On the greatest happiness for the greatest number: beyond Anderson Woods' 1925 opposition
 
Author: Doctor Terence Rajivan Edward
Abstract. This paper responds to Anderson Woods' famous paper against Jeremy Bentham's use of the formula: the greatest happiness for the greatest number. (Or of the greatest number: no distinction made here.) I reject two objections that Woods makes: that the formula, taken literally, specifies two final ends when the intention was to specify one; and that these ends are inconsistent. Both fail because the ends extracted are incorrect and a correct extraction does not fail to specify a final and consistent end. Then I make my own objection: that the formula is misleading at best, because utility monsters, as they are today called, count for more when the aim is maximizing the happiness in the world.
Published in: IJRDO Journal for Social Science and Humanities Research 11(5), 2025.


1. Introduction
        Ethics and the pursuit of happiness: what do they have to do with each other? Some will say nothing, but in the eighteenth century Jeremy Bentham influentially recommended utilitarianism and stated its vision as "the greatest happiness for the greatest number." This formula, as I shall call it, gives rise to various questions, some of which I shall not be concerned with below. One of these other questions is whether Bentham was the person who first devised it. But I will make a remark so as not to mislead readers. Students and many others associate the formula "The greatest happiness for the greatest number" with Bentham, but some sources say that it came originally from the Scottish philosopher Francis Hutcheson (Shackleton cited in Won-chul 2019) while others say that it came from the Italian criminologist Beccaria (Shackelton cited in Burns 2005: 46). I am going to refer to it as Bentham's here, reinforcing the usual association of the formula with his name, but this may be an injustice. My question is also not exactly what is meant by this formula, and simply not whether the formula properly understood expresses a truth. But I will have to say something about what is meant; the question of truth will be ignored. What then is my question? You know how, you sometimes say something and it sounds as if you have worded yourself right but then someone objects and instead of accepting the objection, you say, "This is not what I mean; I have not worded myself right"? My question is whether the formula is a good way of capturing the intended meaning. Bentham himself suggests no. Also Anderson Woods in 1925 has argued that it is not a good way of formulating utilitarianism. My main reason for discontent is different to that of Woods, but I suspect that my reason has occurred to Woods already. He does not state it though. In the next part of this paper, I present two interpretations of the intended meaning, favouring one of these: the normal interpretation. In part three, I present Bentham's own concern about the formula, but only to set aside his engagement with it as puzzling. In part four, I consider one of Woods's objections to this as a formulation of utilitarianism. In part five, I consider another objection. Neither succeeds. In part six, I present my own objection, but also note my suspicion that Woods has conceived it already.


2. The intended meaning
        "The greatest happiness for the greatest number": what does that mean? We can ask, what does it literally mean? Taken literally, it seems incomplete, at least if a sentence expressing a proposition is our paradigm of completeness. This is a complete sentence "We should aim to achieve the greatest happiness for the greatest number," as is "There is now the greatest happiness for the greatest number" and "This policy provides the greatest happiness for the greatest number." But "the greatest happiness for the greatest number" by itself: is that even a whole sentence?
    I am going to consider what someone intends to mean by "We should aim for the greatest happiness for the greatest number." In philosophy, this is normally taken to be a statement of utilitarianism, more precisely the version of utilitarianism called act utilitarianism. Other names for it are total and classical utilitarianism. (Warning: I sometimes simply write "utilitarianism.") Furthermore, in philosophy, the sentence is normally taken to recommend, for an individual to perform, the action which produces the most amount of happiness in the world, in the entire universe. That is the morally right action; anything less is morally wrong. "And happiness?" This is (interestingly) understood as pleasure minus pain. "But what if two alternative actions would both produce the most amount of happiness in the world and all other actions available to a certain individual would produce less?" Then act utilitarianism allows one to do either: to give one's money to charity or to relatives in need perhaps.
        This is a quotation providing a reassuring example of the normal interpretation in our day:
"Utilitarians like John Stuart Mill believe in the greatest happiness principle. That is, instead of just focusing on your own wellbeing, they believe you should try to maximize the total amount of happiness in the world." (Yale Divinity School n.d.) 
The normal interpretation is presupposed by numerous objections, for example the one quoted below:
"It has always been a forceful objection against utilitarianism that it cannot account for distributive justice: it aims at the maximization of the sum total of the good and is indifferent to its pattern of distribution." (Schroth 2008)
However, I have come across another interpretation, or family of interpretations I suspect. These say that what utilitarianism recommends is the greatest amount of happiness but also some distribution of it: spread as equally as possible (Maden 2023; Hargrave/Thakkar?) or spread across the greatest number. But act utilitarianism, as normally understood, does not tell us how happiness should be distributed. For example, if we assume happiness can be measured, and implementing either of two competing policies would both produce 9 billion more units of happiness in the world, more than any other competing policy, but policy 1 would leave each person 1 unit happier and policy 2 would be much less equal, act utilitarianism does not recommend the former policy. "But it says for the greatest number!" you protest. Yes, given the normal interpretation of act utilitarianism, there is a question, my question here: does saying, "Utilitarianism recommends the greatest happiness for the greatest number" - or does an act utilitarian saying, "We should aim at the greatest happiness for the greatest number?" - capture the intended meaning of the act utilitarian? I argue this famous formulation is misleading at best.


3. Bentham's revisions
J.H. Burns, of the institution University College London, which treats Bentham as a spiritual father, has written an article which examines Bentham's changing attitudes towards his recommendation worded as "The greatest happiness for the greatest number."  Bentham was concerned that the wording was compatible with a majority suppressing a minority group, in the name of the greatest happiness for the greatest number. Burns writes:
"His examples are those of the Catholic minority in Great Britain and the Protestant minority in Ireland, either of which (he seems to argue) could, on the 'greatest-number' principle, be enslaved by the relevant minority. And this would not be consonant with what Bentham now firmly decided should be called simply 'the greatest happiness principle'."(2005: 57-58)
There is a question of whether Bentham thinks the principle he originally intended is better worded as the greatest happiness principle (because this would, he thinks, prevent the misunderstanding that it allows for severe suppression of minorities) or whether the principle he originally intended really is the greatest happiness for the greatest number principle, he has realized an objection to that principle (it allows for severe suppression of minorities), and is now advocating a different principle, which he names the greatest happiness principle. Whatever the answer, I cannot see how he avoids the problem of wrongly allowing for the suppression of minorities. We should be aiming at the greatest total happiness according to Bentham, but that will allow for suppression of minorities, if it makes others sufficiently happy.


4. Woods's two ends objection
        Early on in his 1925 paper "The Greatest Happiness Regardless of Number," Woods writes as if Bentham intended to recommend one final end, but his formulation of the end implies two. Woods writes:
"The want of unity in the standard formula of Utilitarianism as declared by Bentham, "The greatest happiness of the greatest number," makes it fatally defective as a statement of the ultimate end. Instead of one such end, the statement seems to contemplate two: (1) the maximum amount of happiness, and (2) the maximum number of people to enjoy it." (2025: 413)
I have doubts about this objection. One doubt is about whether Woods actually achieves a more literal reading of the formula, in order to then be in a position to evaluate its suitability to capture Bentham's intended meaning. If you want to take it more literally than Bentham intended, think of it as assuming that there is always more than one action that produces the maximum amount of happiness that can be produced and then one should perform the action in which the happiness is spread amongst more people. For example, if two possible worlds both have 9 billion units of happiness, but in world 1 this is spread amongst 1 billion people and world 2 amongst 9 billion, then prefer world 2. In 2015, Michael Pressman wrote an article on Woods. Pressman seems to accept the point quoted. I don't, but largely because I don't see why the more literal reading identifies the two final aims Woods extracts or two final aims at all. (By my more literal reading, actions do not seem to be ranked by a simple criterion of the form: action A is better than action B if and only if A has quality ____. Rather: if action A produces more happiness in total than action B, or would do for possible actions, then A is better; and if A and B produces equal total happiness, then A is better if and only if A spreads the happiness amongst more people. But is that two final aims? It is a mistakenly demanding conception of two in this context. A moral system can specify how to rank actions otherwise tied for best.)


5. Woods's  partial consistency objection
Woods makes a second objection, according to which the two final ends he extracts from the formulation must be entirely consistent, for the formulation to be of use to Bentham and they are not:
But two final aims cannot coexist unless they can be proved at all points consistent. (1925: 413)
What if they are not totally consistent but the two finals aims are only inconsistent in situations incredibly unlikely to arise? Will that not do? Anyway, he suggests there is nothing unlikely about the two final ends he extracts from the formulation being not mutually realizable:
It is easy enough to conceive of circumstances under which an increase in population would mean a decrease in aggregate happiness." (1925: "413)
A response to this example is to again consider the two ends he extracts from the formulation of the final end as the greatest happiness for the greatest number and say that even on a  more literal reading, one should not extract these as the recommended final aims. I favour this response. To repeat: there is no second final aim recommended of the greatest number regardless of happiness, to allow for an increase in population which decreases total happiness to count as meeting one of the final aims at least. If you want to take it more literally than Bentham intended, think of it as assuming that there is always more than one action that produces the maximum amount of happiness that can be produced and then one must perform the action in which the happiness is spread amongst more people.


6. My objection
Given the normal interpretation specified in part 2 of this paper, what Bentham actually intended to convey is that the morally right action is the one that produces the most happiness and if multiple possible actions are tied for which would produce the most, then they are each morally acceptable and share top rank as options whereas any action which produces less is prohibited. I think this is poorly conveyed by his famous formulation of the greatest happiness for the greatest number. "WHY?" Because the aim of maximizing happiness in the world can involve privileging one person in some situations. Consider a dinner party in which three attend and one gets happy much more easily than the other two, especially by hearing the other two attempt long complicated discourses which this one will constantly interrupt. Now the other two have to produce these discourses and endure interruption, because that is what most increases happiness in the world. The problem for utilitarianism of people who get happy more easily is nowadays called that of utility monsters (Nozick 1974: 41) and it undermines a characterization of aiming at the highest total happiness in the world as aiming at "The greatest happiness for the greatest number." Utility monsters carry more weight than others when pursuing this aim: satisfying them matters more than satisfying you. (Nevertheless, you count. Any being which can experience pleasure or pain matters for pursuing the aim, though I have conveniently restricted the focus to persons in my hypothetical examples above. There are anti-utilitarians who will say that some people do not count at all, when deciding policy, because they are the lower classes.)
Woods does not make this objection, but I suspect he is aware of it. Later in his article, he considers a situation in which a good, some food, could be distributed evenly between two persons A and B, but instead all of it is given to A. B is severely harmed but A does not immensely benefit, does not benefit to an extent matching the extent to which B is harmed. The nature of this good is such that A has enough without being given B's whole share and much of the share does not bring an added benefit to A. Can it be that Woods went this far into questions of happiness distribution and into challenging misconceptions about when things would be symmetrical (challenging if it harms B to this extent, it surely benefits A to the same extent) and yet missed my simple objection: that given the end of maximum overall happiness in the world, people who get happy easily should carry a larger weight in decision-making and this makes the characterization of this end as "The greatest happiness for the greatest number" misleading at best? Well, it is possible he missed this point; and there are people who grasp complicated points and miss simpler ones in the vicinity. But is it likely? (What should we say if he did not miss it? "He was good and there is some taboo with saying your objection at the time"; or "He is bad and writing so as to give some readers discomfort. He surely knew the objection and he is indirectly sending a message: keep out, clever student from discriminated-against group who grasps it independently; you don't understand this field"? Not sure.)
        An issue I have not considered here is: utilitarianism allows one to make a misleading assertion if it produces more overall happiness. The expression "The greatest happiness for the greatest number" is pleasing and sticks in the memory. But in academic contexts, I think we should prefer specifying the end act utilitarianism recommends as the greatest overall happiness or the greatest total happiness, given our expectations of more accurate discourse. The frustration of these expectations causes unhappiness!


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