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The Impossibility of Maximizing Good Consequences

Lawrence Crocker on lotteries, reasonable actions, and weird outliers.

Take the last day I gave a lecture on ethical theory. I was in the classroom at the scheduled time. I was not on my office computer entering the winning number in an online lottery. As a result, I did not receive a fortune to distribute to the worthiest of charities. I had naïvely thought that I probably did the right thing in meeting my class on time. If, however, I were a utilitarian of the classical Bentham-Mill sort – who sees as moral those acts that produce the greatest amount of benefit – wouldn’t my action have been morally wrong? I didn’t act so as to maximize the net total of good consequences.

The example may irritate you. After all, I could not simply sit down and enter the winning number on an internet lottery. There is the little problem of probability.

Ultimately, you are right, of course; a satisfactory utilitarianism must take the improbability of lottery wins into account. However, what I am concerned with here are some well-accepted definitions in the theoretical underpinnings of consequentialist moral theories such as utilitarianism. Consequentialist theories hold that the morality of an action is to be assessed in terms of its consequences: the best action is the one that brings about the best consequences. In such theories, the ‘best consequences’ are usually defined in terms of the consequences of all physically possible alternative actions – hence the lottery example. It is not physically impossible to win a lottery. You have seen pictures of real people who did that very thing. No force would have prevented me from entering just the right digits had I tried to type them on my key pad. So entering that number on my office computer would seem to be one of the (astronomically large) number of alternative actions I could have performed instead of starting my lecture on time. Nevertheless, you may suspect that the lottery example is a philosophical sleight of hand. I want to persuade you, however, that the lottery example is in fact illustrative of a genuine, general, and deep problem with consequentialism.

Maybe you put your right shoe on first today. The alternative of putting your left shoe on first would have had some minor different consequences, but common sense suggests that those two chains of consequences would have quickly merged for all practical purposes. Some other pairs of alternatives we can expect to diverge more dramatically, at least for a while – for example, putting on your right shoe then throwing your left one into a roaring fire. A few alternatives of an ordinary action would clearly have drastically different consequences that would continue in very long runs; for example, Hitler’s mother’s adding arsenic to the milk in his baby bottle. If we give scope to our imagination among physically possible alternatives, it seems almost inevitable that some of them will have better consequences than what we actually did. There will be alternatives very similar to what we actually did that will have at least slightly better consequences, and very different actions that will have dramatically better consequences.

It gets worse. As I said, common sense has it that small differences in our actions will tend to make little, if any, difference in long-run consequences. However, chaos theory gives us good grounds for thinking that common sense is wrong on this point. It is a primary conclusion of chaos theory that very similar acts will sometimes have vastly different long-run consequences. We humans, if not in some part chaotic systems ourselves, often send our consequences into chaotic environments. Sometimes putting on your left shoe first may have drastically different long-run consequences after all. For twenty-five generations of English speakers, ‘for the want of a nail’ would have come to mind here; now it is ‘the butterfly effect’.

Couple the vast number of things that human beings can choose to do under normal circumstances with the butterfly effect, and it becomes almost inevitable that among the alternative consequences will be some extreme outliers – enormously worse or enormously better long-run consequences than that of the action actually performed. The action that has the very best consequences is sometimes called by consequentialists ‘the objectively right action’. But enormously better possible consequences are a problem for this definition – and it is a problem that will increase with an increase in human population, for a populous distant future will increase dramatically the number of people affected by any given consequence chain as well as likely multiplying the number of downstream branches of those chains. Something with very negative consequences for our generation may turn out, because of consequences thousands of years hence, to be the objectively right action – if there were such a thing.

Lucky Sequences of Alternatives

A consistent consequentialist is, of course, not really concerned with achieving the best possible consequences from a single act, but in producing the best possible consequences over a lifetime. Admittedly, when we move from the consequence-maximizing action at a given moment to the consequence-maximizer of a series of actions over an hour, a day, or a decade, the particular example of the lottery loses its punch. It is, lottery-wise, not so obviously false that I did the right thing in meeting my class. I could have won the lottery in the hour before class and still gotten to class on time.

This may solve the lottery paradox, but it only makes the more general problem worse. When we’re concerned with the best consequences of several actions, we have not only the possibility at different times of picking up many separate weird outliers, but also the possibility of weird combinations of outliers. You play and win the lottery, then visit a casino and win at roulette. Next you head to the horse track and win an accumulator bet – after which you give all your winnings to (what turns out in the long run to be) the optimum combination of charities. Over time, ‘objective rightness’ must cherry pick the best consequences of all combinations of actions, including all outlier combinations of outliers and inliers. Surely hitting the objectively right series of actions is going to be geometrically less likely than getting right a single action. So over time the probability of acting objectively rightly is effectively nil.

Lucky Alternatives & Consequentialist Definitions

What all this establishes is that, understood in terms of good consequence maximization for any very wide set of alternatives, ‘Jenny did the objectively right thing’ is almost always going to be false. However, is this a real problem for consequentialism? Consequentialists can console themselves that most of the practical work of consequentialism is done not by assertions of objective rightness or of best possible consequences, but by its action-guiding statements such as ‘act as best you can to maximise good consequences’ and the expressions of moral praise or blame that attend those who do or do act according to such guiding principles.

Where the lucky lottery and its extensions do pose a significant problem, however, is for definitions linking objective rightness with action-guiding principles. The objective right is what we are told to shoot for. The way consequentialists have often put it is that we should guide our conduct by trying to do the objectively right action within the constraints of efficient deliberation. If we do not try for the best-consequence alternative, we can then be blamed.

However, under our conclusion that the objectively right action will usually be a weird outlier, this would be a disastrous way to proceed. I would waste all my time generating a partial list of weird outlier possibilities for each action, and hitting the one with the best consequences would be at least as hard as hitting that winning lottery number.

We do not improve this situation by recasting the definition in terms of trying to get reasonably close to the objectively right action. All the alternatives reasonably similar to a weird outlier are bound to be pretty weird themselves. Worse, an action very close to an alternative having wonderful consequences may not have at all wonderful consequences. If the winning lottery number is 1-10-13-19-21-28, then you will not throw a party because you entered 1-10-13-19-21-27. Again, where there are chaotic variables – as there are in all of life – we can expect near misses of the objectively right act to be poor choices pretty frequently. So a sensible consequentialism will not lead us to try to perform either the objectively right action, or an action as similar as possible to that hypothetical good consequence maximizer.

Therefore lucky alternative actions do seem to pose a problem for the way maximizing consequentialists have typically defined some key concepts, and for the way some consequentialists of a less theoretical bent have formulated their moral system. Before trying to solve the problem by improving on the definitions, I want to exhibit a yet more serious flaw in the standard formulations, set out in terms of the best consequences of all the agent’s alternatives. Any solution to the lucky alternatives puzzle will have to accommodate this more fundamental problem as well.

The Conceptual Bankruptcy of ‘All Alternatives’

The problem is this: the set of ‘all alternatives’, typically used in basic consequentialist definitions, is, upon close examination, arbitrary in a way that makes the concept utterly self-defeating.

Before arguing this point, I want to consider the soundness of the very idea of the consequences of non-performed actions. Consequentialist theorists normally simply assume that the chain of consequences of an unperformed action, stretching from the instant at which that act was not performed into the unbounded future, is a metaphysically-coherent possibility. But why should we think that?

Let us pass by the already significant problem that there is no unique instant correlated with an action that was never performed. Consider a matter of more interest – the metaphysical bona fides of the first paragraph of John F. Kennedy’s Second Inaugural Address, based on the assumption that the particular actual trigger-pulling had instead been an alternative with the rifle barrel aimed an eighth of a degree to the right. The problem is not just that even given that assumption, we cannot be confident that there would have been such a speech or what its content might have been: the real problem is that there is no very good reason to suppose that this extended counterfactual refers to anything at all, or at least to any one specific thing.

I see one way to save traditionally defined consequentialism from this problem. It’s a somewhat heroic expedient: First assume the truth of physical determinism; second, define an ‘alternative’ to be a completely specific possible world state. Then the laws of physics should generate one unique set of (counterfactual) consequences. I here suppress my suspicion that ‘counterfactual world states’ are themselves metaphysically defective, along with my concern that, even if counterfactual world states do exist in some respect, this might not be a respect in which physical law could apply. For argument’s sake, I will also continue not to worry about the fact that non-acts are associated with no unique times.

If you are willing to accompany me to this level of philosophical heedlessness, you will have some hope for the traditional consequentialist definitions. In fact, the situation is slightly less bleak than I have made out. Determinism is not strictly required: indeterminacy of the probabilistic sort favored by current quantum mechanics will do. There can then be an ‘expected utility’ summation of all the quantumly-possible consequence branches for a given alternative. (‘Expected’ here just means ‘future looking’. It is a summation that may exist only in ‘metaphysical space’, wholly beyond our ken.) However, there would be no such summation for a physical indeterminacy that’s not governed by probability. So for example, the idea that human decisions are ‘radically undetermined’ cannot coexist with consequentialism as traditionally defined. In any event, this very constrained rescue of the concept of ‘consequences’ turns out to put a great deal of pressure on the idea of ‘alternatives’ – to which we now turn.

As we have just seen, one way to give some hope that alternatives have determinable consequences is to think of each alternative as a specific possible state of the world at a moment of time. Maximal specificity is, in fact, the majority view among those who have considered the question of alternatives in depth. It does, however, invite the question of how free we are to be with these specific counterfactual states of the world. The question is particularly pressing when it comes to dealing with what is in the head of the person acting.

Last night I was sitting at my piano. I may well have played the first note of the Liechtenstein national anthem. If I didn’t, certainly I could have played that note, whatever it might turn out to be. Could I have played the whole anthem? Was that one of my alternatives?

Well, I don’t know Oben am jungen Rhein, and I am almost certainly not a good enough pianist to play it even if I had the sheet music, not being much of a pianist at all. So there is an obvious respect in which I could not have played it even had I wanted to. Yet there is also a respect in which I could have played it. After all, my piano has all its keys, and there was no anti-Liechtensteiner lurking around to blow my head off at the third bar. Perhaps with the music in front of me and a great deal of practice, I could play the piece. If so, there is a possible state of my brain that would have resulted in my playing the anthem.

Of course, that conjectured state of my brain was not its state last night. But then, no alternative action, from the most bizarre to the most pedestrian, had a corresponding actual brain state – else it would be the act performed rather than an alternative to it. However, just how large a deviation from what is actually in the actor’s head are we to permit in considering alternative possibilities? Do we also need to adjust the state of the world outside of the actor’s brain to be consistent with the possibility of such a brain state? Could I have played what would in fact be the first three notes of the piece, but not the first three bars? Was one of my alternatives to do a back somersault off the piano bench? Is it relevant that the most obvious somersault scenarios would involve my being coerced into the manoeuvre at gunpoint, or persuaded to it by a substantial monetary offer (neither possibility was apparently in the offing anywhere near my actual piano last night)? There are no non-arbitrary answers to such questions. I submit that we cannot draw a non-arbitrary line between the ‘to be included’ and ‘to be excluded’ possible variations from the actual state descriptions that we may consider.

These nails seal the coffin containing the corpse of the traditional definitions of consequentialism in terms of ‘the best consequences of alternative actions’. It is not just that those definitions need to be made more exacting, adding clauses about information and probabilities to take care of the lucky lottery and the like. It is that the traditional definitions are metaphysically hopelessly defective in relying upon ‘best consequences’ and ‘all alternatives’.

A Proposal

So let’s try to fix the problem. Recall that the function of the defective consequentialist definitions of the morally right action is to link the ideal of seeking best consequences with the working principles: the action-guiding and praise and blame components of the theory. The ‘objective right action’ theorists have attempted to render ‘consequential best’ in a rigorous, objective fashion – that is, not relative to the frailties of individual inclination, circumstance, and ignorance. But this, we now have good grounds to believe, is bound to fail.

The first step in the right direction is to recognize that maximization programs do not require a determinable maximized ideal. Any claim as to the absolute maximum number of points that could be scored by an NBA team in a regulation-length game would depend upon assumptions so numerous and so arbitrary as to be silly. The coach who entreats his players to score as many points as possible is, however, not talking nonsense. Similarly, bringing about the best consequences one can should not be understood as getting as close as one can to a consequentially perfect world: it’s a matter of seeking to do ever better within practical constraints that are themselves generated by the same ideal of doing ever better overall.

By cutting all definitional linkage to the best consequences among all alternatives, then, we can, as a first approximation, set out the working principles of maximizing consequentialism along the following lines: Guide your action by first considering as many and as promising alternative consequences as it is reasonable to consider given the importance of the decision and the time and resources available, and choose the alternative that has the best reasonably-foreseeable consequences, given those same constraints. Praise those who so guide their actions, and blame those who do not.

Using these principles, we still have a concept of the best consequence; but it can now be understood to be nothing more exotic than the winner of a comparison of consequence estimates of a manageable number of candidates. The alternatives don’t have the complete specificity of the theorists’ concept, but are, instead, the sorts of alternatives that we actually think about. For instance, perhaps I considered picking up a cup of coffee on the way and so getting to my lecture a minute late. There are, no doubt, millions of slightly different ways I could have gotten that coffee; the non-bizarre ones I lump together into the single alternative. (If you would like, you could think of an alternative for these purposes as a collection of fully specific actions, but I would advise against thinking of it as a set of such actions in a technical sense. Sets have determinant membership, whereas an alternative is vague at the edges, as is typical of the objects of our mental lives.)

I said that these working principles were only a first approximation. One reason for this caveat is that the ‘reasonableness’ modifier prominent in my formulation is not quite correct. The conscientious maximizing consequentialist will not be satisfied with a ‘reasonable’ performance. She will strive to be at her most creative, given the time and resource constraints, in coming up with alternative actions that might have better consequences. Subject to the practical constraints, she will analyze consequences with the greatest sensitivity to data, perspicacity of analysis, and soundness of judgment. We may not want to blame someone who has deliberated reasonably; but special praise is due to one who acts on a better than merely reasonable deliberation. This modification is necessary to conform to the spirit of maximizing consequentialism: to do the consequentially best that we can.

I conclude that notwithstanding how it fairs in debates with other kinds of moral theories, maximizing consequentialism is sustainable. It is sustainable even though there is no such thing as the set of all an agent’s alternatives; and even though, if there were such a set, it would be madness to seek either its best consequence member or an approximation thereto; and even though such a set, were it to exist, would make all positive assertions that someone has performed an objectively right action false. All we need to do to save consequentialism is to ditch the idea of a rigorously objective criterion of right action and its underlying concept of ‘best consequences of all alternatives’, satisfying ourselves instead with stand-alone action-guiding and praise and blame principles.

Lawrence Crocker studied philosophy at Yale and Harvard, and taught at the University of Washington before a career as a lawyer. He latterly taught philosophy at Dartmouth College in New Hampshire where he is now a Visiting Scholar.