pretty well understood – both by those who thought it a useful concept, and those who had their doubts. It was an ethical norming of ordinal ordering of all the states of the world, provided from outside of positivistic economics. 1938-1951: then come the 13 years mentioned by Samuelson. According to him, Arrow’s impossibility theorem has no bearing on the Bergson-Samuelson social welfare function (henceforth B-S SWF), notably because it relies on an alternative meaning of the very concept of social welfare, the latter surreptitiously but progressively driving out the former sense as traditionally used in welfare economics. But, as I will attempt to demonstrate, this is far from being the only stumbling block between Arrow and Samuelson on this matter. 1 PASP—Paul A. Samuelson Papers, KJAP—Kenneth J. Arrow Papers, Rubenstein Rare Book and Manuscript Library, Duke University and ABP—Abram Bergson Papers, Harvard University Archives. 2 For the different stages of development in welfare economics, see especially Mongin 2002 and Baujard 2016. 2 Although six short years separated the country boy Paul (born in Indiana in 1915) from the young Kenneth (born in New York in 1921), their respective educations and curricula followed two very different paths. Samuelson came from a rather prosperous Polish family and began his undergraduate studies in economics at Chicago at the age of 16. By World War II, the “enfant terrible emeritus” had turned out paper after paper as a Harvard junior fellow from 1937-1940, completed his Wells Prize–awarded PhD dissertation, and been appointed Assistant Professor at MIT (Samuelson 1983; Backhouse 2014, 2015). Samuelson’s profound interest in welfare economics, as well as his fellow student and longtime friend Bergson’s, thus began during the interwar period in the middle of the socialist calculation debates and soon after Robbins’s 1932 Essay firmly rejected the use of values in economics. According to Cherrier and Fleury (2017: 4), “an ‘organicist’ (to use Buchanan’s terms) view of the State then prevailed, so that the values guiding its action were not conceived as deriving from individual choices.” The B-S SWF is no exception to this rule. As depicted by Bergson (1982) and Samuelson (1981, 1983), its elaboration goes back to their Harvard days together during the late thirties, when both tried to understand the subtleties and obscurities of Pareto’s Manuel, Samuelson thus serving as a “helpful midwife” for Bergson’s 1938 Quarterly Journal of Economics paper (Samuelson in Suzumura 2005: 334).3 In this paper, Bergson (then still Burk at that time) develops a function he calls the “economic welfare function” which aims at defining the social welfare from the set of resources available in the society. He then defines different groups of value propositions currently used in the welfare literature at that time to determine the conditions for a welfare maximum and examines how their derivations constrain the shape of the economic welfare function and thus the maximum position. He made clear that “the number of sets [of value propositions] is infinite, and in any particular case the selection of one of them must be determined by its compatibility with the values prevailing in the community the welfare of which is being studied” (Bergson 1938: 323), but with no attempt to derive these values from individual preferences. When turning his 1940 PhD dissertation into the Foundations of Economic Analysis (1947), Samuelson added a whole chapter on welfare economics (Backhouse 2015) and further developed Bergson’s seminal insights. He promptly introduced the concept of an individualistic social welfare function,4 ordinally defined, which aims at ordering in a transitive way the different states of the world and at reflecting “some ethical belief—that of a benevolent despot, or a 3 For a full account of the origins of the B-S SWF, see Backhouse 2013. 4 When speaking about a B-S SWF, most of the subsequent authors in fact refer to an individualistic social welfare function, unless explicitly specified. In the rest of the paper, the B-S SWF should thus be understood as an individualistic social welfare function in Samuelson’s sense. 3 complete egotist, or ‘all men of good will’, a misanthrope, the state, race, or group mind, God, etc.” (Samuelson 1947: 221).
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