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Egalitarianism under Severe Uncertainty

2018; Wiley; Volume: 46; Issue: 3 Linguagem: Inglês

10.1111/papa.12121

1088-4963

Thomas D. Rowe, Alex Voorhoeve,

Political Philosophy and Ethics

By “uncertain” knowledge, let me explain, I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty; (…). Even the weather is only moderately uncertain. The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper (…). About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know.3 It is likely [official translation: there is a chance between 0.66 and 1] that land temperatures over Africa will rise faster than the global land average, particularly in the more arid regions.5 Uncertainty also arises in private decisions, such as when a doctor is considering a novel drug for multiple sclerosis for their patient, and the evidence, combined with the decision-makers' prior beliefs, does not permit them to nonarbitrarily assign precise probabilities to this treatment's effects.6 Given the ubiquity of uncertainty, it is striking that the philosophical discussion of the requirements of egalitarian distributive justice under uncertainty is far less developed than it is for conditions of risk.7 Here, we take a step toward remedying this lack. We take as our point of departure a recent, pluralist egalitarian theory of distributive justice under risk. We propose and defend a novel extension of this view for uncertain situations and trace some key implications for policy decisions. We proceed as follows. In Section II, we summarize the egalitarian view for decision-making under risk that we take as our point of departure. In Section III, we introduce a cautious or “uncertainty-averse” decision criterion that we will appeal to throughout. On this criterion, uncertainty represents a burden in the sense that it reduces the value of a prospect. In subsequent sections, we explore novel implications generated by the interplay of the twin aims of reducing the burden of uncertainty and limiting inequality. In Section IV, we discuss cases where these aims are congruent. We show that our view provides novel reasons to direct resources toward those who have worse prospects or outcomes than others. In Section V, we consider cases where uncertainty aversion and inequality aversion are in tension. We show that our view weakens the egalitarian impulse to ensure that everyone sinks or swims together, because it gives great weight to eliminating the possibility of collective misfortune. In Section VI, we provide a new perspective on the debate between utilitarians and egalitarians. We demonstrate that if aversion to uncertainty is permissible, then utilitarians cannot wield a favorite argument against egalitarians. We summarize our principal findings and their relevance for a range of policy decisions in Section VII, where we also return to our opening H1N1 influenza case. Before proceeding, we emphasize that our aim is merely to propose an egalitarian view that incorporates a set of rationally and morally permissible (rather than required) differential attitudes toward risk and uncertainty. In the service of this aim, we assume orthodox decision theory under risk, because leading alternatives to the orthodoxy under risk see conformity with the orthodoxy as rationally permissible.8 However, we pair it with an unorthodox (although well known) decision principle under uncertainty, which yields the orthodoxy in the special case in which the decision-maker assigns precise probabilities to each outcome. The challenges to the orthodoxy posed by uncertainty are unique, because they involve a decision-maker lacking the grounds for forming reasoned beliefs of the kind that play a central role in making the orthodoxy plausible. It is therefore coherent, and indeed common, to endorse the orthodoxy in risky cases but not in cases of uncertainty.9 This approach also allows us to focus squarely on unexplored issues involved in confronting uncertainty. Pluralistic egalitarianism: We should aim to improve people's prospects for well-being, raise total well-being, and reduce inequality in both people's prospects and in their final well-being (how well their lives end up going). With respect to each individual's fate, we will assume that we are concerned with the distribution of a cardinal, interpersonally comparable measure of lifetime well-being derived from idealized preferences satisfying the von Neumann–Morgenstern axioms under risk. On this measure, a prospect has higher expected well-being for a person just in case it would be preferred after rational and calm deliberation with all pertinent information while attending to that person's self-interest only.11 One prospect has the same expected well-being as another prospect for a person just in case such deliberation would yield indifference between the two prospects. To illustrate our egalitarian view under risk, imagine the following situation of a resource allocation manager in the National Health Service. Two 10-year-old children, Ann and Bea, have just been diagnosed with an illness which, if untreated, will leave them completely blind and with a lifetime well-being of 50 (a moderately good quality of life); if fully cured, each would have a lifetime well-being of 80 (a very good quality of life).12 Both are strangers to the decision-maker and to each other. Unfortunately, the resources at the decision-maker's disposal do not suffice to fully cure both Ann and Bea for sure. Below, we will describe the alternatives open to them. To link up with Ellsberg's paradigmatic presentations of risky and uncertain alternatives, risk will be represented by a random draw from an urn which is known to contain only 50 red balls and 50 black balls.13 (Although it may seem odd to speak of providing treatments that are effective conditional on the draw of a ball of a particular color from an urn, this is merely a device to depict treatments for which the decision-maker rationally assigns precise probabilities to each possible outcome.) Table 1 lists the final well-being for Ann and Bea given each possible draw from this urn for each of the alternatives we will presently consider.14 We use redr and blackr to represent the possible draws from this risky urn, and pred and pblack for the probability of these draws. Throughout, for simplicity, we will consider only Ann's and Bea's well-being; we will not consider how their level of well-being relates to that of further people. Inequality under Certainty: Cure Ann and leave Bea to go wholly blind. Equal Risk, Unequal Final Well-being: This treatment will either cure Ann and be entirely ineffective for Bea (leaving her to go wholly blind), or, instead, be entirely ineffective for Ann (leaving her to go wholly blind) and cure Bea. These results are equally likely. Our pluralist egalitarian view requires choosing the latter. For it is concerned with limiting unfairness, and although both alternatives yield unfair inequality in final well-being, there is, on this view, less unfairness overall when each is given an equal shot at a cure than when one child is given a cure outright and the other has no chance at receiving it.15 Equality under Risk: this treatment will either cure both children, or be wholly ineffective for both, with each result being equally likely. On our egalitarian view, this alternative is superior to the preceding two. For by ensuring that all are in the same boat, it eliminates all unfair inequality without loss of expected total well-being. Equality under Certainty: This treatment will improve both Ann's and Bea's condition to that of a merely partial, but still substantial, visual impairment. We will consider both cases in which the level of well-being associated with this partial impairment is precisely halfway between the well-being associated with complete blindness and a full cure and cases in which this level falls short of this halfway point. The shortfall is given by a cost c, with 0 ≤ c < 15. On our egalitarian view, if c = 0, then Equality under Certainty is of course better than the first two inegalitarian alternatives, because it eliminates inequality at no cost in expected total well-being. Moreover, Equality under Certainty is precisely as good as Equality under Risk. In the absence of inequality, this form of egalitarianism simply tells us to choose a best prospect for each individual; because, for c = 0, both Equality under Risk and Equality under Certainty offer each individual an expected well-being of 65, both are equally good prospects for each person. For a sufficiently small, positive cost (c > 0), Equality under Certainty will still be chosen over the first two alternatives, because it eliminates all inequality with only a small reduction in expected total well-being. However, our egalitarian view will then regard it as inferior to Equality under Risk, because the latter offers each individual better prospects while ensuring equality. We shall now explain how we propose to extend our pluralist egalitarian view to cases of uncertainty. Let us start with a simple, one-person case. Suppose that Ann will go wholly blind unless she is treated. You must choose between providing Ann with an established risky treatment, which, given the extensive evidence available, you confidently believe has a 0.5 chance of curing her and a 0.5 chance of having no effect on her, and providing her with a novel, maximally uncertain treatment, which will either lead to a full cure or else be entirely ineffective. There is no information available on the probabilities associated with these possible outcomes of the uncertain treatment. Moreover, you do not possess precise prior beliefs about the probability of its effectiveness. Which treatment(s) is it morally permissible for you to provide? And which would you choose? There is evidence that many decision-makers' answer to the latter question would be the merely risky treatment. Part of this evidence is that in a wide range of experiments involving self-interested choices, a large share of decision-makers (typically: a majority) strictly prefer a prospect in which they gain if a fair coin comes up heads to the same gain on an event about which they know only that its probability may be anything in a range from 0 to 1.16 They thereby display what is known as “uncertainty (or ambiguity) aversion” on their own behalf. (Those who are indifferent between this risky and uncertain prospect are commonly described as “uncertainty [ambiguity] neutral”; those who strictly prefer the uncertain prospect are known as “uncertainty [ambiguity] seeking.”) And although there are less data on choices that concern others' interests only, uncertainty aversion appears to be just as prevalent in such decisions.17 The argument for holding that this common uncertainty-averse attitude is morally and rationally permissible proceeds in two stages. The first stage pertains to belief formation. In this situation, by hypothesis, the combination of your evidence and prior beliefs is compatible with a wide range of assignments of probabilities to particular outcomes of the novel treatment. You therefore lack sufficient basis for a unique assignment of precise probabilities to the possible outcomes of this treatment. Indeed, to make such an assignment would seem to be arbitrary in the sense that it runs ahead of the information you have and ignores other possible assignments that are no less consistent with your prior beliefs and evidence. Neither rationality nor morality requires the formation of beliefs that lack sufficient foundation in the evidence.18 You are therefore not required to adopt a single precise assignment of probabilities to each possible outcome of the novel treatment. Instead, it is reasonable for you to take account of the full range of probability assignments that are supported by the data and your prior beliefs. In other words, you may consider everything from the worst probability distribution over the outcomes “wholly ineffective” and “full cure” that is consistent with your evidence and prior beliefs (viz., that the novel treatment provides Ann with no chance of a cure) to the best probability distribution consistent with this information and these beliefs (viz., that it is sure to cure her), without reducing them to a single probability distribution. The second stage pertains to how this range of probability assignments over pertinent outcomes can permissibly figure in your decision-making. The central idea is that although you should assign some decision weight to both the worse and better possible probability distributions over outcomes, how much decision weight to assign to each is, within a considerable range of sensible weights, up to you. Cautiously assigning somewhat greater decision weight to the worse possible probability distributions than to the better ones is in this sensible range.19 Such caution in the face of an inability to arrive at precise probabilistic assignments is the central motivation for uncertainty aversion. Our claim is not that uncertainty aversion is the only reasonable attitude. It is merely that a moderate degree of such aversion is perfectly sensible. Caution of the kind outlined could, we believe, be offered as a good reason for a choice of the risky treatment over the uncertain treatment to anyone concerned with Ann's welfare. We note, however, that despite its appeal, the rationality of uncertainty aversion is controversial among decision theorists. The reason is that if one assumes, as we have done, that under conditions of risk it is rationally required to obey the von Neumann–Morgenstern axioms, then uncertainty aversion and a central axiom of decision theory, the Sure Thing Principle, cannot be reconciled.20 Moreover, violation of the Sure Thing Principle has unpalatable implications.21 The debate on whether one should conclude that uncertainty aversion is irrational is extensive. Rather than reviewing this debate, we will simply state our take on it, which is that there is a tension between independently attractive principles of rationality, including, on the one hand, that rationality does not require a decision-maker to posit precise probabilities when they lack sufficient grounds for doing so and that a decision-maker is entitled to be cautious in the face of such a lack, and, on the other hand, that a decision-maker should respect other attractive principles of rational choice. Different ways of “trading off” such incompatible ideal standards of rationality are sensible, and among the sensible ways of making trade-offs are uncertainty-averse decision principles.22 In the remainder of this article, we will therefore explore what would follow if a degree of uncertainty aversion were both rationally and morally acceptable. This question is worth exploring because uncertainty aversion strikes us, many everyday decision-makers, and a considerable number of experts as a reasonable attitude, and it gives rise to underexplored issues of distributive justice. Many uncertainty-averse decision criteria have been proposed. For illustrative purposes, we will here use a simple but popular criterion first put forward by Leonard Hurwicz and later developed together with Kenneth Arrow, which pays attention to only the least favorable and most favorable probability distributions that are consistent with the decision-maker's information and prior beliefs.23 Our conclusions hold for all other leading criteria, including those that give some weight to all probability distributions that the decision-maker regards as consistent with their evidence and beliefs.24 On what is known as the α-Hurwicz or α-maxmin criterion, one values each person's prospect at α × its expected value given the least favorable probability distribution consistent with one's information and prior beliefs plus (1 − α) × its expected value given the most favorable probability distribution that is so consistent, where 0 ≤ α ≤ 1 is the Hurwicz pessimism–optimism index. Uncertainty aversion involves giving more decision weight to the least favorable possible probability distribution than to the most favorable one; in other words, it involves taking α > 0.5. (The criterion reduces to orthodox decision theory when a decision-maker uses a single probability distribution.) In what follows, we will assume a decision-maker who has a fixed, permissible degree of uncertainty aversion both when they evaluate a prospect for the sake of a single individual and when they evaluate a multi-person prospect. This implies a constant α > 0.5 for all decisions. By way of illustration, consider the experimental treatment with which we opened this section and which we represented by a case in which Ann is cured if and only if a red ball is draw from a wholly uncertain urn. An uncertainty-averse decision-maker who uses the α-maxmin criterion will consider both the most pessimistic assessment of the information available—according to which there are no red balls in this urn—and the most optimistic assessment—according to which it contains only red balls. Moreover, they will give at least somewhat greater weight to the former than to the latter. Because of this cautious form of evaluation, they will regard the uncertain treatment as less good for Ann, in prospect, than giving her a risky treatment which would carry a 0.5 probability of a full cure and a 0.5 probability of being wholly ineffective. For example, a moderately uncertainty-averse decision-maker for whom α = 0.6 will regard Ann's wholly uncertain prospect as equivalent to a treatment with an expected value of 62 units of well-being or 3 units of expected well-being less than this risky treatment. (Despite the fact that the criterion permits us to assign such equivalents to uncertain prospects, the value of an uncertain prospect when applying this criterion is not an expected value, because the decision weights applied to different possible probability distributions are not probabilities. When we are discussing uncertain and/or risky prospects, we therefore use the more general term “prospective value.”) A moderately uncertainty-averse decision-maker for whom α = 0.6 will therefore regard this partly uncertain treatment as equivalent to a treatment with an expected value of 63.5 units of well-being or precisely in between the value of the aforementioned wholly uncertain treatment and the value of the aforementioned merely risky treatment, which has a 0.5 chance of effecting a cure. This illustrates that, on this criterion, reducing the range of uncertainty also, naturally, reduces the depressing effect it has on the value of a prospect. We will now review ways in which adding uncertainty aversion to our egalitarian view generates novel implications. We first focus on cases in which the aim of reducing uncertainty does not conflict with the aim of reducing inequality. (We deal with conflicts between these aims in the next section.) Equal Uncertainty, Unequal Final Well-being: This treatment will either cure Ann and leave Bea wholly blind or cure Bea and leave Ann wholly blind, with no information available about the probability of either outcome. These alternatives are displayed in Table 1. We use redu (blacku) to signify the event of a red (black) ball being drawn from an uncertain urn. Our pluralistic view requires that we take account of both the distribution of individuals' prospects and the prospective value of the possible anonymized distributions of final well-being. Let us consider each in turn. The risky alternative ensures equality of prospects, as does the uncertain alternative. However, the uncertain alternative gives each individual a less valuable prospect than its risky counterpart. Considering individuals' prospects, therefore, Equal Risk, Unequal Final Well-being is clearly superior. Furthermore, in terms of the prospective value of the possible distributions of final well-being, the two are equivalent. For, under each of these alternatives, the anonymized distribution of final well-being is certain: one person will be fully cured, another will go wholly blind. One can therefore say that although one of these alternatives contains individual-level uncertainty, neither contains any population-level uncertainty. All things considered, Equal Risk, Unequal Final Well-being is therefore more choiceworthy, but only because it avoids the depressing effect of uncertainty on the value of individuals' prospects. Equality under Uncertainty: This treatment will either cure both children or leave them both to go wholly blind, with no information available about the probability of either outcome. These alternatives are depicted in Table 1. In this case, both a concern for individuals' prospects and a concern for the prospective value of the possible anonymized distributions of final well-being point in the same direction. Equality under Uncertainty offers each individual a less valuable prospect. Moreover, it generates population-level uncertainty, because the decision-maker is uncertain about the anonymized distribution of final well-being. This lowers the value of Equality under Uncertainty, because the worst possible probability distribution (i.e., that the probability that both individuals are cured is 0) receives greater weight than the best possible probability distribution (i.e., that the probability that both are cured is 1). An uncertainty-averse view will therefore have two reasons for judging that it is better to opt for Equality under Risk. So far, we have analyzed cases in which, while keeping inequality constant, a decision-maker can ensure less uncertainty. Now, we will consider a case in which, keeping total uncertainty constant, a decision-maker can equalize its burden. Unequal Uncertainty: Ann is given a novel treatment which will either cure her or instead leave her wholly blind, with no information about the probability of either outcome. Bea is given a distinct treatment which will either, with probability 0.5, cure her or, with probability 0.5, leave her wholly blind. Equal Moderate Uncertainty: Ann and Bea are each given different distinct, moderately uncertain treatments, each of which will either offer a full cure or leave its recipient wholly blind. For each of their treatments, the probability of a cure ranges from 0.25 to 0.75. These alternatives are represented in Table 1. The choice between Unequal Uncertainty and Equal Moderate Uncertainty can be thought of as follows. Ann and Bea each face a draw from a separate urn. Each receives a cure if a red ball is drawn from their urn; if a black ball is drawn, their treatment is ineffective. The decision-maker must fill each urn with 100 balls. They have four bags of 50 balls each: two risky bags containing an equal mix of red and black balls and two wholly uncertain bags about which the decision-maker has no information except that they can be any proportion of red and black. If they empty both uncertain bags into Ann's urn and both risky bags into Bea's urn, then they generate Unequal Uncertainty. By contrast, if they fill each urn with one uncertain and one risky bag, then they generate Equal Moderate Uncertainty. The former places all the burden of uncertainty on Ann's prospects. By contrast, the latter equalizes the burden of uncertainty. Moreover, it is natural to suppose that the total burden created by the uncertain balls is not increased when they are divided equally.27 From the perspective of the distribution of the value of individuals' prospects, therefore, Equal Moderate Uncertainty is clearly superior. We must also consider the prospective value of the possible anonymized distributions of final well-being associated with each of these alternatives. Using the α-maxmin criterion, it is sufficient to consider only the worst and best among the possible probability distributions, which are listed in Table 1. Now, under Unequal Uncertainty, in both the pessimistic scenario (i.e., Ann's urn contains no red balls) and the optimistic scenario (i.e., Ann's urn contains red balls only), an unequal outcome—in which only one person is cured—has a probability of 0.5. (This is the sum of the probabilities for the events {red u, black r} and {black u, red r}.) By contrast, under Equal Moderate Uncertainty, in both the pessimistic and optimistic scenario, the probability of an unequal outcome is 0.375. In other words, Equal Moderate Uncertainty makes an unequal outcome less likely no matter whether the odds are stacked against the person(s) facing uncertainty or whether the odds are in their favor. This makes it better from the perspective of the prospective value of the anonymized distribution of final well-being.28 We can conclude that our uncertainty-averse egalitarian view yields the plausible verdict that one should distribute the burden of uncertainty equally. Our view does not merely posit a novel object of egalitarian concern (the disvalue of uncertainty); it also lends additional force to the egalitarian aim of directing aid toward those who end up less well off than others. By way of illustration, suppose that our decision-maker must choose between Equal Uncertainty, Unequal Final Well-being and Equality under Certainty. For convenience, both are represented in Table 1. Recall that c is the cost of achieving both equality and certainty, with 0 ≤ c < 15. Let us again consider both the value of individuals' prospects and the prospective value of the anonymized distribution of final well-being. Under Equal Uncertainty, Unequal Final Well-being, the value of each individual's prospect is depressed by the fact that the decision-maker has no information about their chance of ending up disadvantaged. The badness of this uncertainty for an individual is determined by the gap between the expected value of this individual's prospects given the possible probability distribution that is least favorable to them and the expected value of this individual's prospects given the possible probability distribution that is most favorable to them. Equality under Certainty is valuable because it altogether eliminates this gap. From the perspective of the value of individuals' prospects, an uncertainty-averse decision-maker should therefore be willing to incur a cost (c > 0) to eliminate this uncertainty. Turning to the prospective value of the possible distributions of final well-being, a drawback of Equal Uncertainty, Unequal Final Well-being is, naturally, the certainty of outcome inequality. An inequality-averse decision-maker will therefore be willing to pay a price (c > 0) to eliminate this inequality. Overall, both uncertainty aversion and inequality aversion will prompt us to incur a cost to remove inequality. Moreover, jointly, they will justify paying a higher price to achieve equality than either alone would. To see why, suppose for the moment that our decision-maker remained inequality averse but became indifferent to uncertainty (i.e., their α = 0.5). They would then evaluate Equal Uncertainty, Unequal Final Well-being as equivalent to Equal Risk, Unequal Final Well-being (the latter is described in Table 1). Suppose that to eliminate the inequality of final well-being in these alternatives, it is right to incur up to, but no more than, a cost to each person of c* units of expected well-being. We can then say that, for an uncertainty-neutral, but inequality-averse decision-maker, both Equal Uncertainty, Unequal Final Well-being and Equal Risk, Unequal Final Well-being are equivalent to giving each of Ann and Bea 65 − c* for certain. Now suppose that our decision-maker regained their uncertainty aversion. They would then regard Equal Uncertainty, Unequal Final Well-being as worse than Equal Risk, Unequal Final Well-being. By transitivity, they would regard the uncertain alternative as worse than giving both Ann and Bea 65 − c* for certain. In other words, they would regard Equal Uncertainty, Unequal Final Well-being as equivalent to Equality under Certainty only for a cost larger than c*. It follows that an uncertainty-averse egalitarian view justifies incurring a larger cost to achieve both equality and certainty than an uncertainty-neutral egalitarian view would countenance. Let us summarize the distinctive implications of our view uncovered in this section. First, and straightforwardly, it will favor situations in which a better basis is available for assigning probabilities to outcomes. This is illustrated by the stylized choices in Tables 1 and 1. In real-world cases, the view will therefore display a tendency to favor policies with an extensive evidence base over ones with a minimal evidence base, keeping other things equal. Under these circumstances, it will also favor familiar over unfamiliar treatments for patients and make the provision of the latter harder to justify.29 Second, the proposed view posits an additional object of egalitarian concern, namely, the burden of uncertainty. In general, it implies that there is unfairness in situations in which some face a greater burden of uncertainty than others, either because there is less information about the likelihood of the possible threats they face or because there is much more at stake for them. The case outlined in Table 1 provides a stylized example. A realistic case in which such inequality is of concern is climate policy. For it is likely that people in poorer nations who inhabit marginal lands and who are dependent on the weather for their livelihood face larger burdens of uncertainty than urbanites in wealthy countries. Third, in uncertain situations in which we know that one person's good fortune will be the counterpart of another's misfortune, uncertainty aversion and inequality aversion point us in the same direction. In such situations, steering benefits to whoever turns out to be less fortunate reduces the stakes for each person