Chapter Eight
Uncertainty and the Utilitarian Strategy

The Case for a "Maximin" Account of Risk and Rationality

A recent U.S. National Academy of Sciences study pointed out that the estimates of increase in bladder cancer, caused by consuming normal amounts of saccharin over seventy years, differed by seven orders of magnitude. Despite these uncertainties, U.S. officials have sanctioned the use of saccharin, justifying their decision on the basis of a liberal risk assessment. As a result of a very conservative risk analysis, however, they banned cyclamates. If the two risk-assessment methodologies were consistent, experts have argued, cyclamates could easily have been shown to present a lower relative risk than saccharin. In Canada, for example, cyclamates are permitted, and saccharin is banned, making Canadian regulations in this area exactly the reverse of those in the United States.1

As the saccharin-cyclamates controversy illustrates, risk evaluations may be uncertain, not only because of the wide range of predicted hazard values, but also because of inconsistent risk models and rules of evaluation. This chapter will assess several of the prominent rules for evaluating risks. To see how alternative rules can generate different risk-management decisions for the same hazard, consider the following case.

The probability of a core melt for U.S. reactors is about I in 4 during their lifetime.2 Risk assessments conducted by both the Ford Foundation-Mitre Corporation and the Union of Concerned Scientists (UCS) agree on the probability and consequence estimates associated with the risk from commercial nuclear fission, but they disagree in their recommendations regarding the advisability of using atomic energy to generate electricity. The UCS risk analysis decided against use of the technology; the Ford-Mitre study advised in favor of it.3

How could hazard assessments and evaluations that agree on the probability and consequences associated with a particular technological accident reach contradictory conclusions about the advisability of using the technology? In many such cases, including that of the UCS-Ford-Mitre controversy, the reason is that the two studies used quite different methodological rules at the third (risk-evaluation) stage of assessment. The Ford-Mitre research was based on the widely accepted Bayesian decision criterion that it is rational to choose the action with the best expected value or utility, where "expected value" or "expected utility" is defined as the weighted sum of all possible consequences of the action, and where the weights are given by the probability associated with each consequence. The UCS recommendation followed the maximin decision rule that it is rational to choose the action that avoids the worst possible consequence of all options.4

To know whether a particular policy analysis provides the best recommendation for rational behavior regarding risk, we obviously need to know under what circumstances a particular decision rule is to be preferred. Ought we to be technocratic liberals and choose a Bayesian rule? Or ought we to be cautious conservatives and follow a maximin strategy?5 The "prevailing opinion" among scholars, according to John Harsanyi, is to use the Bayesian rule,6 even in conditions of uncertainty.7

In this chapter, I argue that the prevailing Bayesian or utilitarian rules are often wrong. Like the expert-judgment strategy and the probabilistic strategy (Chapters Six and Seven), the Bayesian strategy dismisses the views of ordinary people as conservative, pessimistic, and irrational (rather than liberal, optimistic, and rational).8 This chapter argues that there are compelling reasons for rejecting the Bayesian or utilitarian strategy under uncertainty, and that it is often more rational to prefer the maximin strategy.

Harsanyi versus Rawls: Expected Utility versus Maximin

Perhaps the most famous contemporary debate over which decision rules ought to be followed in situations of risk and uncertainty is that between Harvard philosopher John Rawls and Berkeley economist John Harsanyi. Following the utilitarian strategy, Harsanyi takes the Bayesian position that we ought to employ expected-utility maximization as the decision rule in situations of uncertainty, certainty, and risk.9 Typical conditions of uncertainty occur when we have partial or total ignorance about whether a choice will result in a given outcome

with a specific probability; for example, if we use nuclear power to generate electricity, we have partial ignorance about whether that choice will result in the probability that at least 150,000 people will die in a core-melt accident. Under conditions of certainty, we know that a choice will result in a given outcome; for example, if we use nuclear power to generate electricity, we are certain to have the outcome of radwaste to manage. Choices between bets on fair coins are classical examples of decisions under risk, since we can say that we know, with a specific probability, whether a choice will result in a given outcome. (Let's call the Bayesian sense of risk, involving specific, known probabilities, "risk_B " and the sense of risk, often involving uncertainty, with which hazard assessors deal, simply "risk.")

Most technology-related decisionmaking probably takes place in situations of uncertainty. We rarely have complete, accurate knowledge of all the probabilities associated with various outcomes of taking technological risks (e.g., from hazards such as pesticides, liquefied natural gas facilities, and toxic wastes), since very risky technologies are often new. The U.S. National Academy of Sciences confirmed, in a 1983 report, that the basic problems of risk assessment stem from the "uncertainty of the scientific knowledge of the health hazards addressed."10 This statement suggests that many of the difficulties facing risk evaluation concern uncertainty, not "risk_B ." If that is so, then one of the most important questions in the Harsanyi-Rawls expected-utility—maximin debate is what decision rule to follow under the conditions of uncertainty that characterize various technologies.

Harsanyi believes that, under conditions of uncertainty, we should maximize expected utility, where the expected utility of an act for a two-state problem is

u₁p + u₂ (1 - p ),

where u₁ and u₂ are outcome utilities, where p is the probability of S ₁ and (1 - p ) is the probability of S₂ , and where p represents the decisionmaker's own subjective probability estimate.11 More generally, members of the dominant Bayesian school claim that expected-utility maximization is the appropriate decision rule under uncertainty.12 They claim that we should value outcomes, or societies, in terms of the average amounts of utility (subjective determinations of welfare) realized in them.13

Proponents of maximin maintain that one ought to maximize the minimum—that is, avoid the policy having the worst possible consequences.14 Many of them, including Rawls, take the maximin principle as equivalent to the difference principle. According to a simplified version

of this principle, one society is better than another if the worst-off members of the former do better than the worst-off in the latter.15 As previously noted, the obvious problem is that often the maximin and the Bayesian/utilitarian principles recommend different actions. Consider an easy case:

Imagine two societies. The first consists of 1,000 people, with 100 being workers (workers who are exposed to numerous occupational risks) and the rest being free to do whatever they wish. We can assume that, because of technology, the workers are easily able to provide for the needs of the rest of society. Also assume that the workers are miserable and unhappy, in part because of the work and in part because of the great risks that they face. Likewise, assume that the rest of society is quite happy, in part because they are free not to work and in part because they face none of the great occupational risks faced by the 100 workers. (This means, of course, that the compassion of the 900 nonworkers does not induce them to feel sorry for the workers and to feel guilty for having a better life. Hence we must assume that the nonworkers' happiness is not disturbed by any feeling of responsibility for the workers.) We must assume that the nonworkers have been able to convince themselves that each of the workers and their children were given good educations and equal opportunity. Likewise we must assume that the nonworkers believe that the workers were able to compete for the positions of nonworkers, and that, since the workers did not try hard enough, and work diligently enough to better themselves, therefore they deserve their state. With all these (perhaps implausible) assumptions in mind, let us suppose that, using a utility scale of I to 100, the workers each receive I unit of utility, whereas the others in society each receive 90 units. . . . Thus the average utility in this first society is 81.1
Now consider a second society, similar to the first, but in which, under some reasonable rotation scheme, everyone takes a turn at being a worker. In this society everyone has a utility of 35 units. Bayesian utilitarians would count the first society as more just and rational, whereas proponents of maximin and the difference principle would count the second society as more just and rational.16

Although this simplistic example is meant merely to illustrate how proponents of Bayesian utilitarianism and maximin would sanction different social decisions, its specific assumptions make maximin (in this case) appear the more reasonable position. Often, however, the reverse is true. There are other instances, especially situations of risk_B or certainty, in which the Bayesian position is obviously superior. In this chapter, we shall attempt to determine the better decision rule for cases of societal hazard decision under uncertainty (not personal hazard decisions under uncertainty or risk_B ), since environmental hazards are often typified by uncertainty.17 A reasonable way to determine whether the Bayesian/utilitarian or maximin position is superior is to examine

carefully the best contemporary defenses, respectively, of these evaluation rules. The best defenses are probably provided by Harsanyi, an act utilitarian who defends a Bayesian version of utilitarianism,18 and Rawls, a contractarian.

Harsanyi's Arguments

Harsanyi's main arguments in favor of the Bayesian/utilitarian, and against the maximin, strategy under uncertainty are as follows: (1) Those who do not follow the Bayesian/utilitarian strategy make irrational decisions because they ignore probabilities. (2) Failure to follow this strategy leads to irrational and impractical consequences. (3) This failure also leads to unacceptable moral consequences. (4) Using the Bayesian/utilitarian strategy, with the equiprobability assumption, is desirable because it allows one to assign equal a priori probability to everyone's interests.

Do Non-Bayesians Ignore Probabilities?

Choosing the maximin stategy, claims Harsanyi, is wrong because "it is extremely irrational to make your behavior wholly dependent on some highly unlikely unfavorable contingencies, regardless of how little probability you are willing to assign to them."19 To substantiate his argument, Harsanyi gives an example of maximin decisionmaking and alleges that it leads to paradoxes. The example is this. Suppose you live in New York City and are offered two jobs, in different cities, at the same time. The New York City job is tedious and badly paid; the Chicago job is interesting and well paid. However, to take the Chicago job, which begins immediately, you have to take a plane, and the plane travel has a small, positive, associated probability of fatality. If you were to follow the maximin principle, says Harsanyi, you would accept the New York job. The situation can be represented, he claims, on the following table:

In the example, Harsanyi assumes that your chances of dying in the near future from reasons other than a plane crash are zero. Hence, he

concludes that, because maximin directs choosing so as to avoid the worst possibility, it forces one to ignore both the low probability of the plane crash and the desirability of the Chicago job and instead to choose the New York job. However, Harsanyi claims that a rational person, using the expected-utility criterion, would choose the Chicago job for those very two reasons—namely, its desirability and the low probability of a plane crash on the way to Chicago.

How successful is Harsanyi's first argument in employing the counterexample of the New York and Chicago jobs? For one thing, the example is highly counterintuitive; it is hard to believe that the greatest risk comes from dying in a plane crash, since hazard assessors have repeatedly confirmed that the average annual probability of fatality associated with many other activities—driving an automobile, for example—is greater, by an order of magnitude, than that associated with airplane accidents.20 Harsanyi has stipulated, contrary to fact, that the worst case would be dying in a plane crash. Therefore, his stipulation, not use of the maximin rule, could be the source of much of what is paradoxical about the example.

Even if the example in this first argument were plausible, it would prove nothing about the undesirability of using maximin in situations of societal risk under uncertainty—for example, in deciding whether to open a liquefied natural gas facility. Harsanyi makes the questionable assumption, in using this example, that the situation of uncertainty regarding one individual's death, caused by that person's decision to fly to Chicago, is the same as a situation of uncertainty regarding many individuals' deaths, caused by a societal decision to employ a hazardous technology.

Objecting to Harsanyi's example, John Pawls claimed that the ample failed because it was of a small-scale, rather than a large-scale, situation.21 My claim is similar but more specific: Situations of individual risk are voluntarily chosen, whereas situations of societal risk typically are involuntarily imposed ; hence, they are not analogous. Therefore, to convince us that societal decisions in situations of uncertainty are best made by following a Bayesian/utilitarian rule, Harsanyi cannot merely provide an example of an individual decision. Harsanyi, however, disagrees. Answering Rawls's objection, he says: "though my counterexamples do refer to small-scale situations, it is very easy to adapt them to large-scale situations since they have intrinsically nothing to do with scale, whether large or small. . . . [It is a] strange doctrine that scale is a fundamental variable in moral philosophy."22

There are several reasons why Harsanyi is wrong in this claim. In the individual case, one has the right to use expected utility so as to make efficient, economical decisions regarding oneself. In the societal

case, one does not always have the right to use expected utility so as to make efficient, economical decisions regarding others in society, since maximizing utility or even average utility might violate rights or duties. On the individual level, the question is whether the individual's definition of 'risk' is theoretically justifiable. On the societal level, the question is whether a group of people's definition of risk is democratically justifiable.

Rational societal decisionmaking requires an ethical rule that takes account of the fairness of the allocational process (for instance, whether potential victims exercise free, informed consent to the risk), not merely the outcomes.23 And if so, then (as Diamond and others have argued) there are strong reasons to doubt what Sen calls "the strong independence axiom" (and what Harsanyi calls the "sure-thing principle" or the "dominance principle").24 According to this axiom, if one strategy yields a better outcome than another does under some conditions, and if it never yields a worse outcome under any conditions, then decisionmakers always ought to choose the first strategy over the second.25 But if there are grounds for doubting the sure-thing principle, because it ignores ethical process and focuses only on outcomes, then one ought to doubt Bayesian utilitarianism· This is because the sure-thing principle is one of the three main rationality axioms underlying the Bayesian approach.26

If the sure-thing principle fails to provide a full account of rational behavior, especially in the societal case, there are even stronger grounds for questioning Bayesian utilitarianism in situations of decisionmaking under uncertaignty. Democratic process is probably more important in cases where probabilities are unknown than in those where they are certain, since it would be more difficult to ensure informed consent in the former cases. This, in turn, suggests that the individual case has to do more with a substantive concept of rationality, whereas the societal case has to do more with a procedural or "process" concept of rationality.27 That is, the societal case must take account of conflicting points of view, as well as various ethical and legal obligations, such as those involving free, informed consent and due process.

For example, I may have an obligation to help ensure that all persons receive equal protection under the law, even if a majority of persons are unaware of their rights to equal protection, and even if their personal utility functions take no account of these unknown rights. In other words, if I make a decision regarding my own risk, I can ask "How safe is rational enough?" and I can be termed "irrational" if I have a fear of flying. But if I make a decision regarding risks to others in society, I do not have the right to ask, where their interests are con-

cerned, "How safe is rational enough?" In the societal case, I must ask, because I am bound by moral obligation to others, "How safe is free enough?" or "How safe is fair enough?" or "How safe is voluntary enough?"28

Another problem with Harsanyi's first argument is that he begs the very question he sets out to prove—namely, that it "is extremely irrational to make your behavior [taking the job in New York] wholly dependent on some highly unlikely unfavorable contingencies [the Chicago plane crash], regardless of how little probability you are willing to assign to them"; by Harsanyi's own admission, he is attempting to prove that maximin ought not to be used in situations of risk under uncertainty.29 Yet, if the worst consequence, death in a plane crash, is, by his own definition, "highly unlikely," then this consequence has a stipulated low probability.30 The situation is not one of uncertainty but one of risk_B . Harsanyi's example has proved nothing about rational decisions under uncertainty. A related problem with Harsanyi's account is that he claims that people behave as if they maximized utility. In situations of uncertainty, this claim begs the question because it cannot be demonstrated; we do not know the relevant probabilities.

Even as a strategy for rational decisions under risk_B , it is not clear that Harsanyi's principles would always be successful. He claims that reasonable people do not forgo great benefits in order to avoid a small probability of harm. However, it appears equally plausible to argue that many rational people do not wish to gamble, especially if their lives are at stake.31 Moreover, in instances where they might justifiably gamble (with something other than their lives), it is not clear that humans are Bayesian utilitarians at all. Their risk aversion does not necessarily seem to be a linear function of probability.32

Many risk assessors—Bruce Ames, for instance—assume that risk aversion ought to be a linear function of probability, and they criticize laypersons for being more averse to industrial chemicals than to natural toxins (such as the mold in foods) that have a higher probability of causing injury or death. Invoking the concept of "relative risk," they fault laypersons for their "chemophobia," for greater aversion to lower-probability risks than to higher ones.33 As the last two chapters have argued, however, probability is neither the only nor the most important factor determining risk aversion. And if it is not, then we have grounds for doubting both the Bayesian/utilitarian strategy and the probabilistic strategy (discussed in the last chapter). Likewise, as has been mentioned in earlier chapters, Kahneman and Tversky may be right that the Bayesian model does not always capture the essential determinants of the judgment process.34 If subjective probabilities are frequently prone to

error, then (contrary to Harsanyi's first argument) rational people might well avoid them.

Harsanyi's first argument is also problematic because it is built on the supposition that "it is extremely irrational to make your behavior wholly dependent on some highly unlikely unfavorable contingencies regardless of how little probability you are willing to assign to them."35 What Harsanyi is saying is that it is irrational to base decisions on consequences and to ignore either a small or an uncertain probability associated with them. However, suppose that one has the choice between buying organically grown vegetables and those treated with pesticides, and that the price difference between the two is very small. Also suppose that the probability of getting cancer from the vegetables treated with pesticide is "highly unlikely," to use Harsanyi's own words. It is not irrational to avoid this cancer risk, even if it is small, particularly if one can do so at no great cost. Similarly, it is not irrational to avoid a possibly catastrophic risk, such as nuclear winter, even if it were small. In assuming that a low probability, alone, is a sufficient condition for ignoring a risk, Harsanyi has fallen victim to the probabilistic strategy criticized in the last chapter.

Is Maximin Irrational?

Harsanyi defends himself, in part, by claiming that, although the two different decision principles (Bayesian and maximin) often result in the same policies, whenever they differ, it is "always the maximin principle that is found to suggest unreasonable consequences."36 One way to refute this argument is to give an example in which the two decision strategies dictate different actions, but in which the maximin action is clearly superior.

Consider the following (fictitious) example. Suppose that the night-shift foreman has discovered a leak in one of the large toxic-gas canisters at the local Union Carbide plant in West Virginia. Because of past instructions, he must immediately notify both the plant's safety engineer (who will bring a four-man crew with him to try to repair the leak within a half hour) and the president of the company. However, the foreman is still faced with a problematic choice: to notify the local sheriff of the situation, so that he can begin evacuation of the town surrounding the plant, or not to notify him. If he notifies the sheriff, as is required both by the Code of Federal Regulations and by the agreement Union Carbide signed with the town, when it leased the land to the company, then no townspeople will die as a result of the leak.

However, he and five other employees (the safety engineer and his crew) will lose their jobs as a result of the adverse publicity, especially after the Bhopal accident, if they cannot fix the leak within a half hour. Moreover, there are no other jobs available, since this is a depressed area, and even the coal companies cannot hire additional people. If the foreman does not notify the sheriff, and if the safety crew can repair the leak during the first half hour of their work, then he and the members of the five-person safety crew will each receive a $25,000 bonus from the company, not (of course) for disobeying the law, but for avoiding mass panic and adverse publicity. However, if the foreman does not notify the sheriff, and if the safety crew cannot repair the leak during the first half hour of their work, then the ten persons living closest to the plant (all residents of a nursing home for the aged) will die after a half hour's exposure to the fumes; all six of the employees will lose their jobs; and the foreman will have to notify the sheriff anyway.

The foreman uses expected utility to make his decision and employs the following table, consisting of two acts (notifying or not notifying the sheriff) and two states (fixing or not fixing the leak in thirty minutes). Since he is in a state of ignorance, the foreman uses the principle of insufficient reason,37 or what Harsanyi calls "the equiprobability assumption,"38 to assign equal probabilities (0.5) to both possible states. Thinking about all four possible outcomes, the foreman assigns a value or utility (u ) to each of the outcomes. He decides not to notify the sheriff, since the expected utility for this act is higher ((0.5)(38) + (0.5) (- 16) = 11) than the expected utility ((0.5)(16) + (0.5)(4) = 10) for notifying him. The safety engineer agrees with the foreman that the worst outcome is that in which both the jobs and the lives are lost, but he uses the maximin procedure and decides that they ought to notify the sheriff, so as to be sure to avoid this worst outcome.

In the example, the Bayesian/utilitarian and maximin strategies dictate different actions, and the maximin recommendation is arguably superior, for at least three reasons: (1) The Code of Federal Regulations establishes an obligation to notify the sheriff. (2) The lease contract that Union Carbide made with the town establishes an obligation to notify the sheriff. (3) The ten endangered persons have a right to know the risk facing them. The nursing home residents face the worst consequence of anyone, death (the crew and foreman have gas masks). Hence, their right (and the rights of their guardians, if any) to know is more important than the foreman's desire to avoid frightening people and to obtain a bonus. Indeed, their consent may be one of the

most important factors in deciding how to deal with this situation.39 But if the maximin recommendation is superior, then this case provides a counterexample to Harsanyi's (and Arrow's) claim that, whenever the recommendations of the two strategies differ, it is "always the maximin principle that is found to suggest unreasonable consequences."40

It might be objected, at this point, that the counterexample violates Harsanyi's criteria for moral value judgments.41 According to the objector, the foreman's decision is wrong, not because he used Bayesian/utilitarian principles, but because he computed the utilities in a self-interested way. Hence, the example may not show that Bayesianism or utilitarianism leads to wrong consequences, but only that self-interest leads to them.

In response, the foreman could plausibly claim, either that it is right to impose some risks on society, or that he was not acting in self-interest m assigning the utilities he did to the act of not informing the sheriff immediately. He could claim that he was trying to avoid mass panic (a frequently used defense) and needlessly troubling people.42 Also, the foreman could complain that the Bayesian/utilitarian strategy is difficult to use, since it requires agents in situations of uncertainty to rank the lives of members of various societies on a common interval scale. It requires interpersonal comparisons of utility—something very difficult to make, as we shall argue shortly. Therefore, the foreman need not consciously have acted out of self-interest; he may merely have been unable to rank the lives of other people on a common interval scale, particularly if those being ranked were elderly and sick, and the foreman would rather be dead than elderly and sick.43

Does Maximin Lead to Unethical Consequences?

In the Bayesian/utilitarian scheme, warning the elderly and sick makes sense only if it would benefit society and if they deserve it. But this brings us to Harsanyi's third claim. Maximin would lead to unacceptable moral consequences: benefiting the least-well-off individuals, even when they do not deserve it, and even when doing so will not help society. To establish this point, Harsanyi gives two examples.44

In the first example, there are two patients critically ill with pneumonia, but there is only enough antibiotic to treat one of them, one of whom has terminal cancer. Harsanyi says that Bayesians would give the antibiotic to the patient who did not have cancer, whereas maximin strategists would give it to the cancer patient, since he is the worse off. In the second example, there are two citizens, one severely retarded and the other with superior mathematical ability. The problem is whether to use society's surplus money to help educate the mathematician or provide remedial training for the retarded person. The Bayesian utilitarian would spend the surplus money on the mathematician, says Harsanyi, whereas the maximin strategist would spend it on the retarded person, since he is the less well off.

Let us grant, for purposes of argument, that Harsanyi is right on two counts in these examples: on what decisions the respective strategists would make, and on the fact that the Bayesian utilitarian makes the more reasonable decision in each of these two cases. Even if we grant these two points to Harsanyi, however, he has still not established that the Bayesian/utilitarian strategy provides a superior basis for societal decisionmaking under uncertainty.

In the first (pneumonia) case, the risk is of fatality, but one knows, with certainty, that the cancer victim is soon to die, since Harsanyi defines his state as "terminal." In the second case, the risk is of improving the lot of two persons, one retarded and one gifted mathematically. However, Harsanyi tells us that spending money to train the latter "could achieve only trivial improvements in B 's condition," whereas spending the same funds to train A in mathematics would be quite successful, because of A 's interest and ability. Hence, one is not in a state of uncertainty about the probability of success in spending the monies for education in the two cases. Consequently, both examples show that there are cases, decisionmaking under risk_B , in which Bayesianism/utilitarianism dictates reasonable strategies. But that point is not at issue. Hence, Harsanyi has not argued for using Bayesian/utilitarian rules under uncertainty.

A second problem with these examples is that Harsanyi defines the retarded person as "less well off," and therefore deserving of funds for remedial education under the maximin strategy. However, being "less well off" is not merely a matter of intelligence. It is also a matter of financial well-being and of having equal political and social opportunity. If society has given equal consideration to the needs and interests of both the mathematician and the retarded person, if the retarded person is happy and incapable of being made better off, regardless of what society spends on him, then it is not clear that he is less well off than the mathematician. If the mathematician could be made better off through greater societal expenditures, then he may be less well off than the retarded person, who has reached his potential and is as happy as he is capable of being.

Admittedly, Harsanyi speaks of the retarded person as having "greater need" of the resources.45 But if he cannot be bettered by any greater expenditure, does he really have a need? Presumably, one only has a need for that which is capable of bettering him in some way. Being well off is also a matter of having one's needs met to a degree comparable to that of others, perhaps others with differing abilities. It is not merely a matter of intelligence, money, or any other single factor. Consequently, Harsanyi's example may not provide even a case of Bayesian/utilitarian superiority in decisionmaking under risk_B .46

Does the Utilitarian Strategy Treat Persons Equally?

Having given general, Bayesian/utilitarian justifications for his position, Harsanyi provides a final argument that is non-Bayesian. This non-Bayesian defense focuses on what Harsanyi calls "the equiprobability assumption."47 Decisionmakers ought to subscribe to this assumption, says Harsanyi, because doing so enables them to treat all individuals' a priori interests as equal.48 That is, regardless of the social system chosen, one "would have the same probability, 1/n, of taking the place of the best-off individual, or the second-best-off individual, etc., up to the worst-off individual." If everyone has an equal chance of being better off or worse off, Harsanyi claims that the rational person would always make the risk decision yielding the highest "average utility level."49

Although some scholars have alleged that Bayes makes use of the equiprobability assumption, most experts claim that his argument is free of this assumption.50 Bayesian or not, the assumption is central to Harsanyi's defense of utilitarian decisionmaking and hence bears some examination.

A variant of the so-called "principle of insufficient reason," the equiprobability assumption was first formulated by the seventeenth-century mathematician Jacob Bernoulli. It says that, if there is no evidence indicating that one event from an exhaustive set of mutually exclusive events is more likely to occur than another, then the events should be judged equally probable.51

The most basic difficulty with the equiprobability assumption is that, if there is no justification for assigning a set of probabilities, because one is in a situation of uncertainty, then there is no justification for assuming that the states are equally probable.52 Moreover, to assume, in a situation of uncertainty, that states are equally probable is to revert to reliance on a very subjective notion of probability. As Amos Tversky and Daniel Kahneman have argued persuasively, it is often irrational to rely on subjective probabilities,53 since they are often the result of judgmental errors.54 There are other difficulties as well. First of all, to assign the states equal probabilities is to contradict the stipulation that the situation is one of uncertainty.55 In addition, it is often impossible to specify a list of possible states that are mutually exclusive and exhaustive;56 therefore, different ways of defining states could conceivably result in different decision results, different accounts of how best to maximize average utility.57

The equiprobability assumption is also ethically questionable because it does not enable one to assign equal a priori weight to every individual's interests, as Harsanyi claims. It merely postulates that, in a situation of uncertainty and in different social systems or states of affairs, every individual has the same probability of being the best-off individual, or the second-best-off individual, and so on. In reality, however, different states of affairs are rarely equally probable. To assume that they are, when one is in a situation of uncertainty, is problematic in part because equally probable states often affect different individuals' interests unequally.

Using averages also affects individuals unequally. Therefore, even if one granted that it is rational to maximize expected utility in individual decisions, it would not necessarily be rational to choose the average of the expected utilities of different persons. Such a procedure would not maximize my expected utility, but only the average of the expected utilities of members of society.58 Thus, the concepts of "average utility" and "equiprobability" could hide the very problems that most need addressing, the problems of discrimination and inequality. For example, assigning the occurrence of a nuclear core melt an equal probability with the nonoccurrence obviously does not treat people's a priori interests equally. If the core-melt probability is actually higher than

0.5, then the original assignment treats the interests of the consumers of nuclear power with less equality than those of its producers. And if the core-melt probability is actually lower than 0.5, then the original assignment treats the interests of the producers of nuclear power with less equality than those of its consumers.

Moreover, even though the equiprobability assumption assigns every individual the same probability (in every state of affairs) of being the best off, second best off, and so on, this does not guarantee that every individual's interests receive equal weight. Because Bayesian utilitarianism focuses on expected utility and average utility, it dictates that decisions be made on the basis of highest average utility. This rule guarantees that the minority, with less-than-average utility, can receive a disproportionate risk burden. In such cases, one would not be treating the interests of each person in the minority as equal to those of each person in the majority. In at least one important sense, therefore, Harsanyi does not treat people the same, as he claims to do through his equiprobability assumption.59

In confusing equiprobability with equity, Harsanyi assumes that what is average is what is equitable. Obviously it is not, as was illustrated in a recent assessment of the cancer risk posed by emissions from a municipal waste-combustion facility.60 The study concluded that for dioxin, polychlorinated biphenyls, arsenic, beryllium, and chromium, the maximum individual lifetime cancer risk varied across three orders of magnitude. Since phenotypic variation can cause more than a 200-fold difference in sensitivity to toxins among individuals,61 these figures alone are enough to show that one individual could easily bear a risk that was five orders of magnitude greater than that of another person, even though they shared the same average risk. In such a case, averaging the uncertainty and the differences in sensitivity would not mean that all persons were treated equitably.

Moreover, even if the equiprobability assumption did guarantee that everyone were treated the same, such treatment also would not be equitable. Genuinely equal treatment requires that we treat people differently, so as to take account of different degrees of merit, need, rights to compensation or reparation, and the like. Treating people the same, in a situation where existing relationships of economic and political power are already established, merely reinforces those relationships, apart from whether they are ethically defensible. Treating people the same, as most persons wish to do in situations of uncertainty, also ignores the fact that duties and obligations almost always require that people's interests not be treated the same. For example, suppose that Mr. X builds a pesticide-manufacturing plant in Houston. Also suppose

that Mr. Y, who lives next door, has demonstrably damaging health effects from the emissions of the pesticide facilitv. To say that Mr. X 's and Mr. Y 's interests in stopping the harmful emissions ought to be given the same weight is to skew the relevant ethical obligations. It would give license to anyone wishing to put others at risk for his own financial gain.62 Hence, there are rarely grounds for treating persons' interests the same, since they are almost always structured by preexisting obligations that determine whose interests ought to have more weight. Equity of treatment can be achieved only after ethical analysis, not after an appeal to treating everyone the same, in the name of the equiprobability assumption.

A third difficulty with this assumption is that it could lead to disaster whenever the higher/highest actual probability is associated with a catastrophe. Consider the following case:

As this example shows, the decision to use or discontinue nuclear power is one made under uncertainty. If the state having catastrophically bad consequences (that of reactor operators being careless) has the higher actual probability (0.6), then the equiprobability assumption and the expected-utility rule yield a disastrous decision: to continue to use commercial nuclear reactors, since the expected utility of this option is (0.5)(-200) + (0.5)(250) = 25, whereas the utility of its alternative is only (0.5)(10) + (0.5)(30) = 20. However, if the real probability associated with reactor operators' being careless is 0.6, then the expected utility for continuing to use commercial fission is (0.6)(-200) + (0.4) (250) = -20. Likewise, if the real probability associated with their being careful is 0.4, then the expected utility for discontinuing use of nuclear power is (0.6)(10) + (0.4)(30) = 18. The example shows that use of the equiprobability assumption could have catastropic effects.

But if use of the equiprobability assumption could lead to devastating consequences, why do many decisionmakers defend it? One reason is that, as Luce and Raiffa point out, situations rarely involve complete uncertainty.63 Because they do not, one often has some partial information concerning the true state. And if one does have partial information, then use of the equiprobability assumption, together with the Bayesian/utilitarian strategy, makes more sense than in the actual case of uncertainty. Another reason for using the principle of insufficient reason is that, according to Luce and Raiffa,64 it satisfies all the axioms required in situations of partial uncertainty, while maximin satisfies all but one of the axioms. In response, however, it is important to point out that the Luce and Raiffa claims are applicable only to individual decisionmaking under uncertainty. Luce and Raiffa explicitly warned that they were not discussing the societal case. But if not, then their warning provides further evidence that there are strong disanalogies between "event" and "process" rationalities, and therefore that the case of societal decisionmaking is not amenable to Bayesian rationality and the equiprobability assumption.65

Rawls's Arguments

Admittedly, discovering difficulties with Harsanyi's arguments for Bayesian/utilitarian rules is not a sufficient condition for rejecting them. We also need to assess maximin, perhaps the best alternative rule for certain classes of cases under uncertainty. To assess this option, let's evaluate Rawls's analysis. His main arguments to support the maximin strategy in situations of uncertainty (his "original position") are as follows: (1) It would lead to giving the interests of the least advantaged the highest priority. (2) It would avoid using a utility function, designed for risk taking, in the area of morals, where it does not belong. (3) It would avoid the Bayesian/utilitarian use of interpersonal comparisons of utility in defining justice. More generally, (4) it would avoid making supererogatory actions a matter of duty, as do utilitarian theories. And (5) it would avoid the Bayesian/utilitarian dependence on uncertain predictions about the consequences of alternative policies.

Maximin Gives Priority to the Least Advantaged

Consider the first argument in favor of the maximin strategy: It would lead to a concept of justice based on Rawls's "difference principle," which evaluates every possible societal or policy arrangement in accor-

dance with the interests of the least advantaged or worst-off persons.66 The "first virtue" of social institutions, in Rawls's view, is justice or fairness. We could arrive at just or fair social institutions, he believes, if we were all rational individuals caring only about our own interests, and if we negotiated with each other (about the nature of these institutions) behind the "veil of ignorance"—that is, without knowledge of anyone's social or economic positions, special interests, talents, or abilities. Under these circumstances, Rawls claims that we would arrange society so that even the worst-off persons would not be seriously disadvantaged.67 We would simply choose the risk distribution where the least well off are least disadvantaged.68 Also, not knowing our own situation, Rawls argues that we would be more likely to mitigate the "arbitrariness of the natural lottery itself,"69 the natural lottery according to which we receive talents, a beneficial family background, and so on.70

The main objection to this argument is that we ought not to use maximin (or what Rawls calls "the difference principle") because it might not increase the average utility of society, and increasing average utility is more important than helping a subset of persons. Therefore, goes the objection, in the situation of technological risk under uncertainty, one should not try to protect those who are most at risk, since such an action would take away resources from society. Instead, one ought to use a Bayesian/utilitarian strategy, to employ expected utility so as to maximize the average well-being of each member of the group.71

The main problem with this objection is that it could sanction using members of a minority who are most at risk so as to benefit the majority; that is, some persons could be used as means to the ends of other persons—an action condemned by most moral philosophers. Presumably, however, all persons ought to be treated as ends in their own right, not merely as a way to satisfy the desires of someone else, not merely as objects. Moreover, there are good grounds for believing that everyone ought to receive equal treatment, equal consideration of interests: (1) The comparison class is all humans, and all humans have the same capacity for a happy life.72 (2) Free, informed, rational people would likely agree to principles of equal rights or equal protection.73 (3) These principles provide the basic justifications for other important concepts of ethics and are presuppositions of all schemes involving consistency, justice, fairness, rights, and autonomy.74 (4) Equality of rights is presupposed by the idea of law; "law itself embodies an ideal of equal treatment for persons similarly situated."75

If all members of society have an equal, prima facie right to life, and therefore to bodily security, as the most basic of human rights,

then allowing one group of persons to be put at greater risk, without compensation and for no good reason, amounts to violating their rights to life and to bodily security. Indeed, if there were no obligation to equalize the burden of technological risk imposed on one segment of the population, for the benefit of another segment, there could be no authentic bodily security and no legal rights at all. The majority could simply do whatever they wished to any victimized minority. That is why John Rawls called his notion of justice "fairness," and why he spoke about maximin under the rubric of fairness.76

Admittedly, sanctioning equal treatment, in the name of fairness, does not mean guaranteeing the same treatment, as was already argued in this chapter and in Chapter Two.77 Establishing the prima facie duty to treat persons equally, as far as possible, does require that we use maximin in situations of societal risk under uncertainty,78 unless we have relevant moral reasons for treating people differently.79

Efficiency, however, does not appear to provide relevant moral grounds for discrimination, especially discrimination against the least well off, for several reasons. First, discrimination against persons, on grounds of efficiency, is something that would have to be justified for each and every situation in which it occurs. That is, to argue (as we just have) that a principle of equal rights and equal treatment under the law is desirable, but that there may be morally relevant grounds for discrimination, is to argue for a principle of prima facie political equality.80 In this view, sameness of treatment of persons and communities need no justification, since it is presumed defensible; only unequal (different) treatment requires defense.81 Therefore, the burden of proof is on the person who wishes to discriminate, who wishes not to give equal protection to some minority that is exposed to societal risk.

Since the burden of proof is on the discriminator and since, by definition, we are dealing with a situation of decisionmaking under uncertainty, it is difficult to believe that the discriminator (the person who does not want to use maximin) could argue that efficiency provides morally relevant grounds for discrimination.82 The potential grounds justifying such discrimination (for example, empirical factors about merit, compensation, or efficiency) would be, by definition, unknown in a situation of uncertainty.

Efficiency also does not appear to serve any higher interest.83 Admittedly, many risk assessors and policymakers claim that efficiency serves the interests of everyone; they say that "the economy needs" particular hazardous technologies.84 They also claim that certain risk-abatement measures are not cost-effective and therefore are not bene-

ficial to our national well-being.85 However, if efficiency is to serve the overall interest of everyone, it must be "required for the promotion of equality in the long run"; any other interpretation of "serving the overall interest" would be open to the charge that it was built upon using humans as means to the ends of other persons, rather than treating them as ends in themselves.86 We must therefore ask whether efficiency per se (for example, avoiding pollution controls and therefore equal distribution of risk) leads to the promotion of equality in the long run. The problem with answering this question in the affirmative, as Harsanyi would do, is that such an answer would contain a highly questionable factual assumption —namely, that promoting technology, without also seeking equal risk distribution, will lead to greater equality of treatment in the long run. This is false.

Historically, there is little basis for believing that efficiency will help promote a more equitable distribution of wealth, and therefore more political equality.87 In the United States, for example, although there has been an absolute increase in the standard of living in the past thirty-five years, the relative shares of wealth held by various groups have not changed. The poorest 20 percent of persons still receive 5 percent of the wealth, while the richest 20 percent still hold 41 percent; the share of the middle three quintiles has remained just as constant.88 These figures suggest that economic and technological growth, coupled with efficiency in the form of inequity of risk abatement, has not promoted economic equality. Because of the close relationship between wealth and the ability to utilize equal opportunities,89 it is unlikely that such efficiency and economic expansion have promoted equal political treatment.90 If anything, they have probably made inequities even wider.91

Technological expansion (achieved through economic efficiency and through failure to abate technological risks) also does not ordinarily help to create a more egalitarian society, because technology generally eliminates jobs; it does not create them.92 In the United States, for example, the new jobs that have become available in the last thirty years have largely been in the service sector and not in manufacturing or in technology.93 Consequently, it seems difficult to argue that efficiency and Bayesian/utilitarian risk strategies help to equalize opportunities.94 If anything, the plight of the least advantaged, whether the poor or those who bear a heavier burden of technological risk, is exacerbated by technological progress because they must compete more frantically for scarcer jobs. Moreover, because a larger portion of the indigent are unemployable, progress makes little immediate impact on the problem of hard-core poverty.95

Technological progress, without a commitment to equal distribution of societal risks, likewise typically fails to remove distributive inequities because the poor usually bear the brunt of technological hazards. Most environmental policies, including risk policies, "distribute the costs of controls in a regressive pattern while providing disproportionate benefits for the educated and wealthy, who can better afford to indulge an acquired taste for environmental quality [and risk mitigation]."96 This means that, for the poor, whatever risk abatement and environmental quality cannot be paid for cannot be had. A number of studies have shown that "those square miles populated by nonwhites and by all low socioeconomic groups were the areas of highest pollution levels."97 In fact, various adverse environmental impacts, such as higher risk burdens, are visited disproportionately upon the poor, while the rich receive the bulk of the benefits.98 All this suggests that Bayesian/utilitarian strategies, in allowing the poor (persons who are least advantaged economically and therefore most helpless politically) to be further burdened with disproportionate technological risks, are especially questionable. They harm those who already bear many of society's adverse impacts.99 Hence, if one has a moral obligation to help those who are most helpless,100 then Bayesian/utilitarian risk strategies are likely to be wrong. Moreover, it is questionable whether most utilitarians (as Harsanyi assumes) would defend the Bayesian commitment to average utilities, at the expense of the minority who must bear higher-than-average risk burdens. As Brandt points out, "most utilitarians think that inequalities of distribution tend to reduce the total welfare."101

In response to these equity-based arguments against Bayesian utilitarianism, and in favor of maximin, Harsanyi would likely respond that he is misunderstood. After all, when Sen raised equity objections against his position, Harsanyi argued that individual utility functions already reflected concern for social inequities and that imposing equity requirements on expected utilities would be "double counting."102 Such a response does not seem to invalidate equity and distributional objections, however, because individual utility functions do not necessarily reflect concern for equity. These functions could provide, at best, only individual preferences for equity, not an in-principle guarantee that equity must be taken into account by all individuals.103 Harsanyi also cannot guarantee that equity of distribution will be taken into account in his scheme because, by definition, his account is relativistic. It recognizes no standards except personal preferences and tastes.104 In addition, Harsanyi's idealized utility functions specifically do not express distributional concerns. Different humanistic moral codes might make conflicting recommendations regarding social action. Yet, using his ideal-

ized utility function, Harsanyi would have no way of deciding among them.105 Moreover, because he proves that social welfare must be a linear function of individual utilities,106 Harsanyi must be maximizing personal consumption of socially produced goods. But if his welfare functions maximize consumption and are affected only by personal consumption, then they cannot possibly take account of equity, which is not a type of personal consumption.107

Harsanyi's problems with equity can be expressed in the form of a dilemma: If (A) social welfare is a linear function of individual utilities, then interpersonal comparability of utilities is possible. And if it is possible, then Harsanyi has a utilitarian social welfare function, as he claims. But if he has a utilitarian social welfare function, then he cannot possibly deal with equity, as he claims. Alternatively, if (B) social welfare is not a linear function of individual utilities, then interpersonal comparability of utilities is not possible, and Harsanyi has no utilitarian social welfare function. But if not, then he could theoretically deal with equity issues; but, because he has no vehicle for doing so, his account is conceptually incoherent. Hence, if (A), then Harsanyi's claim that he can deal with equity is false. But if (B), then his claim is conceptually incoherent within his system. In either case, Harsanyi appears unable to answer maximin objections based on equity.108

Maximin Avoids Utility Functions

Another argument of maximin proponents is that maximin would avoid using a von Neumann-Morgenstern utility function (designed for risk taking) in the area of morals, where it does not belong. This argument is that utility functions express the subjective importance that people do attribute to their needs and interests, not the importance that they ought to attribute ; hence, there is no way to discriminate rationally or morally among alternative tastes or preferences.109 For maximin proponents, equating preferences with oughts is problematic because people often prefer things (such as cigarettes or a particular marriage partner) that do not actually increase their welfare.110 More generally, maximin proponents say that, if one's welfare is assumed to be identical with one's preferences, at least four undesirable consequences follow: (1) One ignores the quality of the preferences or choices111 and is forced into moral relativism.112 (2) One's choices appear inconsistent with the Bayesian/utilitarian assumption that tastes or preferences are stable, consistent, precise, exogenous, and relevant to outcomes.113 (3) There is no distinction between needs and wants,114 and none between utility

or personal welfare and morality or moral principle.115 (4) One must assume that group welfare is merely the aggregate of individual preferences, as is expressed by summing utilities and getting an average.116 Opponents of Bayesian utilitarianism claim that public well-being is not simply the aggregate of individual preferences, because widespread egoism might serve each individual's personal welfare but might destroy the common good. Moreover, in a rapidly changing situation, where leaders must act on the basis of likely future events, public welfare clearly is not merely the aggregate of present individual preferences.117

Harsanyi's response to arguments such as these, that utility functions ought not be used to decide about morality, is that the argument is based on a misunderstanding. He claims that a utility function is not merely an indication of an individual's attitude toward risk (as he says many moral philosophers suppose); it is also an indication of how much utility or subjective importance the individual assigns to various goals.118 For this reason, Harsanyi would argue, there is no necessary distinction between moral judgments and utility judgments.

But such a response ignores the fact that utility judgments are based on preferences, whereas moral judgments are based on principles. If there is a moral principle to treat equal beings equally, then that moral principle is binding, even if those victimized by nonadherence to the principle do not have a preference for being treated equally. Principles protect everyone, not merely those who have free, well-informed preferences.

Harsanyi's position is also problematic because of an apparent incoherence between his interpretations of the utility function and interpersonal comparisons of utility. Harsanyi wishes to make moral judgments on the basis of subjective utility functions, rather than on the basis of unchanging moral principles (such as the principle that equal justice should be granted to equal beings). For him, weighting the subjective importance attached to things is more important than guaranteeing adherence to moral principles, because people's preferences are different. But if people's preferences are different, then presumably even two people in similar circumstances, with a similar background, could have different preferences.119 And if similar people do have different preferences, then it is questionable whether the utility functions/preferences of all persons are governed by the same psychological laws. If not, then interpersonal comparisons of utility are not possible, because each person's preferences and utility functions may operate according to different psychological laws. But this conclusion contradicts two of Harsanyi's claims: (1) that "preferences and utility functions of all human individuals are governed by the same

basic psychological laws";120 (2) that interpersonal utility comparisons are theoretically capable of being specified completely because they "have a completely specific theoretical meaning."121

If the reasoning in the previous arguments is correct, then Harsanyi cannot coherently claim both that preferences are needed as measures of welfare, because people's preferences/utility functions are different,122and that interpersonal comparisons of utility are possible because people's utility functions "are governed by the same basic psychological laws."123

In response to this argument, Harsanyi would likely claim that interpersonal comparisons of utility are possible and that we make them all the time. But why, then, should utility be based on purely subjective preferences, rather than also on ethical principles, such as those stated by Rawls?124 Likewise, Harsanyi (and, indeed, any Bayesian utilitarian) may have a related problem, in both stipulating the existence of an ideal individual decisionmaker and maintaining that such a person has no individual utility function. In order to treat the problem of societal decisionmaking as an ideal individual decision, Harsanyi must eliminate differences among persons and define rational behavior as average expected utility, rather than in terms of any particular person's decisions. But eliminating differences among persons, so as to obtain an ideal individual decision, eliminates the individuality of the decisionmaker. Hence, Harsanyi cannot consistently claim both that his theory, like Rawls's, formulates the problem of the social contract in terms of an ideal individual decision and that his decisionmaker has no individual utility function.125

Maximin and Preference Orderings

Economists try to resolve these problems with interpersonal comparisons of utility by offering the notion of a rational preference ordering, rather than a Bayesian cardinal scale. Since maximin can use merely an ordinal scale, its proponents argue that it places far fewer burdens on the individual attempting to evaluate risk options and consequences. Such an individual, they say, would not have to make interpersonal comparisons of utility and hence would not have to estimate what utility level he would enjoy if placed in the objective physical, economic, and social conditions of another individual.126 Such an estimate is difficult, because different persons' preferences do not have the same intensity, because stronger preferences are not always better preferences, and because feelings of different persons might not combine linearly.127

Admittedly, despite these difficulties with interpersonal comparisons

of utility, presupposing an ordinal ranking (as do proponents of maximin) also causes problems. For example, one could only obtain such an ordering through direct responses or a questionnaire. Yet, if one were unclear about how to maximize her well-being, then the ordering would not be an indicator of authentic welfare, any more than a decision based on the interval utility scale would be,128 and there is no system that would ever enable her to maximize her welfare. Although this problem is not unique to the maximin approach, the difficulties facing anyone determining ordinal utilities appear to be less than those associated with similar determinations on an interval scale,^[129] for the reasons given earlier in this section. Hence, at least on this criterion, the maximin strategy may be superior to the Bayesian/utilitarian.

Maximin and Supererogation

Another potential problem with Bayesian (and any utilitarian) theories is that they appear to make supererogatory actions a matter of duty.^[130] If Bayesians and utilitarians are correct, then one is always equally obliged to perform both normal duties and heroic actions, since the (Bayesian/utilitarian) criterion for any action is whether it maximizes average utility.^[131] One might be obliged under Bayesianism/utilitarianism, for example, to give up one's own projects and desires in life, including those related to family and profession, and instead dedicate oneself sacrificially to helping third-world victims of environmental risks.^[132] For particularly talented individuals, such a sacrifice of their lives seems likely to maximize average utility and hence to be required of them, on Bayesian grounds (assuming that average utility can be determined). This alleged obligation presents a problem, however, in the light of our ordinary understanding of fairness and what is right and wrong.^[133]

Harsanyi disagrees. He claims that freedom from burdensome moral obligations, such as the duty to perform supererogatory actions, has high utility; therefore, one is not bound to maximize average utility if it imposes burdensome obligations.^[134]

If Harsanyi's response is correct, then his system is not one of Bayesian utilitarianism, but one of Bayesian utilitarianism joined with some deontological principles or side constraints (such as "One ought not to burden individuals for the purpose of maximizing overall utility"). Harsanyi can escape the problem of supererogatory actions, but only at the price of having a theory that admits that maximizing utility sometimes imposes too great a burden.^[135] An analogous problem arises in the case where duty conflicts with maximizing utility. Consider the

following example. Suppose a father sees a building on fire. In one room of the building is his child, and in another room of the building are two other children. He has to decide whether to try to save his child or the other two children. He knows that he can only do one or the other, because the rooms are far apart, and the fire is progressing rapidly. Moreover, he believes that his chances of getting to the different rooms are the same. Parental duty dictates that he try to save his own child, whereas maximizing expected utility dictates that he try to save the two other children. A Bayesian utilitarian could not consistently argue that the father ought to save his child.^[136]

Maximin and Calculating Consequences

A final potential problem with utilitarian theories such as Bayesianism is that they seem to be dependent on uncertain predictions about the results of alternative policies. As a consequence, two well-informed and well-intentioned Bayesians could each come to different conclusions about what is right or wrong, good or bad.^[137] This problem is in part a result of the fact that many variables affect outcomes, and these variables are neither known nor predictable.^[138] Bayesian/utilitarian decision strategies are therefore in trouble, since they rely on one's ability to predict consequences. It might be objected, of course, that the maximin strategy also relies on ability to predict consequences. By definition, although maximin is not concerned with probabilities, it must attempt to avoid the worst possible outcome.

To some degree, this objection is correct, although maximin may have less of a problem with predicting consequences than does the Bayesian/utilitarian strategy, and for several reasons. For one thing, it is often easier to tell which consequences will be the worst than it is to rank the interval-scale utility of each (as was already mentioned). Also, if the worst technological and environmental risks are typically imposed on the poor, it may be possible to look at the existing income distributions in order to assess who, in the future, is likely to be least advantaged and hence more likely to bear some of the highest risks. It may not be difficult to discover the worst outcomes.^[139]

In response, Harsanyi admits that contractarian theories, such as Rawls's, "go a long way toward deciding our moral uncertainties in a fairly unambiguous manner," whereas Bayesian/utilitarian morality has a great many "uncertainties." Harsanyi claims, however, that this ambiguity is an advantage, since it enables Bayesian utilitarians to avoid "simple minded rigid mechanical rules" that do not do justice to the complexity of moral problems.^[140] The difficulty with Harsanyi's re-

sponse, however, is that the absence of second-order rules of priority in Bayesian utilitarianism (rules that Rawls, for example, does have) leaves Harsanyi open to a number of objections.^[141] Because Harsanyi denies that his system has any second-order rules, and because he claims that every decision "must always depend on the balance of the advantages and disadvantages it is likely to yield,"^[142] Harsanyi appears to be an act utilitarian and to face a number of objections associated with this position. For example, a Bayesian utilitarian could well conclude that the welfare of the majority could be served by secretly disenfranchising the minority.^[143] Harsanyi admits as much himself. He says: "Who is the moral philosopher to lay down the law . . . that no amount of economic and social development, however large, can ever justify any curtailment of civil liberties."^[144] This seems to be a classic statement of the position that everyone has his price, and that expediency can supersede duty.

Maximin and Practical/Prudential Considerations

These arguments about the merits of maximin and Bayesian/utilitarian strategies for decisions under uncertainty suggest several general reasons why the maximin principle might be superior in certain situations. For one thing, Bayesianism/utilitarianism might demand both too much and too little of agents. It might demand too much of them in committing them to supererogatory acts, as necessary for maximizing utility. It might demand too little of agents in committing them to maximizing average utility, even in instances when maximum average utility supports a tyranny of the majority against the minority. Furthermore, although the maximin position is also susceptible to its own types of difficulties (for example, it assumes that we can specify ordinal preferences), these problems often appear less troublesome, especially in situations of uncertainty, than those inherent in the Bayesian approach.^[145]

There are also at least three practical arguments for preferring maximin. For one thing, the wording of the 1969 U.S. National Environmental Policy Act (NEPA) makes it clear that federal policymakers should ensure that every individual enjoys safe and healthy surroundings, not merely that government maximizes average safety or utility.^[146] In requiring safety for "all Americans" and for "each person," NEPA clearly rejects the Bayesian/utilitarian notion that it is acceptable to deprive a minority of persons of their health or safety.

Common sense, as well as specific laws such as NEPA, likewise enjoin us to use maximin in situations of societal decisionmaking under un-

certainty. One of the most commonsensical of notions is that bureaucracies are notoriously slow moving and inefficient. For this reason, bureaucracies ought not to be trusted, in the absence of specific requirements, to make reliable and timely decisions about life-and-death matters, especially worst-case situations. Perhaps those decisions should instead be governed by prima facie rules, such as "In cases of technological risk under uncertainty, especially cases of potentially catastrophic risk, follow maximin strategies."^[147]

Pearl Harbor illustrates the inefficiency, irresponsibility, and inability of the bureaucracy to "handle the unexpected":

By December 7, Admiral Kimmel, the Pacific Fleet Commander, had received the following information: a warning from the Navy on November 27 about possible attacks, a report of a change in Japanese codes (evaluated as very unusual), reports of Japanese ships in Camranh Bay, orders to be alert for Japanese action in the Pacific, messages deciphered from Japan's most secure code ordering Japanese embassies to destroy secret papers, government authorization to destroy all American codes and secret papers in outlying islands, and personal warnings from Admiral Stark in Washington. Assuming honesty and competence, a[n] . . . analyst would be led to predict: (1) the fleet would be out of the harbor; (2) the island would be air patrolled; (3) the emergency warning center would be staffed; and (4) the Army would have been notified under the Joint Coastal Frontier Defense Plan. But each of these predictions would have proved incorrect.^[148]

The example suggests that society ought to have procedures for implementing protections, such as the maximin rule, to guard against the inadequacies of bureaucracy. Society might also need a way to avoid the catastrophic consequences of human error. The case of commercial nuclear fission is a classic instance of the need to guard against the results of poor risk evaluations and operator error. "Nowhere are issues of perceived risk more salient or the stakes higher than in the controversy over nuclear power."^[149] The Chernobyl accident occurred at least partly because assessors called the disaster "highly improbable" before it happened.^[150] In a Bayesian/utilitarian scheme, highly improbable accidents are not a significant concern in decisionmaking. But in a maximin scheme, the fact that a worst-case nuclear core melt could kill 150,000 persons^[151] would be a significant cause for concern. Had regulators implemented a maximin strategy, with appropriate procedures for ensuring it, then the Chernobyl accident might have been less likely.

If technological rulemaking created a "climate" of maximin, a climate in which decisionmakers aimed at avoiding worst cases, both they and society would likely be more aware of potential accident conse-

quences, more aware of erroneous subjective probabilities, and more aware of human errors in risk assessment. In their classic works, as was already mentioned, Tversky and Kahneman showed that virtually everyone falls victim to a number of characteristic biases in the interpretation of statistical and probabilistic data. These biases are the result of following erroneous intuitions, and they often result in disastrous consequences. For example, as was mentioned earlier, people often follow an intuition called "representativeness," according to which they believe that various samples are similar to one another and to the population from which they are drawn. In subscribing to this bias, both experts and laypeople are insensitive to such matters as the prior probability of outcomes, sample size, the inability of sampling to obtain a good prediction and to correct itself, the inaccuracy of predictions based on redundant and correlated input variables, and regression toward the mean—despite the fact that training in elementary probability and statistics warns against all these errors.^[152]

Both risk assessors and statistics experts also typically fall victim to a bias called "availability"^[153] and to the "anchoring" bias.^[154] These systematic and predictive errors of experts are significant because risk assessment is based on complex theoretical analyses that "include a large component of judgment. Someone, relying on educated intuition, must determine the structure of the problem, the consequences to be considered, and the importance of the various branches of the fault tree."^[155] According to Kahneman and Tversky, "people do not follow the principles of probability theory in judging the likelihood of uncertain events,"^[156] and "the same type of systematic errors . . . can be found in the intuitive judgments of sophisticated scientists." These findings indicate that risk assessment, especially Bayesian/utilitarian risk assessment, is likely to produce many erroneous analyses.^[157] After all, the experts were wrong when they said that irradiating enlarged tonsils was harmless. They were wrong when they said the X-raying feet, to determine shoe size, was harmless. They were wrong when they said that irradiating women's breasts, to alleviate mastitis, was harmless.^[158] And they were wrong when they said that witnessing A-bomb tests at close range was harmless.^[159]

More specifically, psychometric researchers have concluded that risk experts typically overlook six common "pathways to disaster": (1) They fail to consider the ways in which human error can cause technical systems to fail, as at Three Mile Island. (2) They have too much confidence in current scientific knowledge, even though inadequate scientific knowledge caused such catastrophes as the 1976 collapse of the Teton Dam. (3) They fail to appreciate how technical systems, as a

whole, function. For example, engineers were surprised when cargo-compartment decompression destroyed control systems in some airplanes. (4) Experts also do not take into account chronic, cumulative effects, as in the case of acid rain. (5) They fail to anticipate inadequate human responses to safety measures, such as the failure of Chernobyl officials to evacuate immediately. (6) They fail to anticipate "common-mode" failures simultaneously afflicting systems designed to be independent. A simple fire at Brown's Ferry, Alabama, for example, damaged all five emergency core-cooling systems for the reactor.^[160] The fact that experts typically overlook these six "pathways to disaster" suggests that they are often unable to model risk situations correctly. As Kahneman and Tversky point out, however, "the usefulness of the normative Bayesian approach to the analysis and the modeling of subjective probability depends primarily . . . on whether the model captures the essential determinants of the judgment process."^[161] It is important, therefore, both to avoid the errors frequently made by experts and to correct our risk models. By definition, we cannot avoid errors and correct models under uncertainty. Therefore, prudence dictates that we use conservative risk-evaluation rules, such as maximin.

Some Objections to Using Maximin

An important objection to using maximin is that it violates a rationality axiom. This objection loses some of its force if one recalls that Bayesian utilitarians have a similar problem. They ignore ethical and democratic processes and emphasize only outcomes. As was argued earlier, this emphasis provides grounds for doubting the adequacy of the sure-thing principle (one of the three main rationality axioms underlying Bayesianism),^[162] especially in cases of societal risk under uncertainty.

Another objection to maximin is that it appears to sanction an anti-progress, antiscience notion of risk assessment. To this claim, one could respond that use of Bayesian methods for evaluating societal risks under uncertainty has itself resulted in highly publicized scientific failures, such as the Chernobyl disaster. Such disasters, in turn, have thwarted nuclear progress. If the dependence of Bayesian/utilitarian rules on subjective decisionmakers has contributed to such catastrophes, then restricting the use of Bayesian rules to cases in which they are successful—namely, individual hazards under uncertainty and risk —is likely to promote respect for science, for technical progress, and for Bayesian methods.^[163]

Utilitarians also complain that maximin approaches are more expensive than Bayesian/utilitarian approaches to hazard assessment,

since it costs more to protect society against worst-case, highly improbable hazards than against more probable lesser harms.^[164] The obvious response to this objection, however, is that worst-case occurrences, such as Bhopal and DES liability, are extremely costly. Moreover, one knows that preventing worst cases is more costly only if one has the assurance that they are highly improbable, which, by definition, one cannot know in a case of uncertainty.

Apart from cost considerations, some experts also allege that maximin is not obviously the only moral choice under uncertainty. This objection, formulated by a statistician,^[165] is that positive utility attaches to being moral. Hence, for example, the Union Carbide chemical spill could not be justified on Bayesian grounds under conditions of uncertainty. However, there is no in-principle duty under Bayesian utilitarianism to consider moral or legal obligations and prima facie rights. Hence, Bayesian utilitarianism permits, but does not guarantee, avoidance of situations like the Union Carbide chemical spill.