# What are the arguments for maximising total utility as opposed to average utility?

I couldn't actually understand that it says that some people argue that attempting to maximise total utility (here utility=happiness) of the human population as opposed to average utility.

I know SE is not intended for debates, so instead of proving me wrong, I'd like some useful resources or texts that may help one understand the point of view of a supporter of total utility maximisation.

• I don't get the second sentence. It doesn't parse right. – Dave May 20 '17 at 13:15
• I'm not really grasping what the question you have that we can answer is. Can you try further editing your question? – virmaior May 22 '17 at 3:11

The main issue with average utility is that killing anyone below the current average happiness will increase the average happiness. At an extreme, killing everyone but the happiest person would maximize average happiness (until we take into account the effect of that on that person's happiness, of course).

So average utility suffers from the problem that adding more happy people makes things "worse", if their happiness is less than the average happiness.

A lot of this depends on intuition, so if your intuition says that a few people at 10001 happiness is better than lots of people at 10000 happiness, there's not much to say to that, other than discuss how other people's intuition says otherwise. If you view happiness as an additive thing, that someone being happy is certain amount of "goodness", and another person at the same happiness is "twice as good", then that leads to total utility.

• `The main issue with average utility is that killing anyone below the current average happiness will increase the average happiness.` While this is an argument that some raise, it requires some massive asterisks. 1) Killing someone does not remove their life from the utilitarian calculus. The negative utility they generate during their life must still be accounted for. – eclipz905 Feb 7 at 16:14
• 2) A policy of "kill everyone below average happiness" will likely negatively impact everyone. Those to be killed generate extra negative utility while awaiting their execution. Among the survivors, their happiness is negatively impacted as they see their friends and family executed. Those near the threshold experience increased anxiety as they wonder when the executioners gaze will set on them. All of this would drag down the average happiness. – eclipz905 Feb 7 at 16:14

▻ AVERAGE AND TOTAL DO NOT NECESSARILY DIFFER

There is no necessary difference of result between the two criteria. Take a single society with a population of 100. The greatest total utility for this society (at a time) is 1000 utils, let's say. That's the absolute limit, the maximum total utility possible. The average utility will be 10. The average utility cannot be higher since maximum utility has been reached at 1000 - nor can it be lower. 1000 divided by 100 gives an average of 10 whatever the case.

▻ WHEN THEY DIFFER, WHAT IS THE CASE FOR PREFERRING AVERAGE TO TOTAL UTILITY?

But if you take two societies, even if they are egalitarian and each member gains the same amount of utility, it is rational to choose the society which has the highest average utility. How so? Suppose Society A has a total utility of 10,000 and 5000 members; and Society B has a total utility of 5000 and 100 members. In society A, total utility is higher but average utility is 2 utils. In Society B, total utility is lower but average utility is higher at 50 utils.

My rational choice would be to go by average utility. As a rational agent, all else equal, I'd rather have 50 utils than 2.

▻ IS THERE NO CASE FOR PREFERRING TOTAL UTILITY ?

There is a case, especially as concerns future generations. You need to go into specialist literature here. But one argument, relating to future generations, is sketched as follows :

The total utility criterion was first applied to the study of optimal population paths by Meade (1966). A rigorous analysis in the context of a Solow-Swan model of growth was provided by Dasgupta (1969). In his model, the optimal rate of population growth can be positive. Although the present generation may be better off consuming all the capital stock and having no descendants, the present gain in utility is outweighed by the loss in utility of the future generations.This result sharply contrasts with the ones obtained under the average utility criterion. ( A. Rodriguez, 'The Dependency Ratio and Optimum Population Growth: The Total Utility Case', Journal of Population Economics, Vol. 1, No. 2 (Oct., 1988), 141. Further references aplenty.)

▻ BOGUS MATHEMATICS

Talk of numerical utils is only a mode of convenience. Utility cannot be measured with any mathematical precision in real life. But we can and do make judgements of rough relative magnitude, and the above calculations are based only on this assumption.

Henry Sidgwick, The Methods of Ethics, New York: Dover, 1966/ 1907, 415.

John Rawls, A Theory of Justice, Cambridge, Mass., Harvard University Press, 1971, chapters 1 & 3.

Gregory S. Kavka, 'Rawls on Average and Total Utility', Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, Vol. 27, No. 4 (Apr., 1975), 237-253.

A. Rodriguez, 'The Dependency Ratio and Optimum Population Growth: The Total Utility Case', Journal of Population Economics, Vol. 1, No. 2 (Oct., 1988), 141-156.

Try a proof by contradiction. Assume that you are deciding between average utility and total utility. If you deny total utility, you are left with average utility. But then it turns out that a world consisting of a single person who is averagely happy (albeit lonely...) would be as good a world as the one we currently live in. Even if you value some goods that come from community or variety or difference of cultures, you could have a world that supports these with a fraction of our world's current population.

Imagine a world consisting of 0.1% of our population (7 million). One in which people were no more happy nor materially better off than in ours. Wouldn't such a world be worse in respect of its smaller population? Think of how vanishingly unlikely it would be for you to be included within this lucky 7 million. Assuming you think your life has some value, ask yourself why the world would be no worse (or negligibly worse) if you were simply not to exist. Or consider the birth of someone who turns out to be happy, but less than averagely happy. On an 'average' view, the world made worse by the birth of this person.

You can play around with these examples to create intuition pumps against average utility. A plausible way to deal with these problems is to say that each person's happiness makes the world a better place irrespective of the effect of this on the average.

The problem with total utility you point to is sometimes called the repugnant conclusion (or Mere addition paradox),

``````Doesn't it also give a reason to say, have a 100 billion, say artificially produced people who are mildly happy, as compared to just a billion people who are really happy.
``````

This paradox was first described by Derek Parfit in Reasons and Persons. There are plenty of resources on this:

• Have other avenues between average and total utility been explored? Because that's a very narrow scope. You can still, for example, have a utility function that depends on `n`, but doesn't increase linearly with it. For example, if it's `(Total utility)/sqrt(n)` then it's still good to create more people with high utility, but you avoid the repugnant conclusion (i.e. one person with `x` utility is still better than `n` people with `x/n` utility but worse than `n` people with `x` utility). – Bridgeburners Jun 19 '17 at 19:25
• @Bridgeburners I think a lot of people will have the same intuition: that total and average utility both matter and we should find some way to give weight to both of them. The trouble is finding a principled basis for this view. It still entails that adding a new population of happy people (though less than averagely happy people) can be worse. & the repugnant conclusion still arises: you just need to compare the existing population to n squared rather than n. So in fact you are left with both problems! – Guambra Feo Jun 20 '17 at 10:06
• I would recommend this video in particular in relation to the repugnant conclusion youtube.com/watch?v=vqBl50TREHU – Guambra Feo Jun 20 '17 at 10:08
• The argument here falls apart at the parenthetical '(albeit lonely)' People like having a variety of other people around, so the denser population would be better, but that is still a factor in average utility, as the OP noted. – jobermark Dec 18 '17 at 18:42

Any argument you get will be mathematically vacuous. One of these is better for entirely mechanical reasons that can't really be refuted.

Since individual utility can be tied to population density, total utility is a special case of average utility (where happiness increases linearly with the availability of other people to interact with). But average utility cannot be captured by total utility. The case that covers both options is obviously adequate whichever one is best.

So, once this distinction occurs to anyone the only meaningful argument for not averaging would be in terms of tractability, simplicity, stability and feedback loops. This is not much of an argument because these are tests that meaningful utility functions fail in general, even in the simplest cases. Who cares if the impossible complexity should have one division step added to each already-intractable computation?

The real appeal here is traditionalism and the fact that existing arguments by great names need to be discarded if the overall criteria change. Historically, the earliest proponents of these techniques lived in obviously underpopulated societies, so these two approaches looked the same, and straight summation was easier to describe. If Bentham grew up in Mumbai, we would have average utility from the start.

In a society like that of Bentham's England, one could argue that more people means faster improvement in whatever optimal state already exists. (A 'la Frank Herbert's xeno-biological appendix to Dune: 'Life alone begets the conditions for living.') So greater numbers predict faster rising potential happiness in the future. But one can only buy that argument if one has never encountered excessive mechanization, global shortage of real necessities, or a modern society like ours that runs out of work not because there is no need to have it done but because of the sheer complexity of making people ready to perform it.

If you want to provide for the future in the computation, you need to roll up the rational expectations people have for their descendants or the ideas into the utility function directly, instead of relying upon dodges like this.

Think of utilitarianism as the combination of two claims:

1. The right thing to do is what maximizes the amount of intrinsic moral goodness in the universe.
2. The only thing which is of intrinsic moral goodness is happiness.

(2 isn’t important for this discussion)

Utilitarians and others who view morality as involving maximizing argue for 1 on the grounds that it is just part of the nature of reasoning about action that if x is better than y, then we should choose x over y. Think of an example: \$1000 can buy all the same goods and services that \$100 can buy, plus more. Therefore it is better to have \$1000 than \$100. If, therefore, I can choose between receiving \$1000 and \$100, all other things being equal, the only reasonable choice is \$1000, because that is the choice that maximizes my benefit.

Moral theories that deny 1 above, are committed to saying there are some reasons to choose \$100 over \$1000, other things being equal. And this, utilitarians say, is absurd.

But utilitarians also have to distinguish their views from another position called egoism. Like utilitarians, egoists say morality is about maximizing, however egoists think I should always act to maximizes my own benefit. Utilitarians disagree. According to Utilitarians, our maximizing calculations should be “agent-neutral”, i.e. no particular person’s happiness is weighted more than another’s. And that is just what 1 above says.

For these two reasons, utilitarians have to endorse 1. If they argued that what maters is average happiness, they would have to admit that there could be good reasons to choose \$100 over \$1000, other things being equal, which would then give them no reason to say moral theories based on exceptionless rules, like Kant’s, are wrong. Further, utilitarians have to make their conception of maximization agent neutral to keep their views from devolving into egoism.

There is an additional complication here caused by two different ways of conceiving what one is trying to maximize (whether one is maximizing the utility caused by a specific action [Act utilitarianism] or whether one is trying to maximize the utility caused by society adopting a specific rule [rule utilitarianism]). But we need not go into that because even rule utilitarians have to agree with 1 and therefore can’t adopt a principle of increasing average utility.