# On Balance: Matthew D. Adler, Measuring Social Welfare: An Introduction, Oxford University Press, 2019. Review by James K. Hammitt, Harvard University

Benefit-cost analysis (BCA) is loosely interpreted as a method for determining whether a policy is ‘in the public interest’. More formally, BCA measures the effect of a policy change on each individual’s wellbeing as a monetary value and sums these values over the population. If the sum is positive, the policy change is declared a potential Pareto improvement, meaning the change plus some set of cost-free money transfers would be Pareto superior to the status quo (or other comparator).

BCA is described as evaluating efficiency or the size of the social pie. It does not depend on how the pie is distributed. Recognizing that the public interest depends on distribution as well as efficiency, policy-evaluation guidance routinely calls for analysis of the distributional effects of a policy. Moreover, out of concern for distributional effects, BCA in practice sometimes departs from its textbook foundation by substituting population-average values for individual-specific values. For example, although an individual’s value per statistical life (VSL) depends on her income, age, and other characteristics, BCA in practice almost always applies the same value across the population.

Distributional analyses rarely quantify the extent to which one distribution is better than another and may not even rank distributions. Little attention is given to how decision makers should integrate the efficiency and distributional effects of a policy, i.e., to clarify how much efficiency should be sacrificed for what change in distribution.

Into this breech steps an alternative framework, the social welfare function (SWF). It combines efficiency and distribution in a single measure. Indeed, some attractive SWFs can be written as the product of total wellbeing and a measure of inequality. A concomitant difficulty of applying SWFs is that the population distribution of benefits and costs must be estimated.

A familiar example is the utilitarian SWF, which adds changes in utility across people. Under the usual assumption that the marginal utility of income is decreasing, the utilitarian SWF is sensitive to income inequality and counts a gain in income as more valuable if goes to a poor than to a rich person. Other SWFs are sensitive to inequalities in wellbeing; these include prioritarian, leximin, and rank-weighted SWFs.

Matthew Adler believes that SWFs are a practical and ethically superior framework for policy evaluation. In *Measuring Social Welfare*, he provides a comprehensive and rigorous overview of the topic, including mathematical, ethical, and axiomatic perspectives.

Adler characterizes SWFs as having three elements: a measure of individual wellbeing, an evaluation rule for aggregating individuals’ wellbeing, and an uncertainty module for reckoning with uncertainty about outcomes. The choice of each of these elements has ethical ramifications. For the evaluation rule and uncertainty module, alternative choices are characterized by the axioms they satisfy.

Perhaps the greatest difference between SWFs and BCA is in the measure of wellbeing. Since the ordinalist revolution of the early 20th century, many economists have tried to avoid making interpersonal comparisons of levels or changes in wellbeing. SWFs require such comparisons. For a utilitarian SWF, changes but not levels of wellbeing must be interpersonally comparable; for prioritarian and other SWFs that are sensitive to differences in wellbeing, both changes and levels must be interpersonally comparable.

Measures of wellbeing can be based on individuals’ preferences, lists of objective goods (e.g., autonomy, physical integrity, accomplishment, deep personal relations), or experiences (e.g., happiness or subjective wellbeing). If preference-based, measures can be based on von Neumann-Morgenstern utility, equivalent income, or other alternatives. Wellbeing is measured over a lifetime. This has implications for SWFs that are sensitive to who is better and worse off, as the effect of improving an individual’s wellbeing can depend on both her past and likely future wellbeing, unlike BCA which is forward-looking.

For many of the SWFs Adler describes, the evaluation rule is a sum over individuals, of wellbeing or of some transformed measure of wellbeing. This has the advantage that policy evaluation does not require information about people whose wellbeing is unaffected, but the disadvantage that social preferences over outcomes that are correlated across people cannot be incorporated. Other SWFs can account for preferences such as catastrophe aversion, the judgment that a clustering of deaths from the same event is worse than the same number of deaths scattered across different events.

Adler advocates the prioritarian SWF, which evaluates the sum of individuals’ transformed wellbeing. The transformation gives greater weight to improving the wellbeing of an individual the lower her level of wellbeing and hence favors more equal distributions. Under uncertainty, there is an interesting difference between ex-ante and ex-post prioritarian SWFs. The ex ante form evaluates individuals by their lotteries over future outcomes and gives priority to those with lower expected utility, i.e., worse lotteries. The ex post form evaluates the possible outcomes and gives priority to individuals when their realized outcome is poor, in effect adding a degree of social risk aversion to the individual’s own risk aversion over outcomes. The difference between these approaches is similar to the preference for equality of opportunity or equality of outcome.

The book is logically organized. It begins with an introduction to SWFs, describing the three elements identified above. This is followed by a chapter on wellbeing measures, with a concluding section that challenges many economists’ knee-jerk rejection of the possibility of making interpersonal comparisons of wellbeing. The next chapters provide an overview of the SWF landscape followed by discussion of which SWF (and which functional forms and parameter values) to choose, highlighting the contrasts between prioritarian, utilitarian, and other SWFs.

These concepts are illustrated by an application of utilitarian and prioritarian SWFs and BCA to a stylized problem calibrated to the U.S. population. The policies reduce mortality risk and their costs reduce consumption, both for the current year; risk reductions and costs can be targeted by age or income. Both SWFs rank policies that distribute costs in proportion to income better than those that allocate costs uniformly; BCA ranks these cost allocations equally. All three approaches rank risk reductions for the young as better than uniform risk reductions. In contrast, the prioritarian SWF ranks risk reductions for the poor better than uniform risk reductions while BCA and the utilitarian SWF do the opposite. BCA as commonly practiced (using a VSL that is independent of age and income) would evaluate all of the policies as equivalent.

The final chapters address the institutional role of SWFs, including legal permissibility, division of labor and responsibility among government agencies, and citizens’ ethical views, plus research frontiers.

While the book is described as an introduction, it is rigorous and precise. The text uses no complicated mathematics but includes lots of simple mathematical notation (symbols and subscripts). Mathematical details are provided in an extensive appendix. To make the material more accessible, many numerical examples are set off in tables to illustrate key points.

SWFs may seem like foreign territory to scholars and practitioners of BCA, yet many SBCA members would profit from reading this book. SWFs are sometimes used for practical policy evaluation and influence the practice of BCA. Evaluation of tax policy, where distributional effects loom large, is heavily dependent on SWFs. Integrated assessment models used in climate policy and the declining discount rate advocated for long time horizons are frequently based on SWFs applied to multiple generations. Policy evaluation by SWFs can be mimicked by adding distributional weights to BCA; the British guidance for policy evaluation specifies a set of weights based on household size and income. Adler’s book serves as an elegant primer on the theory and ethics of social welfare functions and will deepen any reader’s understanding of these issues.

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