Inequality and uncertainty: theory and legal applications.

• Author: Adler, Matthew D.

"Welfarism" is the principle that social policy should be based solely on individual well-being, with no reference to "fairness" or "rights." The propriety of this approach has recently been the subject of extensive debate within legal scholarship. Rather than contributing (directly) to this debate, we identify and analyze a problem within welfarism that has received far too little attention--call this the "ex ante/ex post" problem. The problem arises from the combination of uncertainty--an inevitable feature of real policy choice--and a social preference for equality. If the policymaker is not a utilitarian, but rather has a "social welfare function" that is equity regarding to some degree, then she faces a critical choice. Should she care about the equalization of expected well-being (the ex ante approach), or should she care about the expected equalization of actual well-being (the ex post approach)? Should she focus on the equality of prospects or the prospects for equality?

In this Article, we bring the ex ante/ex post problem to the attention of legal academics, provide novel insight into when and why the problem arises, and highlight legal applications where the problem figures prominently. We ultimately conclude that welfarism requires an ex post approach. This is a counterintuitive conclusion, because the ex post approach can conflict with ex ante Pareto superiority. Indeed, this Article demonstrates that the ex post application of every equity-regarding social welfare function--whatever its particular farm--must conflict with ex ante Pareto superiority in specific situations. Among other things, then, this Article shows that legal academics who care about equity must abandon either their commitment to welfarism or their commitment to ex ante Pareto superiority.

INTRODUCTION I. BASIC CONCEPTS: SOCIAL WELFARE FUNCTIONS, EQUITY REGARD, AND EX ANTE VERSUS EX POST SOCIAL WELFARE ANALYSIS A. Social Welfare Functions Under Certainty B. Equity Regard Under Certainty C. Adding Uncertainty: Ex Post vs. Ex Ante Social Welfare Analysis II. UNDERSTANDING THE DIVERGENCE BETWEEN EX POST AND EX ANTE APPROACHES TO SOCIAL CHOICE A. The Basic Phenomenon B. Rank Uncertainty, Rank-Weighted Social Welfare, and the Gini Coefficient C. Strictly Concave Social Welfare Functions D. Permuting Policies E. Prioritarianism and Separable Social Welfare Functions F. A Summary III. COMPENSATION AND INSURANCE A. Will Compensating Policy Losers Eliminate the Ex Ante/Ex Post Divergence? 1. Free Transferability of Utility Across Individuals 2. Free Transferability of Utility Across States 3. General Case B. The Suboptimality of Compartmentalizing Equity Concerns C. Private Insurance IV. EX ANTE PARETO SUPERIORITY VERSUS EX POST SOCIAL WELFARE V. WHAT IS THE CORRECT APPROACH TO WELFARIST SOCIAL CHOICE UNDER UNCERTAINTY: EX POST OR EX ANTE? A. The Connection Between the Sure-Thing Principle and the Ex Post Approach B. Is the Sure-Thing Principle Attractive ?. 1. Diamond's Example 2. Welfare Contractarianism 3. Time Inconsistency of the Ex Ante Approach C. Violating Ex Ante Pareto Superiority VI. LEGAL APPLICATIONS A. Risk-Reduction Policies for Widely Borne Risks (Herein of Terrorists. Asian Birds. and British Cows) B. Risk Compensation (Herein of Workers' Compensation, Unemployment Insurance, and the Compensated Siting of "LULUs") C. "Population Risk" Versus "Individual Risk" and the Problem of Statistical Versus Identified Lives D. Pain-and-Suffering Damages E. Criminal Law F. Capital Gains and Lotteries G. Tax Policy Norms CONCLUSION MATHEMATICAL APPENDIX A. Utilitarianism and the Equivalence of Ex Ante and Ex Post Social Welfare Calculations B. Equity Regard C. Rank-Weighted Social Welfare and the Gini Coefficient D. Transfers That Are Disequalizing Ex Post and Equalizing Ex Ante E. Strict Concavity F. Permuting Policies G. Separable Social Welfare H. Compensation I. Nonfreely Transferable Utility J. Time Inconsistency of the Ex Ante Approach K. Application: Spending on Prevention INTRODUCTION

Imagine a social decision maker--a legislator, a regulator, a judge--who cares about inequality. This is not, let us say, her only concern--she would not be satisfied to see everyone equally wretched. But it does inform her choices and is sometimes decisive. Suppose further that she has to decide whether to encourage a certain new technology. The technology will make most individuals better off. But a few will die. Maybe the new technology is the automobile, and the few are the pedestrians who will be run down. Or maybe it is a new vaccine for a contagious disease, and the few are those who will have a fatal reaction. When she arrives at the portion of her policy analysis that concerns inequality, how should she assess the equity effects of this technology,? Would it help if everyone were equally likely to be a pedestrian casualty, or have an adverse reaction to the vaccine? Would her concern for inequality be assuaged, in other words, by an "equality of prospects"? Or would she reason that what matters is what actually happens, and what actually happens is in all cases disequalizing? That is, would she locus on the certainty that some will pay dearly while others benefit, and regard as irrelevant the uncertainty regarding who will end up in which position?

There are likely as many ways to approach this problem as there are philosophies of social choice. Our concern in this Article is how the problem should be addressed within the bounds of a particular approach to social choice called "welfarism." Welfarism holds that social choices should be evaluated solely according to how they affect the well-being of society's members. Importantly, the approach is broad enough to allow concern for inequality of well-being across individuals. But it does not admit criteria like "fairness," "rights," or "justice"--at least not as foundational criteria for choice. (1)

Debates about welfarism have, in recent years, consumed much energT within legal scholarship and related fields. Within legal studies, Louis Kaplow and Steven Shavell's recent book defending welfarism, Fairness Versus Welfare, (2) has prompted a vigorous and extensive debate. (3) Similar scholarly discussions appear within normative economics, although welfarism remains the dominant posmon. (4) Within philosophy, a third arena of dispute, welfarism and related views are surely not dominant, but they remain important contenders. (5)

We take a different tack. Rather than contributing directly to the debate about welfarism, our primary object is to identify and grapple with a large problem that arises within welfarism. For purposes of this Article, we take welfarism as given--although, as we shall explain below, the Article should also be of much interest for nonwelfarists, and for those engaged in the debate between welfarism and nonwelfarism.

Call the problem illustrated by our initial hypothetical the "ex ante/ex post" problem. Although it has received little attention, especially within legal scholarship, the ex ante/ex post problem is the natural product of two essential specifications for any systematic approach to normative discourse about law. (6) The first is the ability to account for the fact that policy outcomes are often uncertain--an inescapable difficulty of real-world policy analysis. The second is the ability to incorporate a social dispreference for inequality--a feature most would probably regard as important (to varying degrees) and one of the advertised attractions of welfarism. (7)

Because these specifications are so central to real-world policy discourse, the ex ante/ex post problem that they generate is ubiquitous in law and policy. Part VI of this Article reviews but a sampling of the kinds of the legal and policy issues that implicate the ex ante/ex post problem. How much should be spent on security against terrorist acts and other dangers that put many at moderate risk, but severely harm relatively few? What is the proper scale and scope for social insurance? What are we to make of the fact that residents in a particular neighborhood voluntarily agree to accept compensation in return for living near a toxic waste site with potential health risks? Is that the end of the issue? Should so-called "individual risk" tests continue to be used in environmental regulation? Should plaintiffs be allowed to recover for pain-and-suffering damages? Who should bear the burden of proof at trial? How severely should we sanction violations of the law? At what rate should we tax capital gains?

To be more concrete about the nature and extent of the ex ante/ex post problem we must also become more abstract. Suppose then that we are in control of a society consisting of two individuals, call them JANET and JOHN. Imagine we face a choice between two alternative policies, UNCERTAIN and CERTAIN. The outcome of UNCERTAIN is, as its name indicates, uncertain. Half the time it increases JANET's well-being by 900 units with no effect on JOHN's. Half the time it increases JOHN's well-being by 900 units with no effect on JANET'S. The policy CERTAIN always increases JOHN's well-being by 400 units and JANET'S by 400 units also. Which policy should we choose?

In conformity with the limited information given in the example, assume that we are welfarists, so that we must decide solely on the basis of how the two policies affect JOHN and JANET's well-being. Let us further assume that we care not just about "efficiency"--the total amount of well-being summed over the two individuals--but also about "equity"--how evenly the total amount of well-being is distributed across the two individuals.

If both policies had but a single certain outcome, our task would be (relatively) simple. We would evaluate the policies along the two dimensions of equity and efficiency. In the event that neither policy was superior along both dimensions, our choice would depend upon the precise manner in which we...