On Balance: Measuring Social Welfare

Measuring Social Welfare: An Introduction (Oxford University Press 2019) is an overview of the “social welfare function” (SWF) framework for policy analysis. The book covers the underlying theory of SWFs in some detail, here drawing upon both welfare economics and the philosophical literature on well-being and distributive justice. Measuring Social Welfare also demonstrates how SWFs can be used as a practical policymaking tool. One chapter of the book offers a detailed study of the use of SWFs, as compared to benefit-cost analysis (BCA), with respect to fatality risk regulation. (Adler 2019, ch. 5)


The SWF framework may not be familiar to everyone in the BCA community. The concept of a “social welfare function” actually has deep root in welfare economics.  It originates with work by Abram Bergson and Paul Samuelson from the 1930s and 1940s (Bergson 1938; Samuelson 1947), and was revitalized by Amartya Sen in response to Arrow’s theorem (Sen 1970). There is now a very large theoretical literature on SWFs (reviewed in Bossert and Weymark [2004]; Weymark [2016]). The SWF framework is also the linchpin of the economic literature on “optimal tax theory” (Tuomala 2016) and is widely employed in climate economics (Botzen and van den Bergh 2014).

The SWF framework has three key components, described in detail in the book.  It includes, first, a well-being measure, whereby outcomes (the possible consequences of policy choice) are converted into vectors (lists) of well-being numbers, one for each member of the population.  The second component is the SWF proper, which is a rule for ranking well-being vectors. Measuring Social Welfare focuses specifically on two types of SWFs: the utilitarian SWF, which adds up well-being numbers; and “prioritarian” SWFs, which add up well-being numbers plugged into a concave transformation function, thereby giving extra weight (priority) to those who are worse off.  The third component of this framework is what the book terms an uncertainty “module,” namely a procedure for applying the SWF to policies understood as probability distributions across outcomes. The outcomes of policy choice are uncertain (risk regulation epitomizes this: we don’t know for certain which individuals would have their deaths averted by a risk reduction), and so an uncertainty module along with a well-being measure and SWF is a critical part of the SWF framework.

Why should the SWF framework be of interest to BCA scholars and practitioners?  One reason is this:  BCA is insensitive to distributional considerations. By “BCA”, I mean the sum of individuals’ unweighted willingness-to-pay/accept amounts (compensating or equivalent variations)—a standard definition, at least in the U.S. (Adler 2019, pp. 289-90, provides a formal statement.)  Because willingness-to-pay/accept amounts are unweighted, a transfer of income from one group to another is seen by BCA as socially neutral. (Adler 2019, pp. 30-37, 192-200). What the recipients are willing to pay for the transfer equals what the transferors are willing to accept. In an era of pronounced inequality and keen political sensitivity to inequality, the BCA community should give serious attention to policy tools that do take account of distribution. President Biden, in a memo issued on his first day in office, directed OMB to make “recommendations for improving and modernizing regulatory review,” including proposals for “procedures that take into account the distributional consequences of regulations” (Biden 2021).

The SWF framework offers a systematic methodology for doing so. The utilitarian SWF is sensitive to the distribution of income. This is true, at least, if the well-being measure displays “diminishing marginal utility”: a unit of income produces a smaller increase in well-being if received by someone at a higher level of income. A prioritarian SWF is sensitive not only to the distribution of income, but indeed to the distribution of well-being itself.   Assume that our well-being measure is such that a $100 increment to the income of someone earning $50,000 is equal (in well-being terms) to a $200 increment to the income of someone earning $100,000. (This would be true if well-being equals the logarithm of income.). Utilitarianism would be indifferent between giving $100 to the first person and $200 to the second. Prioritarianism would prefer giving $100 to the first person, since the same well-being delta is benefiting someone at a lower well-being level.

Incorporating the SWF framework into the regulatory review process in the U.S. government would not require displacing BCA. SWF-based analysis could be used in tandem with BCA. Evaluating an array of regulatory alternatives with both techniques would illuminate whether distributional considerations are choice-relevant or not in a given situation. It should also be noted that SWF-based analysis can be approximated by adding distributional weights to BCA. (Adler 2016; Boadway 2016).   

A longstanding criticism of SWFs is that they require interpersonal comparisons of well-being (Adler 2019, ch. 2). The well-being numbers that are a key component of the framework are indeed interpersonally comparable.  If Ayla is assigned a higher well-being number than Billie, this indicates that Ayla is better off than Bille. Economists who work with SWFs are comfortable with interpersonal well-being comparisons, but others remain skeptical. Measuring Social Welfare discusses, in detail, how to construct an interpersonally comparable well-being metric, using so-called von Neumann-Morgenstern utility functions that encapsulate individuals’ risk preferences.

A different criticism is that the choice of SWF requires normative judgment. Deciding whether to use the utilitarian SWF, a prioritarian SWF, or some other functional form is a normative question. If prioritarianism is selected, picking the degree of priority for the worse off (the concavity of the transformation function) is also normative.  That said, BCA is hardly normatively neutral. BCA plays a central role in regulatory review in the U.S. by virtue of executive orders dating back to President Reagan (Renda 2011; Wiener and Alemanno 2017).  Presidents have legal authority to make normative judgments and, in the BCA executive orders, have done so.  Bringing the SWF framework into regulatory review would presumably require a change in the BCA executive order, or at least a decision to do so by an official with authority to make normative judgements on behalf of the administration (such as the head of OIRA or OMB)  (Adler 2019, pp. 209-15). 
I mentioned that one chapter of Measuring Social Welfare illustrates the use of SWFs with respect to fatality risk regulation.  Fatality risk policies are, of course, one of the most important applications of BCA in the U.S. government and in academic work. The value of statistical life (VSL) is the critical tool that BCA employs to value risk reduction. An individual’s willingness to pay for a risk reduction is the reduction multiplied by her VSL.  This chapter is one part of a broader research agenda that I am engaged upon—here collaborating with Maddalena Ferranna, James Hammitt, and Nicolas Treich—to compare SWF-based measures of the value of risk reduction with VSL (Adler, Ferranna, Hammitt, Treich 2021). We find major differences between the two approaches, both in formal analysis and in empirical simulations.

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