Monday, June 06, 2005

The Population Paradox

Let 'the baseline' refer to that level of well-being below which a life is not worth living. How's this for an inconsistent triad:

1) It's better to have a world that is moderately populated with flourishing people than a world which contains a huge number of people whose lives are barely above the baseline.

2) A state of affairs cannot be made worse by adding more people (all of whom are above the baseline) and leaving everyone else entirely unaffected.

3) A state of affairs can be improved by greatly benefitting a worse-off person at moderate (lesser) cost to someone who is better-off.

This is a concise version of Derek Parfit's "mere addition paradox". The problem is that if we start off with a flourishing population, by #2 we can add a further group of people who are less well-off, and then by #3 we can improve the welfare of the new group at the cost of the former. By repeated iterations, we eventually reach a state of affairs in which everybody is barely above the baseline. But at no step did we make the state of affairs any worse than it was in the previous step.

It doesn't seem that either #2 or #3 can be plausibly denied. But that means we are left with "the repugnant conclusion" of denying #1, and accepting that a swarm of dull (near-baseline) lives is better (or at least no worse) than a more moderate population of flourishing lives. Can you see any way out?


  1. When will you stop writing as if there was a fixed amount of stuff just sitting there waiting to be distributed?

    The way you distribute wealth affects whether it exists at all. If everyone receives the same amount then there is no incentive to produce (except maybe a threat of being sent to the Gulag), and hence nobody gets anything.

    Many of the goods and services implicitly referred to in 3 will exist if and only if they are not redistributed.

    3 can be plausibly denied, in fact beyond a certain point it definitely will not hold.

  2. You're missing the point. This has absolutely nothing to do with wealth redistribution or incentives; that whole debate is entirely irrelevant to the present point.

    But perhaps that is my own fault for employing somewhat sloppy language. There is no causal link between the 'benefit' to one person and the 'cost' to another, since we are comparing changes across possible worlds (rather than within a single one). No redistribution ever takes place.

    To make it clearer, consider the following two worlds...

    w1: Anna has 100 utiles (of well-being), Ben has 50.

    w2: Both Anna and Ben have 80 utiles of well-being.

    The question is, which world is better? And the only possible answer is w2. It is better in almost every possible respect: higher total utility, higher average, better for the worst off, etc. And this is all that #3 is claiming. The only way to deny it is to say that the welfare of the best-off matters more than the welfare of other people. This is not even remotely plausible.

  3. For this to mean anything you need to assume that the two worlds can be arrived at from the same starting position. If the two worlds have nothing in common then why compare them?

    You say the alternative to 100-50 is 80-80. I say if you aim for 80-80 you will get 80-40. You can reduce the gap by making everyone poorer but cannot eliminate it unless everyone is dead.

    Even if you could magically create a world with the 80-80 distribution it would not stay that way if there were human beings in it.

    So 3 is hopelessly counter-factual.

    Now that I've looked at this again, I think 1 and 2 are incompatible. If average utility is used, 2 is false. If total utility is used, there is nothing repugnant about denying 1.

  4. "If the two worlds have nothing in common then why compare them?"

    The point is to provide a theory of value. We (at least, philosophers) want to know what possible state of affairs are better or worse than others. One we settle on a theory, it will also have practical consequences in terms of, e.g., population control. But you're trying to bring in practical irrelevancies far too soon.

    I'm not saying we "aim" at 80-80. I'm stipulating that this is the result in that world. (We may also stipulate that the utility levels remain constant across time in each scenario. If I can magically create a world, then I can magically keep it that way. Perhaps more resources fell from the skies as they were needed. It's a thought-experiment, the details don't matter. Your practical objections simply have no bearing on the theoretical matter at hand.)

    #1 and #2 are perfectly compatible if you deny #3. Of course we would thus be using neither total nor average utilities. Total utility is inadequate because the denial of #1 patently is repugnant. And average utility is inadequate because it entails the denial of #2, which is likewise implausible.

    The point is that we require some compromise or alternative to/between 'total' and 'average' methods of utility aggregation. But there is no possible aggregating method that will satisfy all three requirements. That's the problem.

  5. The problem is with premise 2, I believe.
    You define the base line as "a level of well-being below which life is not worth living." To me, this means people who live by inertia. Their life is not so pain-filled that they wish for death, but they don't have any purpose or goal aside from getting through another day. This, to me, isn't happiness. One might assign these people a small negative util value, in my opinion. The reason that we still consider these people to have lives worth living is that death is scary and painful, and thus has move negative utils than another boring day.

    Obviously, if there are people with negative utils who choose to remain alive, adding more of them doesn't directly make the world a better place. I would say that the negative utils actually make it a worse place, overall, although very slowly. (Just like the slow decrease of quality of life in the paradox.)

    The other option is to say that the baseline is the place at which people begin to gain positive utils. If this is true, then the first statement is not negated if we consider anyone with positive utils to be flourishing, then we get a restatement of the conclusion that says, "A large poplulation of flourishing lives is no worse than a moderate population of more flourishing lives."

    I think that it is likely that this is true. Being "more happy" when one is already happy is in and of itself somewhat of an illusionary goal. One who is happy does not think, "Man, this is great, but I could be more happy." Only a person who is unhappy considers the ups and downs of their state of affairs.

  6. Yes, I meant for the baseline to be "the place at which people begin to gain positive utils."

    By 'flourishing' I mean a very high-quality life, i.e. a great many utils. The dull life, by contrast, contains nothing bad (so no negative utils), but only a few positive utils. By stipulating that it is (just barely) a life that's worth living, it seems difficult to deny #2 and claim that it would have been better if that person had never existed. How could their existence be worse than nothing, if we've stipulated that it is (if just barely) a life worth living?

    (I like your response though. I think it might have some promise, if we can resolve the problems I've outlined above.)

  7. Ok, after serious consideration, it occurs to me that another thought experiment is better suited as a rebuttal for premise two.

    In your situation, we have group A, all of which have x utils. We add group B, which has y utils, where y is less than x.

    Our initial assumption is to say that this is no worse than the original situation, assuming that y is more than the baseline.

    However, my perception, at least, changes, if we instead start with the same group A, and this time add group B with x utils each. This time we say that for some of the members of group A, their utils are reduced to y. In other words, this time a new group comes in and reduces the standard of living of members of the old group.

    In the end, these two situations are the same, but I precieve them differently. I see at least the possibility of a decrease in utility in the second experiment.

    While it's difficult to tell exactly what the overall utility will be, I would like to mention that I think there's a bias to initally say, the more conciousnesses, the better, without a real reason why. Using the average utility, with a lower bound on the population based on realist constraints, may be the most reasonable way to measure things.

    I would probably be smarter if I weren't tired....

  8. I grant that it might be worse if a new group came along and made the original group worse off. But that is no counterexample to #2, for it fails to "leave everyone else entirely unaffected".

    It's much harder to deny #2 when we bear this proviso in mind. Is it really plausible to say that adding more (post-baseline) people can make a situation worse even when nobody is made worse off?

  9. I don't have much of a problem with denying #1. Especially when you replace "flourishing people" with, say "decadent, overconsuming, mindless hedonists". But I guess that's why I don't really believe in utilitarianism.

  10. Utilitarianism has nothing to do with it. (We are here concerned with what is good, not what is right.)

    Let the 'flourishing' people create great art, eat French cuisine, and listen to Beethoven; whilst the swarm of dull lives consists in eating gruel and listening to Britney Spears. (Okay, maybe we're edging into negative utility here... better add some drugs into their bloodstream to cheer them up. Maybe they get to play a game of cards every now and then, which makes it all worthwhile. Whatever is necessary to keep them just above the baseline.)

    It strikes me as very odd to say that the swarm of dull lives could be better than the flourishing alternative. I don't think most people would be willing to accept that conclusion. Quality is more important than quantity.

  11. I wrote: "It strikes me as very odd to say that the swarm of dull lives could be better than the flourishing alternative."

    I worded that poorly. Of course each individual dull life is worse than each individual flourishing life. Nobody is disputing that. I meant instead to say that it seems odd that a world containing many dull lives could be a better world than one containing (albeit fewer) flourishing lives.

  12. Here is your way out.
    Maximise utility over time.
    you hve X units of resources (consider entropy) - these resources can be used to create florishing lives over time but only a limited amount of lives adding a new life may or may not help but you cant just keep on adding because you sacrifice the future in order to do so. You can create them now or later.
    Also one person living 100 years would tend to beat 2 people living 50 yrs and one might have to consider two nearly suicidal people to be lower than one happy person.

  13. Time is irrelevant -- like I said in response to Nigel, we can stipulate that the utility levels are held constant across time, and that the necessary resources magically fall from the sky if need be.

    (Again, it may help to think of the alternatives as two separate worlds, rather than one to which you "add" various things. We want to avoid any confounding variables that might be influenced by such "additions".)

  14. > Time is irrelevant, and that the necessary resources magically fall from the sky if need be.

    haha well fundimentally I think a scenario that can't exist can't have a real answer. If somthing is possible then the hypothetical "exists" to a certain extent but if it is not then the universe need not have a solution for it or any of it or a description of its atributes.
    But to adress the hypothetical.

    Yes 1 is better because you have defined it as a higher energy state (and thus is better) there isn't anything repugnant about it.

    However the end result within the powers of any leader (excuse me for getting back to reality) wont produce many nearly suicidal people because they have low value in utility but still cost a reasonable amount of resources, and probably not much equality. Interestingly the result may well be similar to the current situation.

  15. actually higher energy state is probably wrong I should say defying of entropy. imagine if you invented a machine that did such a thing - its implications are fundimental enough to obscure the rest of any debate. it reminds me of the exam question "what if this car had no friction" besides 'it wont go" and "it will fall apart" a nice answer is "I'd sell it to NASA for a billion dollars" ;)

    Your real problem of course emerges when one does what logic would suggest would make a life more flourishing and yet it makes the person suicidal - a quirk in their humanity or some such thing.

  16. It seems to me that part of the problem lies in repeatedly imposing moderate costs. At some point these must sum to a substantial cost, with the original members of the population sustaining the highest costs.

    There is an underlying affinity with paradoxes that rely on the sum of an infinite series being a finite number.

    I think this is what Genius was getting at with the "over time" angle.

    Also, isn't there a little verbal sleight of hand here? Rule 2 states that new additions must leave the original population unaffected. However, you propose that every exercise of rule 2 be followed by rule 3, which imposes a cost on that population. Thus additions do NOT in fact leave the original group entirely unaffected.

    Lastly, can we allow that regret at not achieving a higher level of utility than you currently have is a negative util? Because then, if I fail to achieve my utility potential because resources are withheld from me (perhaps for redistribution to others) then my utility is not merely held the same but is actually decreased.

    I'm not really sure about this "paradox". I understand that these propositions are not mutually consistent, but I think that Rule 3 in fact can be plausibly denied, given the latitude inherent in "great" and "moderate".

    Aren't economists who study people as they are discovering that actually, happiness partly derives from perceived status relative to other people? In a world where individual self-evaluate utility, I don't see any of these propositions holding up very well. The baseline of Rule 1 is no longer stable in that world.

  17. Stephen, the propositions here deal in "all-things-considered", finalized utility. So we need not worry about envy or regret - that has all been taken into account already. If we say a person is made better off, then we mean that he really is better off, even counting envy, etc.

    I really can't see how #3 can be denied. Like I said in my first response to Nigel, the second world is better in almost every possible way: higher total utility, higher average, better for the worst off, etc. The only way to deny it is to say that the welfare of the best-off matters more than the welfare of other people. This is not even remotely plausible.

    We don't need to deal in infinities at all. Suppose each universe only exists for century (or, at least, that is the only time interval that we are assessing the value of). Then everything is finite. No problems.

    "Also, isn't there a little verbal sleight of hand here?"

    Good spotting. But Parfit pre-empts this objection, by stating the scenario more carefully:

    Imagine that our world has two groups. If asked whether it would be better if the less well-off (but still post-baseline) group had never existed, we surely must answer "no" (thus affirming #2). We also think it would be better to benefit the worse-off group at lesser cost to the flourishing group (thus affirming #3).

    We thus judge that the world (w2) with many moderately well-off people is better than our world (w1), and that the world with only the flourishing group (w0) is not better than our world. From this it follows that w2 is better than w0. That is, the 'repugnant conclusion' that quantity can outweigh quality of life.

  18. Are these worlds like normal worlds in which a finite quantity of resources are transformed into utils by some (non-decreasing) function?

    It seems to me that #1 implies some kind of trade-off between flourishing lives and more baseline lives. If resources can fall from the sky whenever we want then #1 isn't very interesting because any state without an infinite number of flourishing people is going to be pretty bad.

    If resources are finite then #2 doesn't come into play because adding more baseline people will not leave the existing people unaffected.

  19. The three propositions are describing the end result, in utils.
    Just take these as given, and don't worry about how they got there. It simply isn't relevant. There's no need to discuss resource-related issues, they would just provide practical distractions that aren't relevant to the theoretical problem.

    (So no, there are not infinite resources if that would preclude #1's scenario. And if a fixed number would get in they way of #2's scenario, then we don't have that either. Just suppose that God fiddles with the resources to ensure that we get the stipulated results in each of #1, 2, and 3.)

  20. Richard, could you describe in a little more detail what is meant by "the state of affairs?"

    It seems to me that in proposition 1, the reason it is preferable is that utility PER PERSON is maximised.

    In the repugnant conclusion, utility per person has been decreased (at least as far as the original w1 population are concerned). Parfit's careful scenario still dodges the point that 3 violates the "unaffected" stipulation of 2. The "state of affairs" in 2 and 3 seems to refer to aggregate utility rather than per-person utility.

    This still feels like a integral calculus problem...

  21. oops, i meant "original w0 population".

  22. The point of Parfit's restatement is that the w0 population is not "original". The original population is w1, and we compare it to the counterfactuals w2 and w0. This allows us to satisfy the "unaffected" proviso, since only a previously existing state of affairs can be changed or 'affected'. But w0 is never changed into w2, so ipso facto is not 'affected' by it.

    Regarding aggregate vs. average utility, see my second response to Nigel at the top of this thread.

    A "state of affairs" is just a snapshot of the universe. We want to be able to judge that some are better than others. But, as the paradox shows, we have inconsistent intuitions about what makes one SoA better or worse than another. The challenge is to somehow resolve this inconsistency, and find a theory of value that can give plausible answers to the whole range of problems.

    (I'm most inclined towards an 'averaging' account, though this means rejecting #2, which is very difficult to stomach!)

  23. Late arrival .. How about this ?
    Proposition 2 is complete in itself and acceptable.
    Proposition 1 and 3 are conditional on number balance .
    Now iterate within the correct limits.
    Who dreams up these things ?

  24. But why are they "conditional on number balance"? If it's just ad hoc, that doesn't make for a very plausible solution.

    Besides, let's fill it in with some actual numbers and see what happens:

    1') Better to have 10 billion people with 1000 utils each, than 20 billion people with just 550 utils each.

    2') a world with 10b @ 1000 utils each + 10b @ 50 utils each, is no worse than a world with just 10b @ 1000 utils each.

    3') 20b @ 550 utils each, is better than a world with: 10b @ 1000 utils each + 10b @ 50 utils each.

    Which of 1' or 3' would you reject here?

  25. What is the baseline
    "worth being alive" (from the universe's point of view) utils the individual must create I assume you are setting it at <50 Utils
    and defining the effect of an additional person as only upon himself.

  26. Yeah, I figure the baseline is zero, so that a life not worth living would be in the negatives. And, as always, the util values are the "end result", so there are no interference effects from adding the extra people.

  27. Here's an idea I'm considering that I've never heard discussed before.

    1. People can have preferences that can be thwarted, even if they never find out about it. For instance, if someone prefers their spouse not cheat on them, their spouse harms them by cheating on them regardless of whether or not they ever find out.

    2. People have preferences about the existence and utility of other people. One can prefer a person with a much lower utility level than you come into existence, because of the large unwanted duty to help them that would inflict upon you (or for some other reason).

    3. Therefore, premise #2 of the argument is logically impossible. Creating the barely-above-baseline population harms the existing population, even if they never any of the new people.


Visitors: check my comments policy first.
Non-Blogger users: If the comment form isn't working for you, email me your comment and I can post it on your behalf. (If your comment is too long, first try breaking it into two parts.)

Note: only a member of this blog may post a comment.