The Greatest Happiness of the Greatest Number

Any good ethics textbook will tell you that “the greatest happiness for the greatest number” is something of a useless chimera of an ethical precept—imagine a gazelle with the legs of a tuna. There are two rather different principles jammed together here. “Promote the greatest happiness” is a principle exhorting us to maximize the quantity of happiness. “Promote happiness for the greatest number” tells us to seek the widest distribution of happiness. But these two principles don’t necessarily jive—they can flatly contradict.

Suppose the population is evenly divided between blue people and green people. Green people are usually just a little bit happy (say, averaging 3 on a scale of +10 to -10. [I'm going to use averages here, for convenience sake. The example doesn't create a difference between average and total utility.]) But blue people are either extremely happy (+10) or almost not happy at all (1), depending on how happy green people are. If green people are not happy at all (< +1), then blue people are elated (+10), otherwise, barely happy (1). The “greatest happiness” principle then says that we want a world in which green people are not at all happy. That’s a world with an average of 5 on our scale. The “greatest number” principle seems to say we want a world in which everyone is at least a little happy. That’s the world with an average of 2 on our scale.

Eminent utilitarians like Bentham, Mill, Sidwick, and Parfit end up embracing the maximizing principle and simply dropping the distribution principle. But what is left over fails badly to capture the upshot of the Enlightenment conception of “public happiness” or “social happiness” which the “greatest happiness” principle is attempting to capture. If screwing over the green people is what maximizes the total… well, nobody said morality is easy. Well, harumph.

I propose that the maximizing utilitarian interpretation, as influential as it has been, is a wrong turn down a dead end—a heretical gloss on Enlightenment gospel. As any member of the Eastern Christian church will tell you, orthodoxy and heresy are not matters of popularity. Therefore, the fact that it is a minority view will not stop me from declaring that what I will call the “fuzzy contract” interpretation is the correct and therefore orthodox interpretation.

The two parts of the “greatest happiness for the greatest number” principle reflect two separate but conceptually related aspects of the Enlightenment creed. First, happiness is each person’s moral goal. Second, people and their lives are of equal worth. Mainstream heretical utilitarianism chokes on both ideas.

Mill’s attempt to cross the chasm from individual to aggregate happiness is an infamous example of the fallacy of composition. A classic example of the fallacy would be: atoms are invisible, therefore aggregates of atoms are invisible. Mill’s argument, that since happiness is good for each of us, then the general happiness is good for the aggregate of people, really is like that. Sidgwick, the most clear-headed of heretical utilitarians, leaves us at the end of The Methods of Ethics with the famous “dualism of practical reason,” unable to reconcile heretical utilitarianism with orthodox Enlightenment moral individualism. On Sidgwick’s account, we arrive at the value of the aggregate only through a mysterious intuition.

Regarding the egalitarianism embodied in the “greatest number” principle, heretical utilitarianism does even worse. Utilitarians make a big deal out of the fact that each person’s pleasures and pains count equally. But the equality of pleasures and pains is a far cry from the equality of persons. Rawls and Nozick’s separateness of persons criticisms get it right. The thing that counts equally is not feelings, but lives. To conceive of us as containers for pleasures and pains simply doesn’t take persons and their life-constituting projects seriously.

Let’s step back and think again about the “greatest happiness for the greatest number.” It’s not a bad principle, really. And there’s a way of reasonably parsing it so that makes good sense. Don’t start with “greatest happiness.” Start with “greatest number.” The greatest number of people in society is, well, everybody—each individual, that is. So we’re thinking about each person. Got it? Now we move on to “greatest happiness.” For each person, we want the greatest happiness, for them. For each person, we’re going to try to see it their way.

This puts us in the neighborhood of the contract view. Everybody desires to achieve happiness by succesfully implementing his or her life-plan. Now, imagine we’re all deliberating together about policy. Gary proposes policy P, because it’s good for him. Lucy, who is well-informed and rational about her own interests, testifies that P would seriously hinder her ability to realize her life-plan and achieve happiness. So P doesn’t promote the greatest happiness for Lucy. Now, on the interpretation I’m after, the “greatest happiness for the greatest number” principle states a presumption against imposing P, even if Gary’s gain is happiness is bigger than Lucy’s loss. The Pareto conception of social welfare is a sort of like this. We consider a change in policy an improvement just in case it makes someone better off and no one worse. (Pareto wasn’t talking about happiness, though, he was talking about preference satisfaction—ophelimity!)

Now, on the the strict contractarian bargaining model, each person has a veto. Unanimity is required to make a move. Now, there’s a lot you can do to achieve unanimity. If P is worth n+$.01 to Gary, then he’ll put n on the table for Lucy to get her to change her vote. Etc. Of course, in the real world, we can’t always actually bargain, can’t actually offer each other side-payments, and can rarely get a unanimous decision. So our contractarian method is going to have to be fuzzy around the edges to work. The degree of gains and losses matters. What matters is not so much the quantity of feelings, as the impact on a life. If P would make Gary, Sara, and Delores rather better off, and would make Lucy just a little worse off, and no alternative that would be better for Lucy would be equally good as P for the others, then we should probably go ahead and just implement P. Sorry Lucy! Now, this is in the neighborhood of Scanlon’s “reasonable rejectability” criterion. (But isn’t the same: Scanlon rejects the idea that happiness is the sole consideration.) Even if Lucy knows P won’t be as good for her as some alternative, she’s benevolent, cares about other people, and knows their projects count too. And when other future hard choices arise, Lucy hopes that others would be will not hold out for every last scrap of satisfaction when doing so would place a significant burden on others. So it just wouldn’t be “reasonable” for Lucy to object to P. However, if P really screwed up Lucy’s projects and happiness in a deep way, then it wouldn’t be reasonable for the others to press it.

There is a balancing to perform between the “greatest happiness” for each individual and that of all the others individuals, “the greatest number.” The fact that this balancing is required isn’t a symptom of incoherence. Quite the opposite: it’s a sign of realism in a world in which the pursuit of happiness is intricately interdependent. Our diverse ends aren’t automatically reconciled—our interests aren’t harmonized by magic. “Public happiness” requires ongoing give and take. Almost every real world change produces a loser. We should aim to keep losses small and gains broad, to create a stable system of institutions where everyone in pursuit of happiness is able to take a lot, and is required to give only a little. That’s what I think the “fuzzy contract” view comes to. That’s what I think the pre-heretical exponents of “the greatest happiness for the greatest number” had in mind, and that’s largely what the American Founders were thinking when they talked about public of social happiness.

May the true principle of “the greatest happiness for the greatest number” be blessed. And may heretics be damned!

23 thoughts on “The Greatest Happiness of the Greatest Number

  1. “To conceive of us as containers for pleasures and pains simply doesn’t take persons and their life-constituting projects seriously.” is rhetoric that is not always true. Some utilitarians do take persons and their life-constituting projects seriously.

  2. “To conceive of us as containers for pleasures and pains simply doesn’t take persons and their life-constituting projects seriously.” is rhetoric that is not always true. Some utilitarians do take persons and their life-constituting projects seriously.

  3. Of course they do. And when they take them seriously enough, they stop being utilitarians.

  4. No, they don’t have to stop being utilitarians to take them seriously enough. Many utilitarians take persons’ life-constituting projects so seriously that they want to maximize their realization. On the other hand, many libertarians do not take persons’ life-constituting projects so seriously but instead want to impose their libertarian morality on them, which results in less realization of life-constituting projects.

  5. No, they don’t have to stop being utilitarians to take them seriously enough. Many utilitarians take persons’ life-constituting projects so seriously that they want to maximize their realization. On the other hand, many libertarians do not take persons’ life-constituting projects so seriously but instead want to impose their libertarian morality on them, which results in less realization of life-constituting projects.

  6. Not only does the “greatest happiness for the greatest number” create conflicting mandates, the greatest number principle is actually pretty much nonsense as a goal. There is no line between happiness and sadness; indeed, the whole idea of a line makes no sense. Thus designating any emotional state as “zero” is arbitrary. Therefore, having a as a goal a situation in which as many people are happy as possible is nonsense; everyone is happy and everyone is sad, it is just a matter of degree.

    That said, the greatest number principle is possible as a rule of action. We can say that we want to make as many people as possible happier with every decision we make. Of course the problem with this is that we are not aiming at maximizing happiness in any way. We could be systematically making the world worse off without violating this principle. Say killing someone makes everyone else better off because it decreases overpopulation. If I kill off everyone in the world (except myself) one at a time, I will not be violating this rule. Thus, I do not care about what actually happens to anyone, I just care about following a rule.

    If you aim at “greatest happiness” you actually have a goal. Giving a method of comparing happiness across individuals, it gives a method of weighing the interests of each individual equally. It is therefore the only logical way to understand “public happiness” or “social happiness”. As Bentham said, “It is vain to talk of the interest of the community, without understanding what is the interest of the individual.”

    Going on to your proposed moral framework, it sounds a lot like preference utilitarianism. “Lives” or “life projects” are not very specific. Are you arguing that people’s preferences matter, not their mental states (a la preference utilitarianism)? If not, are you arguing that only specific preferences matter? If so, how do you determine which ones matter? Furthermore, I’m not sure what valuing preference satisfaction has to do with rejecting aggregation. Those two are completely separate.

    You start your theory off with: “Don’t start with “greatest happiness.” Start with “greatest number.” The greatest number of people in society is, well, everybody—each individual, that is. So we’re thinking about each person. Got it? Now we move on to “greatest happiness.” For each person, we want the greatest happiness, for them. For each person, we’re going to try to see it their way.” That is exactly how utilitarianism does it. But it has nothing to do with the greatest number principle. Again as Bentham says, utilitarianism is about considering each and every individual. We want to maximize happiness for every person. The problem is, sometimes what makes one person happier makes another less happy. So you need some way of determining how to make the trade-off. Utilitarianism says we want to maximize aggregate happiness, which makes the most sense to me. Any principle in which we are not supposed to maximize aggregate happiness means that certain people are valued more than others based on some circumstance.

    Your example of Gary and Lucy poses two problems. The rule you are using for this situation means that we cannot do anything which makes anyone worse off. The first problem is that this is not a goal, but a rule of action, and is problematic in a way similar to the rule in which we are required to make as many people as possible happier. That is, we could continue to follow this rule and drive everyone as a whole into greater and greater misery by failing to help anyone when someone else might get hurt. The second problem with this is that, this rule is impossible to follow because instead of a rule which says to make as few people as possible worse off, you want to make no-one worse off. For almost every decision, however, there will be someone who is negatively affected no matter what you chose.

    You propose to solve the second problem with compensation for anyone who is made worse off. Presumably, this is a paired decision – that is, every decision which hurts someone must have a paired decision which compensates those people. Utilitarianism would be rather indifferent about compensation if it would work because the distribution of utility doesn’t matter. However, redistribution of utility is impossible without losing some utility along the way.

    Happiness/preference satisfaction is simply not redistributable like money is. For example, the compensation cannot be monetary unless money produces the same marginal utility for the people who lose it and the people who gain it. Because of diminishing marginal utility, compensation of wealthier people by less wealthy people is bound to result in a reduction of aggregate utility. More fundamentally, almost all redistribution requires effort or results in some cost. Any effort can be used to generate utility, so effort used to merely redistribute utility is wasted utility. Thus, if we try to redistribute utility there must be a loser, and if we try to compensate that loser there is another loser. Compensation of all losers is impossible because compensation continually reduces the available utility. (The only way it would work would be if the compensation creates utility as a side effect. If it created exactly enough utility as a side effect to compensate for the opportunity cost of compensation, utilitarianism would be indifferent about it. If it created more than the opportunity cost, it would be required by utilitarianism. Less, and it would be immoral.)

    Your solution to these problems seems to be to get rid of the compensation requirement. Compensation would be nice, you say, but not required. Then you say if three people gain from an act, and one person loses a little bit, the act is still moral. The problem is what constitutes “just a little worse off”, and why this degree of “worse off” is not arbitrary. It makes sense to me that the act is moral if the gains to the three people are larger than the loss to the one. Anything short of that constitutes unequal consideration; why should the one matter more than the three?

  7. Not only does the “greatest happiness for the greatest number” create conflicting mandates, the greatest number principle is actually pretty much nonsense as a goal. There is no line between happiness and sadness; indeed, the whole idea of a line makes no sense. Thus designating any emotional state as “zero” is arbitrary. Therefore, having a as a goal a situation in which as many people are happy as possible is nonsense; everyone is happy and everyone is sad, it is just a matter of degree.

    That said, the greatest number principle is possible as a rule of action. We can say that we want to make as many people as possible happier with every decision we make. Of course the problem with this is that we are not aiming at maximizing happiness in any way. We could be systematically making the world worse off without violating this principle. Say killing someone makes everyone else better off because it decreases overpopulation. If I kill off everyone in the world (except myself) one at a time, I will not be violating this rule. Thus, I do not care about what actually happens to anyone, I just care about following a rule.

    If you aim at “greatest happiness” you actually have a goal. Giving a method of comparing happiness across individuals, it gives a method of weighing the interests of each individual equally. It is therefore the only logical way to understand “public happiness” or “social happiness”. As Bentham said, “It is vain to talk of the interest of the community, without understanding what is the interest of the individual.”

    Going on to your proposed moral framework, it sounds a lot like preference utilitarianism. “Lives” or “life projects” are not very specific. Are you arguing that people’s preferences matter, not their mental states (a la preference utilitarianism)? If not, are you arguing that only specific preferences matter? If so, how do you determine which ones matter? Furthermore, I’m not sure what valuing preference satisfaction has to do with rejecting aggregation. Those two are completely separate.

    You start your theory off with: “Don’t start with “greatest happiness.” Start with “greatest number.” The greatest number of people in society is, well, everybody—each individual, that is. So we’re thinking about each person. Got it? Now we move on to “greatest happiness.” For each person, we want the greatest happiness, for them. For each person, we’re going to try to see it their way.” That is exactly how utilitarianism does it. But it has nothing to do with the greatest number principle. Again as Bentham says, utilitarianism is about considering each and every individual. We want to maximize happiness for every person. The problem is, sometimes what makes one person happier makes another less happy. So you need some way of determining how to make the trade-off. Utilitarianism says we want to maximize aggregate happiness, which makes the most sense to me. Any principle in which we are not supposed to maximize aggregate happiness means that certain people are valued more than others based on some circumstance.

    Your example of Gary and Lucy poses two problems. The rule you are using for this situation means that we cannot do anything which makes anyone worse off. The first problem is that this is not a goal, but a rule of action, and is problematic in a way similar to the rule in which we are required to make as many people as possible happier. That is, we could continue to follow this rule and drive everyone as a whole into greater and greater misery by failing to help anyone when someone else might get hurt. The second problem with this is that, this rule is impossible to follow because instead of a rule which says to make as few people as possible worse off, you want to make no-one worse off. For almost every decision, however, there will be someone who is negatively affected no matter what you chose.

    You propose to solve the second problem with compensation for anyone who is made worse off. Presumably, this is a paired decision – that is, every decision which hurts someone must have a paired decision which compensates those people. Utilitarianism would be rather indifferent about compensation if it would work because the distribution of utility doesn’t matter. However, redistribution of utility is impossible without losing some utility along the way.

    Happiness/preference satisfaction is simply not redistributable like money is. For example, the compensation cannot be monetary unless money produces the same marginal utility for the people who lose it and the people who gain it. Because of diminishing marginal utility, compensation of wealthier people by less wealthy people is bound to result in a reduction of aggregate utility. More fundamentally, almost all redistribution requires effort or results in some cost. Any effort can be used to generate utility, so effort used to merely redistribute utility is wasted utility. Thus, if we try to redistribute utility there must be a loser, and if we try to compensate that loser there is another loser. Compensation of all losers is impossible because compensation continually reduces the available utility. (The only way it would work would be if the compensation creates utility as a side effect. If it created exactly enough utility as a side effect to compensate for the opportunity cost of compensation, utilitarianism would be indifferent about it. If it created more than the opportunity cost, it would be required by utilitarianism. Less, and it would be immoral.)

    Your solution to these problems seems to be to get rid of the compensation requirement. Compensation would be nice, you say, but not required. Then you say if three people gain from an act, and one person loses a little bit, the act is still moral. The problem is what constitutes “just a little worse off”, and why this degree of “worse off” is not arbitrary. It makes sense to me that the act is moral if the gains to the three people are larger than the loss to the one. Anything short of that constitutes unequal consideration; why should the one matter more than the three?

  8. People are able to rate feelings in order of preference and even able to mention that they neither sad nor happy, so it not impossible to construct a line between happiness and misery and to set a zero. Happiness and misery being matters of degree does not invalidate maximization of happiness.

  9. People are able to rate feelings in order of preference and even able to mention that they neither sad nor happy, so it not impossible to construct a line between happiness and misery and to set a zero. Happiness and misery being matters of degree does not invalidate maximization of happiness.

  10. I agree that maximization of happiness is possible, I just think it doesn’t make sense to maximize the number of people who are happy. Sure, you could theoretically make a line between happiness and sadness, but I think it would be arbitrary. People might say they are neither sad nor happy, but this might encompass a whole range of feelings. Different people might say this at different points. I think feelings are to complex to set a zero point like that.

  11. I agree that maximization of happiness is possible, I just think it doesn’t make sense to maximize the number of people who are happy. Sure, you could theoretically make a line between happiness and sadness, but I think it would be arbitrary. People might say they are neither sad nor happy, but this might encompass a whole range of feelings. Different people might say this at different points. I think feelings are to complex to set a zero point like that.

  12. In later editions of The Principles of Morals and Legislation, Bentham added this footnote in the first chapter, when mentioning the principle of utility:

    “1. Note by the Author, July 1822.
    To this denomination has of late been added, or substituted, the greatest happiness or greatest felicity principle: this for shortness, instead of saying at length that principle which states the greatest happiness of all those whose interest is in question, as being the right and proper, and only right and proper and universally desirable, end of human action: of human action in every situation, and in particular in that of a functionary or set of functionaries exercising the powers of Government. The word utility does not so clearly point to the ideas of pleasure and pain as the words happiness and felicity do: nor does it lead us to the consideration of the number, of the interests affected; to the number, as being the circumstance, which contributes, in the largest proportion, to the formation of the standard here in question; the standard of right and wrong, by which alone the propriety of human conduct, in every situation, can with propriety be tried. This want of a sufficiently manifest connexion between the ideas of happiness and pleasure on the one hand, and the idea of utility on the other, I have every now and then found operating, and with but too much efficiency, as a bar to the acceptance, that might otherwise have been given, to this principle. “

  13. In later editions of The Principles of Morals and Legislation, Bentham added this footnote in the first chapter, when mentioning the principle of utility:

    “1. Note by the Author, July 1822.
    To this denomination has of late been added, or substituted, the greatest happiness or greatest felicity principle: this for shortness, instead of saying at length that principle which states the greatest happiness of all those whose interest is in question, as being the right and proper, and only right and proper and universally desirable, end of human action: of human action in every situation, and in particular in that of a functionary or set of functionaries exercising the powers of Government. The word utility does not so clearly point to the ideas of pleasure and pain as the words happiness and felicity do: nor does it lead us to the consideration of the number, of the interests affected; to the number, as being the circumstance, which contributes, in the largest proportion, to the formation of the standard here in question; the standard of right and wrong, by which alone the propriety of human conduct, in every situation, can with propriety be tried. This want of a sufficiently manifest connexion between the ideas of happiness and pleasure on the one hand, and the idea of utility on the other, I have every now and then found operating, and with but too much efficiency, as a bar to the acceptance, that might otherwise have been given, to this principle. “

  14. Stuart, Thanks. The von Neumann and Morgenstern passage is great. Of course, it would be a mistake to think that a good moral principle would need to be a strict mathematical function. “Do the best you can for everyone involved” is perfectly intelligible, though no decision rule can ever tell us how to do the balancing when trading one person’s welfare against another’s. We end up with rules of thumb like “Small losses for big gains are OK,” and “Big losses are not OK, no matter how big the gains,” and so forth. But no rule for how big big needs to be to force a small loss.

    Tim, Great quote!

  15. Stuart, Thanks. The von Neumann and Morgenstern passage is great. Of course, it would be a mistake to think that a good moral principle would need to be a strict mathematical function. “Do the best you can for everyone involved” is perfectly intelligible, though no decision rule can ever tell us how to do the balancing when trading one person’s welfare against another’s. We end up with rules of thumb like “Small losses for big gains are OK,” and “Big losses are not OK, no matter how big the gains,” and so forth. But no rule for how big big needs to be to force a small loss.

    Tim, Great quote!

  16. One really must wonder about the supposed “contradiction”, here, between distribution and optimization. Try as I might, I cannot find one. I only find a practical dilemma, which is sometimes solvable, sometimes not.

    In a world of blues and greens, utilitarianism seems like a travesty. But it perhaps, instead of blaming utilitarianism for the preferences of the world, we should blame the blues and the greens for having stupid preferences.

  17. One really must wonder about the supposed “contradiction”, here, between distribution and optimization. Try as I might, I cannot find one. I only find a practical dilemma, which is sometimes solvable, sometimes not.

    In a world of blues and greens, utilitarianism seems like a travesty. But it perhaps, instead of blaming utilitarianism for the preferences of the world, we should blame the blues and the greens for having stupid preferences.

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