1.2.1 Consequentialist Decision Theory

Consequentialist decision theory specifies a welfare function and an expression of uncertainty as primitives. It then seeks reasonable criteria to make decisions. The most prevalent recommendation has been maximization of expected utility. One places a probability distribution on the state space and chooses an action that maximizes the expected value of welfare with respect to this distribution.

To assist decision makers who do not find it credible to express uncertainty through a probability distribution, decision theorists have mainly studied criteria that, in some sense, works uniformly well over all of the state space. Two prominent interpretations of this broad idea are the maximin and minimax regret criteria. I will formalize these criteria in Section 1.3 and apply them throughout the book, particularly minimax regret.

The decision theory used in my research on planning is consequentialist. I suppose that the objective is to make substantively good societal decisions in particular settings. To accomplish this, I suppose that a planner specifies a suitable welfare function, expresses uncertainty in a credible manner, and uses these primitives to make a decision. The suitability of a welfare function and the credibility of an expression of uncertainty are context specific. These matters will be discussed in general terms in Sections 1.4 and 1.5 and in specific contexts in Part II.

1.2.2 Axiomatic Decision Theory

Axiomatic decision theory poses principles, called axioms, for consistency of hypothetical behavior across a class of potential choice problems. Researchers introspect and assert it to be reasonable, or rational, that a decision maker should adhere to these choice axioms. The central research activity of axiomatic decision theorists has been to pose and prove representation theorems establishing that adherence to a specified set of axioms is equivalent to acting as if one wants to use some consequentialist decision criterion, coping with uncertainty in some manner.

Perhaps the most famous representation theorems are those of Von Neumann and Morgenstern (Reference Von Neumann and Morgenstern1944) and Savage (Reference Savage1954). Both theorems establish that adherence to certain axioms is equivalent to maximization of expected utility. They differ mainly in that the probability distribution on the state space used to form expected utility is pre-specified in the former work and determined within the theory in the latter. Von Neumann and Morgenstern (VN-M) viewed the probability distribution as a primitive concept. Savage viewed the distribution as a construct that may in principle be inferred from analysis of choice behavior. I explain this distinction further on. I emphasize that in neither theorem does the probability distribution have any necessary connection to an objective reality.

Axiomatic theorists have long debated which axioms have normative appeal. Appraisal of normative appeal rests on introspection, so there should be no expectation that consensus will emerge. Indeed, decision theorists exhibit considerable difference in opinion. Binmore (Reference Binmore2009) catalogues and assesses a wide spectrum of consistency axioms.

Why should one consider the VN-M, Savage, or other axioms to be compelling? No theorem answers this question. Instead, decision theorists call for introspection. In lecture notes for a Ph.D. course in decision theory, Kreps (Reference Kreps1988) counseled a decision maker contemplating application of the VN-M theorem that he must first (p. 5): “Decide that you want to obey the axioms because they seem reasonable guides to behavior.”

Considering the matter at length, Savage (Reference Savage1954) put it this way (p. 7):

After discussing the positive role of logic in guiding actual human behavior, Savage wrote (p. 20):

Then, addressing his basic axiom P1, which assumes that the decision maker places a complete binary preference ordering on all potential actions, he wrote:

Thus, Savage opined that humans may want their behavior to be consistent beyond the degree required by logic, but he was unable to explain why.

In a famous critique of the Savage axioms, Ellsberg (Reference Ellsberg1961) sharply questioned the Savage conclusion that a rational decision maker must behave as if he places a subjective probability distribution on the state space. He observed that thoughtful persons sometimes exhibit behavioral patterns that violate the Savage axioms in ways implying that they do not hold subjective distributions. Considering this behavior, he wrote (p. 669):

When studying consistency axioms of the types posed by VN-M and Savage, decision theorists ordinarily do not differentiate between private entities and social planners. The presumption is that all decision makers should behave consistently in the same manner. However, some theorists have proposed that social planners should adhere to additional ethical axioms that require them, in some sense, to respect the preferences of their populations and/or behave fairly. Review articles include Fleurbaey (Reference Fleurbaey2018) and Mongin and Pivato (Reference Mongin, Pivato, Adler and Fleurbaey2016).

1.2.3 The Institutional Separation of Research on Planning and Actual Planning

Decision theory presumes a unitary setting in which a planner performs his own research to inform policy choice. I observed in Manski (Reference Manski2013c) that modern democratic societies have created an institutional separation between policy analysis and decision making, with professional analysts reporting findings to representative governments. Separation of the tasks of analysis and decision making, the former aiming to inform the latter, appears advantageous from the perspective of division of labor. No one can be an expert at everything. In principle, having researchers study planning problems and provide their findings to law makers and civil servants enables these planners to focus on the challenging task of policy choice, without having to perform their own research.

I also observed that the current practice of policy analysis with incredible certitude does not serve planners well. The problem is that the consumers of policy analysis cannot trust the producers. I argued that, to improve analysis and to increase trust, research on planning should transparently face up to uncertainty rather than hide it.

Some think this idea to be naive or impractical. I have repeatedly heard policy analysts assert that policy makers are either psychologically unwilling or cognitively unable to cope with uncertainty. Some economists with experience in the federal government of the United States have suggested to me that concealment of uncertainty is an immutable characteristic of the American policy environment. Hence, they assert that the prevailing practice of policy analysis with incredible certitude will have to continue as is.

A more optimistic possibility is that concealment of uncertainty is a modifiable social norm. My hope is that salutary change will occur if awareness grows that incredible certitude is harmful. Then I anticipate that the scientific community will reward policy research based on credible analysis more than optimization exercises performed with ill-conceived assumptions. Planners and the public will want researchers to provide reasonable policy recommendations that recognize the subtlety of planning under uncertainty, not unequivocal ones that lack foundation.

1.3.1 The Choice Set, State Space, and Welfare Function

I now deepen the discussion of uncertainty in consequentialist decision theory. The starting point is to suppose that the planner or other decision maker faces a predetermined choice set C and believes that the true state of nature s* lies in a state space S. The welfare function w(∙, ∙): $\text{C}\times \text{S}\to {\text{R}}^1$ maps actions and states into welfare. The planner wants to maximize w(∙, s*) over C but does not know s*. Hence, maximization is infeasible except in special cases.

The state space S provides the basic decision theoretic expression of uncertainty. In lay language, S is a list of “known unknowns.” States of nature that are not elements of S are presumed impossible to occur. Decision theory supposes that the decision maker does not contemplate the possible existence of unlisted “unknown unknowns.”

Discussions of the state space often consider it to express uncertainty purely about the physical and social environment within which choice takes place. However, a state space can also express uncertainty about the welfare function that a planner should maximize. This often occurs when the planner is utilitarian. Then the planner must know the preferences of the population to maximize welfare, but this knowledge may not be available. See Chapter 4 for further discussion.

Being a primitive of the decision problem, the state space is necessarily subjective. This does not imply, however, that it is an arbitrary construction. Credibility is a fundamental matter in consequential decision theory in general and in the study of social planning specifically. If planning decisions are to enhance welfare in the real world, the planner should specify a state space that embodies some reasonable sense of credibility. Research seeks to help by providing at least a partially objective basis for specification of the state space. This basis is obtained by combining plausible theory with empirical analysis. I discuss this further in Section 1.4.

1.3.2 Decision Criteria

It is generally accepted that decisions should respect dominance. Action $\text{c}\in \text{C}$ is weakly dominated if there exists a $\text{d}\in \text{C}$ such that $\text{w(d},\text{s)}\ge \text{w(c},\text{s)}$ for all $\text{s}\in \text{S}$ and $\text{w(d},\text{s)}>\text{w(c},\text{s)}$ for some $\text{s}\in \text{S}$. To choose among undominated actions, decision theorists have proposed various ways of using w(∙, ∙) to form functions of actions alone, which can be optimized. In principle, one should only consider undominated actions, but it is often difficult to determine which actions are undominated. Hence, in practice it is common to optimize over the full set of feasible actions. I define decision criteria accordingly.

I initially consider settings without sample data, describing three prominent criteria. I extend these criteria to settings with sample data in Section 1.3.3. Consequentialist decision theory views the welfare function, state space, and decision criterion as meta-choices made by a decision maker. It views these meta-choices as predetermined rather than matters to be studied within the theory. In this sense consequentialist theory requires introspection, as does axiomatic theory.

A familiar idea is to place a subjective probability distribution $\text{π}$ on the state space, average state-dependent welfare with respect to $\text{π}$, and maximize subjective expected welfare (SEW) over C. The criterion solves:

(1.1)$\underset{\text{c}\in \text{C}}{\text{max}}\int \text{w}\left(\text{c},\text{s}\right)\text{d}\text{π}.$

Observe that, given a subjective distribution $\text{π}$ on S, one need not average over $\text{π}$. Any criterion respecting stochastic dominance has a consequentialist claim to be reasonable. For example, Manski (Reference Manski1988) studied maximization of quantile welfare. However, the prevalent practice has been to average over $\text{π}$.

In the absence of a subjective distribution on S, a prominent idea is to choose an action that, in some sense, works uniformly well over all of S. This yields the maximin and minimax regret (MMR) criteria. The maximin criterion maximizes the minimum welfare attainable across S, solving the problem:

(1.2)$\underset{\text{c}\in \text{C}}{\text{max}}\underset{\text{s}\in \text{S}}{\text{min}}\text{w}\left(\text{c,}\text{s}\right)\text{.}$

The MMR criterion solves:

(1.3)$\underset{\text{c}\in \text{C}}{\text{min}}\underset{\text{s}\in \text{S}}{\text{max}}\left(\underset{\text{d}\in \text{C}}{\text{max}}\text{ w}\left(\text{d},\text{s}\right)-\text{w}\left(\text{c},\text{s}\right)\right).$

Here ${\text{max}}_{\text{d}}{}_{\in \text{C}}\text{w(d},\text{s)}-\text{w(c},\text{s)}$ is the regret of action c in state s. The true state being unknown, one evaluates c by its maximum regret over all states and selects an action that minimizes maximum regret. The maximum regret of an action measures its maximum distance from optimality across states. Hence, maximum regret is uniform nearness to optimality.

The maximin and minimax regret criteria are sometimes confused with one another but they yield the same choice only in certain special cases. Whereas the maximin criterion considers only the worst outcome that an action may yield, MMR considers the worst outcome relative to the best achievable in a given state of nature. Hence, the two criteria generically differ. The leading case where the two criteria coincide occurs when the best achievable welfare has the same magnitude in every state of nature; that is, ${\text{max}}_{\text{d }\in \text{ C}}\text{w(d},\text{s)}$ is constant across $\text{s}\in \text{S}$. Then (1.3) reduces to (1.2) up to this additive constant.

It is also noteworthy that a decision maker who places a subjective probability distribution $\text{π}$ on the state space might choose to minimize subjective expected regret rather than maximum regret, subjective expected regret being $\int [{\text{max}}_{\text{d}\in \text{C}}\text{w(d,}\text{s)}-\text{w(c,}\text{s)}]\text{d}\text{π}$. The expression $\int {\text{max}}_{\text{d}\in \text{C}}\text{w(d,}\text{s)}\text{d}\text{π}$ is constant across the feasible actions $\text{c}\in \text{C}$. Hence, minimization of subjective expected regret is equivalent to maximization of subjective expected welfare.

I will discuss criteria (1.1) to (1.3) throughout this book. Readers should be aware that these three, which arguably have been the most prominent in decision theory, are not the only criteria that may warrant attention. For example, Hurwicz (Reference Hurwicz1951) suggested modification of the maximin criterion to maximize instead a weighted average of the minimum and maximum welfare attainable across the state space.

Other decision theorists have studied settings intermediate between the polar cases in which a planner asserts either a complete subjective distribution on the state space, or none. A planner might instead assert a partial subjective distribution, placing lower and upper probabilities on states, as in Dempster (Reference Dempster1968) or Walley (Reference Walley1991), and then maximize minimum subjective expected welfare or minimize maximum expected regret. These criteria combine elements of averaging across states and concern with uniform performance across states. Statistical decision theorists refer to them as Γ-maximin and Γ-minimax regret (Berger, Reference Berger1985). The former has drawn attention from axiomatic decision theorists, who call it “maxmin expected utility” (Gilboa and Schmeidler, Reference Gilboa and Schmeidler1989).

1.3.3 Statistical Decision Theory

Abraham Wald, in a series of contributions culminating in Wald (Reference Wald1950), extended consequentialist decision theory to encompass settings where the decision maker observes sample data. Wald’s formulation of statistical decision theory supposes that a decision maker observes data generated by a sampling distribution which is a known function of the state of nature. To express this, let the feasible sampling distributions be denoted $({\text{Q}}_{\text{s}},\text{s}\in \text{S})$. Let ${\text{Ψ}}_{\text{s}}$ denote the sample space in state s; ${\text{Ψ}}_{\text{s}}$ is the set of samples that may be drawn under distribution Q_s. The literature typically assumes that the sample space does not vary with s and is known. I do likewise and denote the sample space as Ψ. A statistical decision function (SDF), $\text{c(}\cdot \text{)}:\text{Ψ}\to \text{C}$, maps the sample data into a chosen action.

An SDF is a deterministic function after realization of the sample data but it is a random function ex ante. Hence, an SDF generically makes a randomized choice of an action. The only exceptions are SDFs that make almost-surely data-invariant choices. An SDF c(⋅) is almost-surely data-invariant in state s if there exists a $\text{d}\in \text{C}$ such that ${\text{Q}}_{\text{s}}[\text{c(}\text{ψ}\text{)}=\text{d}]=1$.

Given that SDFs are random functions, welfare using a specified SDF is a random variable ex ante. Wald’s theory evaluates the performance of SDF $\text{c(}\cdot \text{)}$ in state s by ${\text{Q}}_{\text{s}}\{\text{w[c(}\text{ψ}\text{)},\text{s]}\}$, the ex ante distribution of welfare that it yields across realizations $\text{ψ}$ of the sampling process. Thus, statistical decision theory is frequentist. In particular, Wald measured the performance of $\text{c(}\cdot \text{)}$ in state s by its expected welfare across samples; that is, ${\text{E}}_{\text{s}}\{\text{w}\text{[c(}\text{ψ}\text{)},\text{s]}\}\equiv \int \text{w}\text{[c(}\text{ψ}\text{)},\text{s]}{\text{dQ}}_{\text{s}}$. Not knowing the true state, a planner evaluates $\text{c(}\cdot \text{)}$ by the state-dependent expected welfare vector $\left({\text{E}}_{\text{s}}\right\{\text{w}\text{[c(}\text{ψ}\text{)},\text{s]}\},\text{ s}\in \text{S})$, which is computable.

One need not measure the sampling performance of an SDF by its expected welfare across samples. Manski and Tetenov (Reference Manski and Tetenov2023) observe that any criterion respecting stochastic dominance has a claim to be reasonable. In particular, they study measurement of sampling performance by quantile welfare. However, the prevalent practice has been to measure performance by expected welfare across samples.

Statistical decision theory has mainly studied the same decision criteria as has decision theory without sample data. Let Γ denote the set of feasible SDFs, which map $\text{Ψ}\to \text{C}$. The statistical versions of criteria (1.1), (1.2), and (1.3) are:

(1.4)$\underset{\text{c}(\cdot )\in \text{Γ}}{\text{max}}\int {\text{E}}_{\text{s}}\left(\text{w}\left(\text{c}\left(\text{ψ}\right),\text{s}\right)\right)\text{d}\text{π},$

(1.5)$\underset{\text{c}(\cdot )\in \text{Γ}}{\text{max}}\underset{\text{s}\in \text{S}}{\text{min}}{\text{E}}_{\text{s}}\left(\text{w}\left(\text{c}\left(\text{ψ}\right),\text{s}\right)\right),$

(1.6)$\underset{\text{c}(\cdot )\in \text{Γ}}{\text{min}}\underset{\text{s}\in \text{S}}{\text{max}}\left(\underset{\text{d}\in \text{C}}{\text{max}}\text{ w}\left(\text{d},\text{s}\right)-{\text{E}}_{\text{s}}\left(\text{w}\left(\text{c}\left(\text{ψ}\right),\text{s}\right)\right)\right).$

In settings of choice between two actions, SDFs can be viewed as hypothesis tests. However, evaluation of tests in the Wald theory differs fundamentally from Neyman–Pearson hypothesis testing, which I will discuss in Chapter 6. The Wald theory does not restrict attention to tests that yield a predetermined upper bound on the probability of a Type I error. Nor does it aim to minimize the maximum value of the probability of a Type II error when more than a specified minimum distance from the null hypothesis. Wald proposed for binary choice, as elsewhere, evaluation of the performance of SDF c(∙) in state s by the expected welfare that it yields across realizations of the sampling process. See Chapter 6 and Manski (Reference Manski2021a) for further discussion.

1.3.4 Minimax Regret Planning

Among the decision criteria posed above, maximization of SEW places a subjective distribution on the state space, whereas maximin and MMR do not. Concern with the basis for specification of a subjective distribution motivated Wald (Reference Wald1950) to study the minimax criterion (maximin in my description), writing (p. 18): “a minimax solution seems, in general, to be a reasonable solution of the decision problem when an a priori distribution … does not exist or is unknown.”

I am similarly concerned with decision making with no subjective distribution on states. However, I have mainly measured performance of decisions by maximum regret rather than by minimum welfare. The maximin and MMR criteria both provide ex ante evaluations of the worst result that a decision maker may experience ex post. However, the criteria are equivalent only in special cases, particularly when optimal welfare is invariant across states. They differ more generally. Whereas maximin considers the worst absolute outcome that an action may yield across states, MMR considers the worst outcome relative to what is achievable in a given state.

As I see it, a conceptual appeal of using maximum regret to measure performance is that it quantifies how lack of knowledge of the true state of nature diminishes the quality of decisions. The term “maximum regret” is shorthand for the maximum suboptimality of a decision criterion across the feasible states of nature. A decision with small maximum regret is uniformly near optimal across all states. Introspecting, I think this a desirable property. Each study in Part II of this book applies the MMR criterion. Some consider the maximin criterion as well.

MMR has drawn diverse reactions from axiomatic decision theorists. In a famous early critique, Chernoff (Reference Chernoff1954) observed that MMR decisions are sometimes inconsistent with the choice axiom known as independence of irrelevant alternatives (IIA). Chernoff considered this a serious deficiency, writing (p. 426):

This passage is the totality of Chernoff’s argument. He introspected and concluded that a reasonable decision criterion should always adhere to IIA, without explaining why he felt this way. He did not argue that minimax regret choices have adverse consequentialist consequences.

Chernoff’s view has been endorsed by some modern decision theorists, including Binmore (Reference Binmore2009). Indeed, Ken Binmore used picturesque language to express this view in my presence during a conference, declaring that violation of IIA is “Death to minimax regret” (statement made in a presentation at the Kellogg School of Management conference on “Decision Theory and its Discontents,” May 1, 2009). On the other hand, Sen (Reference Sen1993) argued that adherence to the IIA axiom does not per se provide a sound basis for evaluation of decision criteria. He asserted that consideration of the context of decision making is essential.

Manski (Reference Manski2011a) argued that adherence to the IIA axiom is not a virtue per se. What matters is how violation of the axiom affects welfare. The MMR decision is necessarily undominated when it is unique. There generically exists an undominated MMR decision when the criterion has multiple solutions. Hence, I concluded that violation of the IIA axiom is not a sound rationale to dismiss minimax regret.

1.4.1 Identification Analysis

It has become standard in econometrics to specify the state space as a set of objective probability distributions that may possibly describe the system under study. Haavelmo (Reference Haavelmo1944) did so for economic systems when he introduced The Probability Approach in Econometrics. Studies of treatment choice do so when they consider the population to be treated to have a distribution of treatment response.

The Koopmans (Reference Koopmans1949) formalization of identification analysis contemplated unlimited data collection that enables one to shrink the state space, eliminating states that are inconsistent with accepted theory and with the information revealed by observation of data. For most of the twentieth century, econometricians commonly thought of identification as a binary event – a feature of an objective probability distribution (a parameter) is either identified or it is not. Empirical researchers applying econometric methods combined available data with assumptions that yield point identification, and they reported point estimates of parameters. Economists recognized that point identification often requires strong assumptions that are difficult to motivate. However, they saw no other way to perform empirical research.

Yet there is enormous scope for fruitful research using weaker and more credible assumptions that partially identify population parameters. A parameter is partially identified if the sampling process and maintained assumptions reveal that the parameter lies in a set, its identification region or identified set, that is smaller than the logical range of the parameter but larger than a single point. I explain below.

1.4.2 Statistical Imprecision

Whereas identification analysis contemplates unlimited data collection that enables one to shrink the state space, the data observed in a finite sample generated by a sampling distribution generally are not informative enough to shrink the state space. Nevertheless, Wald’s development of statistical decision theory shows how sample data can be informative.

In Wald’s paradigm, statistical imprecision is expressed through the state-dependent ex ante distributions $\left[{\text{Q}}_{\text{s}}\right\{\text{w}\text{[c(}\text{ψ}\text{)},\text{s]}\},\text{ s}\in \text{S}]$ of welfare that an SDF yields across realizations $\text{ψ}$ of the sampling process. Wald’s concept of an SDF embraces all mappings [data → action]. An SDF need not perform conventional statistical inference; that is, it need not use data to directly draw conclusions about the true state of nature. The prominent decision criteria that have been studied – maximin, minimax regret, and maximization of subjective expected welfare – do not explicitly perform inference on the true state.

Although SDFs need not perform conventional inference, some do. These have the form [data → inference → action], first performing inference and then using the inference to make a decision. There seems to be no accepted term for such SDFs, so I have called them inference based (Manski, Reference Manski2021a).

The general absence of conventional inference in statistical decision theory is striking. Familiar measures of statistical imprecision, such as confidence sets and standard errors, play no role in the Wald theory. On the other hand, statistical imprecision is measured when one computes the maximum regret of an SDF; that is, its maximum distance from optimality. Maximum regret is determined jointly by the identification problem faced and by the statistical imprecision of sample data. When the true state of nature is point identified, maximum regret purely measures statistical imprecision. I will expand on this in Chapter 6 in the context of analysis of randomized trials.

1.5.1 The New Welfare Economics

One route was taken in the 1930s and 1940s by the economists who initiated the study of the new welfare economics, a term apparently first used by Hicks (Reference Hicks1939). Wary of any criterion to choose among policies that benefit some people but harm others, they retreated to the study of Pareto efficiency with extension to the fictional redistributions proposed by Kaldor (Reference Kaldor1939) and Hicks (Reference Hicks1939). However, this restriction on their domain of concern drastically limited their ability to study actual planning problems. This led Chipman and Moore (Reference Chipman and Moore1978) to write (p. 548): “In this paper we shall argue that, judged in relation to its basic objective of enabling economists to make welfare prescriptions without having to make value judgments and, in particular, interpersonal comparisons of utility, the New Welfare Economics must be considered a failure.” Efficiency in the fictional Kaldor–Hicks sense has become at most a peripheral topic in economic theory, but it continues to be used in applied benefit–cost analysis, as I explain below.

1.5.2 Utilitarian Welfare

Within the body of economic research that studies planning when policies benefit some people but harm others, it has been common to specify a utilitarian welfare function. The standard theory of rational individual behavior under certainty requires only an ordinal personal concept of welfare. A utilitarian social welfare function specifies interpersonally comparable cardinal personal welfares and sums them. This gives formal expression to what Bentham (Reference Bentham1776) may have had in mind when he wrote (p. ii): a “fundamental axiom, it is the greatest happiness of the greatest number that is the measure of right and wrong.”

In utilitarian welfare analysis, concern with equity is expressed through specification of the personal welfare functions, measured on a commensurate scale, that are summed to compute social welfare. A prominent example is the Mirrlees (Reference Mirrlees1971) analysis of optimal income taxation. There, personal welfare was taken to be a concave function of income, thus expressing “diminishing marginal utility of money.” It follows that, all else equal, transferring a dollar from a wealthy person to a poor one increases social welfare. In the Mirrlees analysis, this motivates progressive income tax schedules that impose higher tax rates on persons with higher incomes and lower (or negative) rates on those with lower incomes. Mirrlees showed that the structure of an optimal tax schedule is complex because the schedule generally affects the amount of labor that persons choose to supply. This consideration affects how much redistribution a society is able to accomplish in practice.

1.5.3 Maximin Welfare

One need not sum cardinal personal welfares to develop social welfare functions that respect Pareto efficiency. Among alternatives, the work of Rawls (Reference Rawls1971) has received considerable attention outside of economics. He recommended evaluation of policy by the minimum value of interpersonally comparable ordinal personal welfares. He argued that society should evaluate social welfare in this manner, rather than the utilitarian one.

1.5.4 Optimal Paternalism in Populations with Bounded Rationality

The norm in the study of utilitarian planning has been to assume that members of the population maximize their personal welfare. However, the realism of this assumption has long been questioned. Simon (Reference Simon1955) put it this way in the article that spawned the modern literature in behavioral economics (p. 101): “Because of the psychological limits of the organism (particularly with respect to computational and predictive ability), actual human rationality-striving can at best be an extremely crude and simplified approximation to the kind of global rationality that is implied, for example, by game-theoretical models.” This idea has come to be called bounded rationality. Simon put forward this mission for research on behavior (p. 99):

A recent development in the field of public economics has been the initiation of research on utilitarian planning in populations with bounded rationality. Behavioral economists have suggested that planners should limit the choice options available to individuals to ones deemed beneficial from a utilitarian perspective or, less drastically, should frame the options in a manner thought to influence choice in a positive way. Thaler and Sunstein (Reference Thaler and Sunstein2003) evocatively wrote that such policies express (p. 175): “libertarian paternalism.” However, here and elsewhere, their discussion has been verbal rather than formal.

An early expression of formal analysis was given by O’Donoghue and Rabin (Reference O’Donoghue and Rabin2003), who began their article as follows (p. 186):

Economists have subsequently performed a growing set of analyses of the type sought by O’Donoghue and Rabin, addressing different classes of policy choices and assuming various distributions of preferences and deviations from utility maximization.

Research in the developing field of behavioral public economics has thus far assumed that the planner understands bounded rationality in the population well enough to be able to optimize social welfare. Thus, authors have assumed that, while members of the population are boundedly rational, the planner is globally rational. However, detailed knowledge of population preferences and deviations from global rationality is rare. Manski and Sheshinski (Reference Manski and Sheshinski2023) argue that a utilitarian planner with limited knowledge should not seek to optimize policy invoking assumptions that lack credibility. Instead, the planner should use a reasonable criterion to plan under uncertainty.

1.5.5 Nonpersonalist Welfare Functions

I have so far discussed research that assumes the social welfare function somehow aggregates personal welfare across society. Sen (Reference Sen1977) called such research welfarism, writing (p. 1559): “The general approach of making no use of any information about the social states other than that of personal welfares generated in them may be called ‘welfarism.’” He then wrote that (p. 1559): “welfarism as an approach to social decisions is very restrictive.” Sen’s perspective warrants serious attention, but it seems to me that the word “welfarism” does not express his concern well. I shall instead use the word “personalism.”

Nonpersonalist welfare functions place direct societal value on certain ethical concepts, beyond their possible manifestations as determinants of personal welfare. These concepts have been given many appealing names, including justice, fairness, and equity. However, they are devilishly difficult to interpret. Moreover, interpretations vary across the persons who use the concepts. See Backhouse et al. (Reference Backhouse, Baujard and Nishizawa2021) for multiple discussions.

Economists have long sought to pose and analyse concepts of fairness. For example, Tobin (Reference Tobin1970) posed a concept of “specific egalitarianism.” This idea moves away from utilitarianism, which concerns itself with the overall utility that a person experiences, instead supposing that society desires that (p. 264): “certain specific scarce commodities should be distributed less unequally than the ability to pay for them.” Tobin discussed medical care as a leading case of such a specific commodity.

Foley (Reference Foley1967) and Varian (Reference Varian1974) formalized concepts of envy-free and fair allocations of resources within a population. Manski, Mullahy, and Venkataramani (Reference Manski, Mullahy and Venkataramani2023) formalized concepts of disparity aversion. In this book, Chapter 5 discusses welfare functions that formalize the idea of equal treatment of equals. Considering policing in Chapter 7, I specify welfare functions that value the personal welfare of law-abiding citizens but do not similarly value the preferences of criminals.

1.5.6 Pragmatic Welfare

Research in welfare economics and moral philosophy has mainly been abstract. In contrast, studies of realistic classes of planning problems have specified pragmatic welfare functions. I use the word “pragmatic” to mean that researchers motivate their welfare functions by some combination of conjecture regarding societal values, empirical study of population preferences, and concern for analytical tractability.

For example, the literature on optimal taxation stemming from Mirrlees (Reference Mirrlees1971) has assumed a utilitarian welfare function and has placed various restrictions on the population distribution of labor–leisure preferences; see Chapter 4 for further discussion. Research on government spending to optimize macroeconomic growth has assumed utilitarian welfare and a representative infinite-lived household, as in Barro (Reference Barro1990). Integrated assessment studies of optimal climate policy has assumed that the objective is to maximize present-discounted gross world product, as in Nordhaus (Reference Nordhaus2008); see Chapter 9 for further discussion. Analysis of optimal medical care may assume that the objective is to maximize a population survival rate or mean quality-adjusted life years (QALYS) net of treatment cost; see Chapters 5 through 8. Benefit–cost analyses of transportation projects quantify and weigh an array of societal project benefits and costs; see US Department of Transportation (2023).

When academic researchers specify pragmatic welfare functions, they may believe that these functions have sufficient social acceptability to make them worthy of study. However, they usually do not argue that actual planners should necessarily use these welfare functions to make decisions. The less ambitious goal is to learn what decisions would be optimal if specified welfare functions were to be used. This perspective is maintained throughout my own work. Research should be distinct from advocacy.