Cost-Benefit Analysis and Social Welfare Functions

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Cost-benefit analysis has become a routinized part of policymaking. Probing what justifies this methodology helps us to see how it might be improved.

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Cost-benefit analysis (CBA) has become a routinized part of the policymaking process in the United States. Still, it remains important to ask: What justifies this methodology? Probing this question helps us to see how CBA might be improved, or alternatively, gives assurance that changes are not needed.

One traditional justification appeals to the concept of Kaldor-Hicks efficiency (potential Pareto superiority). If a regulation passes a cost-benefit test, the total willingness-to-pay among the regulation’s beneficiaries exceeds the total willingness-to-accept among those made worse off by it. Accordingly, the enactment of a regulation that passes this test will, together with appropriate transfers from the first group to the second group, be universally beneficial (a “Pareto superior” outcome).

But there are many difficulties with this defense of CBA. The deepest objection is this: either a regulation is actually Pareto superior (which we can test for directly; the apparatus of CBA is not needed), or it is not, in which case the fact that the regulation could be converted into a Pareto-superior result via transfers that will not in fact be enacted is no justification at all.

A different perspective, one put forth in much of the economic theory literature, views CBA as a proxy for a social welfare function. While CBA measures impacts on individuals in terms of money (individual willingness-to-pay or accept), the social welfare function methodology relies on an interpersonally comparable utility function. A given outcome (a possible consequence of policy choice) is converted into a “vector,” or list, of utility numbers, one for each person in the population. These vectors are then ranked by some rule—most simply a utilitarian rule, that adds up utility numbers, or perhaps a “prioritarian” rule, which gives extra weight to those at lower utility levels.

If income and other determinants of individual utility are symmetrically distributed among the winners and losers of a given policy choice, CBA is a reasonable proxy for a utilitarian social welfare function. Alternatively, individual willingness-to-pay amounts could be scaled up or down by so-called distributional weights, which allow CBA to mimic a utilitarian or prioritarian social welfare function. Or, regulatory analysis with traditional CBA could be supplemented by a social welfare function-based analysis.

To be sure, talk of a “social welfare function” raises many questions. Among others: What is the basis for an interpersonally comparable utility function converting each individual’s “bundle” of attributes (income, health, leisure, and the like.) into a single number measuring her well-being? And, how are we to choose between the utilitarian social welfare function, the prioritarian social welfare function, and other possible functional forms for the rule for ranking utility vectors?

I grappled with these questions in my 2012 book, Well-Being and Fair Distribution: Beyond Cost-Benefit Analysis. And the social welfare function methodology is one of the central themes (although certainly not the only theme!) in the recently published Oxford Handbook of Well-Being and Public Policy, which I co-edited with Marc Fleurbaey.

Many Handbook chapters focus on well-being. These include philosophical chapters that review the contending philosophical theories of individual well-being: preference-based theories; experientialist theories—which reduce well-being to the occurrence of various kinds of mental states, such as feelings of pleasure or happiness—and those that see well-being as being based in “objective goods.” (For policy purposes, the “objective good” approach means that the contribution of attributes such as income, health, leisure, etc., to an individual’s well-being is seen as being independent of her particular preferences or the effect of these attributes on her happiness.) Other chapters review the burgeoning empirical literature on happiness, or focus on the measurement of well-being.

The social welfare function methodology is, in principle, compatible with any theory of well-being. By this I mean that if an interpersonally comparable utility measure corresponding to the theory can be constructed, outcomes can be conceptualized as vectors of utilities of that sort. For example, the social welfare function approach can be coupled with a happiness view of well-being if we have available utility numbers that reflect levels of happiness. It can be coupled with an objective-goods view through utility numbers that reflect individuals’ attainment of the goods.

In most of the extant literature on social welfare functions, a preference-based view of well-being is adopted. This is the standard view of well-being in welfare economics, and its adoption aligns the social welfare function approach more closely with CBA, which of course also revolves around preferences.

One must then ask: how are we to construct a measure of well-being that respects individual preferences (so that if Olivia prefer outcome x to outcome y, her utility number is higher in the first outcome), and also is interpersonally comparable? Indeed, what does it mean to make interpersonal comparisons among individuals with different preferences?

Two Handbook chapters grapple with these specific questions. My own chapter develops an approach to preference-based, interpersonally comparable utilities that builds upon work by the great welfare economist John Harsanyi. Simply stated, the idea is this: each person has a so-called von Neumann/Morgenstern (vNM) utility function representing her risk preferences with respect to lotteries over bundles of attributes. And the interpersonally comparable utility number assigned to her attributes, given her preferences, is just a rescaling of this vNM function.

Marc Fleurbaey, in his Handbook chapter, offers a different approach—the idea of “equivalent income.” We can specify a reference bundle of non-income attribute. An individual’s “equivalent income” in some outcome is her actual income adjusted to take account both of her preferences, and of the gap between her actual non-income attributes and the reference bundle. We can then use these adjusted income levels as the input to whatever social welfare function we might favor.

There is, evidently, a wide range of normative choices involved in the specification of the social welfare function methodology. The proponent of the methodology should frankly acknowledge as much. Specifying a social welfare function is not “value neutral”—but neither is the decision to use traditional CBA. The Handbook helps to bring to the surface vital questions regarding well-being and the aggregation of individuals’ interests that we—as public policy academics, engaged citizens, or governmental officials—need to grapple with in thinking about which assessment frameworks regulators ought to use in designing and selecting their policies.

Matthew D. Adler

Matthew D. Adler is the Richard A. Horvitz Professor of Law and Professor of Economics, Philosophy, and Public Policy at Duke University. His work focuses on both welfare economics and normative ethics and addresses cost-benefit analysis, happiness and public policy, and risk regulation.