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A Short History of the Bergson–Samuelson Social Welfare Function

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Paul Samuelson

Part of the book series: Remaking Economics: Eminent Post-War Economists ((EPWE))

Abstract

The so-called Bergson–Samuelson social welfare function was first introduced in 1938 by Abram Bergson, and subsequently developed by Paul Samuelson in his 1947 Foundations of Economic Analysis. However, the very existence of the social welfare function was called into question by Arrow’s (1951) landmark impossibility theorem, which states that under a set of reasonable conditions, the social welfare function can be shown not to exist. Yet social welfare functions are today still widely used in a range of fields in order to formulate policy ends. It thus seems that the use of such functions has flourished independently of the theoretical debate about their existence. The objective of this chapter is to offer a short history of the social welfare function, from its origins in the late 1930s up to the present day.

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Notes

  1. 1.

    Note that these conditions are those described in the second edition of Social Choice and Individual Values published in 1963, since the first version contained some mistakes identified by Blau in 1957.

  2. 2.

    For a more technical analysis of the implications of the condition of independence of irrelevant alternatives in this debate, particularly in connection with the issue of interpersonal comparisons of utility, see Fleurbaey (2003) and Fleurbaey and Mongin (2005).

  3. 3.

    Note that Little is the first to have introduced into the literature the term “Pareto optimality” (see Suzumura 2005: 335).

  4. 4.

    After Arrow (1951), the Little criterion was further analyzed and criticized; see, in particular, Meade (1959), Sen (1963), and Chipman and Moore (1978).

  5. 5.

    Although the aims of the Little criterion and the Bergson–Samuelson social welfare function are conceptually similar, i.e. to go beyond Pareto optimality, it must be stressed that they can be seen as alternatives (see, for instance, Schofield 1987; Little 1999: 16–17).

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Authors and Affiliations

  1. University of Strasbourg, Strasbourg, France

    Herrade Igersheim

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  1. Herrade Igersheim
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Correspondence to Herrade Igersheim .

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Editors and Affiliations

  1. London, UK

    Robert A. Cord

  2. Center for Economics and the Environment, Lindenwood University, St. Charles, MO, USA

    Richard G. Anderson

  3. Department of Economics, University of Kansas, Lawrence, KS, USA

    William A. Barnett

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Igersheim, H. (2019). A Short History of the Bergson–Samuelson Social Welfare Function. In: Cord, R., Anderson, R., Barnett, W. (eds) Paul Samuelson. Remaking Economics: Eminent Post-War Economists. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-137-56812-0_12

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  • DOI: https://doi.org/10.1057/978-1-137-56812-0_12

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