# The Mere Cable Channel Addition Paradox

The following is a dialogue intended to illustrate what I think may be a serious logical flaw in some of the conclusions drawn from the famous [Mere Addition Paradox](http://en.wikipedia.org/wiki/Mere_addition_paradox). 

EDIT:  To make this clearer, the interpretation of the Mere Addition Paradox this post is intended to criticize is the belief that a world consisting of a large population full of lives barely worth living is the _optimal_ world. That is, I am disagreeing with the idea that the best way for a society to use the resources available to it is to create as many lives barely worth living as possible.  Several [commenters](/lw/dso/the_mere_cable_channel_addition_paradox/73ie) have [argued](/lw/dso/the_mere_cable_channel_addition_paradox/73op?context=3) that another interpretation of the Mere Addition Paradox is that a sufficiently large population with a lower quality of life will always be better than a smaller population with a higher quality of life, even if such a society is far from optimal.  I agree that my argument does not necessarily refute this interpretation, but think the other interpretation is common enough that it is worth arguing against.

EDIT: On the [advice of some of the commenters](/r/discussion/lw/dso/the_mere_cable_channel_addition_paradox/73er) I have added a shorter summary of my argument in non-dialogue form at the end.  Since it is shorter I do not think it summarizes my argument as completely as the dialogue, but feel free to read it instead if pressed for time.

**Bob**: Hi, I'm with R&P cable. We're selling premium cable packages to interested customers. We have two packages to start out with that we're sure you love. Package A+ offers a larger selection of basic cable channels and costs $50. Package B offers a larger variety of exotic channels for connoisseurs, it costs $100. If you buy package A+, however, you'll get a 50% discount on B.

**Alice**: That's very nice, but looking at the channel selection, I just don't think that it will provide me with enough utilons.

**Bob**: Utilons? What are those?

**Alice**: They're the unit I use to measure the utility I get from something. I'm really good at shopping, so if I spend my money on the things I usually spend it on I usually get 1.5 utilons for every dollar I spend. Now, looking at your cable channels, I've calculated that I will get 10 utilons from buying Package A+ and 100 utilons from buying Package B. Obviously the total is 110, significantly less than the 150 utilons I'd get from spending $100 on other things. It's just not a good deal for me.

**Bob**: You think so? Well it so happens that I've met people like you in the past and have managed to convince them. Let me tell you about something called the "Mere Cable Channel Addition Paradox."

**Alice**: Alright, I've got time, make your case.

**Bob**: Imagine that the government is going to give you $50. Sounds like a good thing, right?

**Alice**: It depends on where it gets the $50 from. What if it defunds a program I think is important?

**Bob**: Let's say that it would defund a program that you believe is entirely neutral. The harms the program causes are exactly outweighed by the benefits it brings, leaving a net utility of zero.

**Alice**: I can't think of any program like that, but I'll pretend one exists for the sake of the argument. Yes, defunding it and giving me $50 would be a good thing.

**Bob**: Okay, now imagine the program's beneficiaries put up a stink, and demand the program be re-instituted. That would be bad for you, right?

**Alice**: Sure. I'd be out $50 that I could convert into 75 utilons.

**Bob**: Now imagine that the CEO of R&P Cable Company sleeps with an important senator and arranges a deal. You get the $50, but you have to spend it on Package A+. That would be better than not getting the money at all, right?

**Alice**: Sure. 10 utilons is better than zero. But getting to spend the $50 however I wanted would be best of all.

**Bob**: That's not an option in this thought experiment. Now, imagine that after you use the money you received to buy Package A+, you find out that the 50% discount for Package B still applies. You can get it for $50. Good deal, right?

**Alice**: Again, sure. I'd get 100 utilons for $50. Normally I'd only get 75 utilons.

**Bob**: Well, there you have it. By a _mere addition_ I have demonstrated that a world where you have bought both Package A+ and Package B is better than one where you have neither. The only difference between the hypothetical world I imagined and the world we live in is that in one you are spending money on cable channels. A mere addition. Yet you have admitted that that world is better than this one. So what are you waiting for? Sign up for Package A+ and Package B!

And that's not all. I can keep adding cable packages to get the same result. The end result of my logic, which I think you'll agree is impeccable, is that you purchase Package Z, a package where you spend all the money other than that you need for bare subsistence on cable television packages.

**Alice**: That seems like a pretty repugnant conclusion.

**Bob**: It still follows from the logic. For every world where you are spending your money on whatever you have calculated generates the most utilons there exists another, better world where you are spending all your money on premium cable channels.

**Alice**: I think I found a flaw in your logic. You didn't perform a "mere addition." The hypothetical world differs from ours in two ways, not one. Namely, in this world the government isn't giving me $50. So your world doesn't just differ from this one in terms of how many cable packages I've bought, it also differs in how much money I have to buy them.

**Bob**: So can I interest you in a special form of the package? This one is in the form of a legally binding pledge.  You pledge that if you ever make an extra $50 in the future you will use it to buy Package A+.

**Alice**: No. In the scenario you describe the only reason buying Package A+ has any value is that it is impossible to get utility out of that money any other way. If I just get $50 for some reason it's more efficient for me to spend it normally.

**Bob**: Are you sure? I've convinced a lot of people with my logic.

**Alice**: Like who?

**Bob**: Well, there were these two customers named Michael Huemer and Robin Hanson who both accepted my conclusion. They've both mortgaged their homes and started sending as much money to R&P cable as they can.

**Alice**: There must be some others who haven't.

**Bob**: Well, there was this guy named Derek Parfit who seemed disturbed by my conclusion, but couldn't refute it. The best he could do is mutter something about how the best things in his life would gradually be lost if he spent all his money on premium cable. I'm working on him though, I think I'll be able to bring him around eventually.

**Alice**: Funny you should mention Derek Parfit. It so happens that the flaw in your "Mere Cable Channel Addition Paradox" is exactly the same as the flaw in a famous philosophical argument he made, which he called the "Mere Addition Paradox."

**Bob**: Really? Do tell?

**Alice**: Parfit posited a population he called "A" which had a moderately large population with large amounts of resources, giving them a very high level of utility per person. Then he added a second population, which was totally isolated from the other population. How they were isolated wasn't important, although Parfit suggested maybe they were on separate continents and can't sail across the ocean or something like that. These people don't have nearly as many resources per person as the other population, so each person's level of utility is lower (their lack of resources is the only reason they have lower utility). However, their lives are still just barely worth living. He called the two populations "A+."

Parfit asked if "A+" was a better world than "A." He thought it was, since the extra people were totally isolated from the original population they weren't hurting anyone over there by existing. And their lives were worth living. Follow me so far?

**Bob**: I guess I can see the point.

**Alice**: Next Parfit posited a population called "B," which was the same as A+. except that the two populations had merged together. Maybe they got better at sailing across the ocean, it doesn't really matter how. The people share their resources. The result is that everyone in the original population had their utility lowered, while everyone in the second had it raised.

Parfit asked if population "B" was better than "A+" and argued that it was because it had a greater level of equality and total utility.

**Bob**: I think I see where this is going. He's going to keep adding more people, isn't he?

**Alice**: Yep. He kept adding more and more people until he reached population "Z," a vast population where everyone had so few resources that their lives were barely worth living. This, he argued, was a paradox, because he argued that most people would believe that Z is far worse than A, but he had made a convincing argument that it was better.

**Bob**: Are you sure that sharing their resources like that would lower the standard of living for the original population? Wouldn't there be economies of scale and such that would allow them to provide more utility even with less resources per person?

**Alice**: [Please don't fight the hypothetical](/lw/bwp/please_dont_fight_the_hypothetical/). We're assuming that it would for the sake of the argument.

Now, Parfit argued that this argument led to the "Repugnant Conclusion," the idea that the best sort of world is one with a large population with lives barely worth living. That confers on people a duty to reproduce as often as possible, even if doing so would lower the quality of their and everyone else's lives.

He claimed that the reason his argument showed this was that he had conducted "mere addition." The populations in his paradox differed in no way other than their size. By merely adding more people he had made the world "better," even if the level of utility per person plummetted. He claimed that "For every population, A, with a high average level of utility there exists another, better population, B, with more people and a lower average level of utility."

Do you see the flaw in Parfit's argument?

**Bob**: No, and that kind of disturbs me. I have kids, and I agree that creating new people can add utility to the world. But it seems to me that it's also important to enhance the utility of the people who already exist.

**Alice**: That's right. Normal morality tells us that creating new people with lives worth living and enhancing the utility of people that already exist are both good things to use resources on. Our common sense tells us that we should spend resources on both those things. The disturbing thing about the Mere Addition Paradox is that it seems at first glance to indicate that that's not true, that we should only devote resources to creating more people with barely worthwhile lives. I don't agree with that, of course.

**Bob**: Neither do I. It seems to me that having a large number of worthwhile lives and a high average utility are [both good things](/lw/cbn/alan_carter_on_the_complexity_of_value/) and that we should try to increase them both, not just maximize one.

**Alice**: You're right, of course. But don't say "having a [high average utility](/en.wikipedia.org/wiki/Average_and_total_utilitarianism)." Say "use resources to increase the utility of people who already exist."

**Bob**: What's the difference? They're the same thing, aren't they?

**Alice**: Not quite. There are other ways to increase average utility than enhancing the utility of existing people. You could kill all the depressed people, for instance. Plus, if there was a world where everyone was tortured 24 hours a day, you could increase average utility by creating some new people who are only tortured 23 hours a day.

**Bob**: That's insane! Who could possibly be that literal-minded?

**Alice**: You'd be surprised. The point is, a better way to phrase it is "use resources to increase the utility of people who already exist," not "increase average utility."  Of course, that [still leaves some stuff out](http://wiki.lesswrong.com/wiki/Complexity_of_value), like the fact that it's probably better to increase everyone's utility equally, rather than focus on just one person. But it doesn't lead to killing depressed people, or creating slightly less tortured people in a Hellworld.

**Bob**: Okay, so what I'm trying to say is that resources should be used to create people, and to improve people's lives. Also equality is good. And that none of these things should completely eclipse the other, they're each too valuable to maximize just one. So a society that increases all of those values should be considered more efficient at generating value than a society that just maximizes one value. Now that we're done getting our terminology straight, will you tell me what Parfit's mistake was?

**Alice**: Population "A" and population "A+" _differ in two ways, not one_. Think about it. Parfit is clear that the extra people in "A+" do not harm the existing people when they are added. That means they do not use any of the original population's resources. So how do they manage to live lives worth living? _How are they sustaining themselves_?

**Bob**: They must have their own resources. To use Parfit's example of continents separated by an ocean; each continent must have its own set of resources.

**Alice**: Exactly. So "A+" differs from "A" both in the size of its population, and the amount of resources it has access to. Parfit was not "merely adding" people to the population. He was also adding resources.

**Bob**: Aren't you the one who is fighting the hypothetical now?

**Alice**: I'm not fighting the hypothetical. Fighting the hypothetical consists of challenging the likelihood of the thought experiment happening, or trying to take another option than the ones presented. What I'm doing is challenging the logical coherence of the hypothetical. One of Parfit's unspoken premises is that you need _some_ resources to live a life worth living, so by adding more worthwhile lives he's also implicitly adding resources. If he had just added some extra people to population A without giving them their own continent full of extra resources to live on then "A+" would be worse than "A."

**Bob**: So the Mere Addition Paradox doesn't confer on us a positive obligation to have as many children as possible, because the amount of resources we have access to doesn't automatically grow with them. I get that. But doesn't it imply that as soon as we get some more resources we have a duty to add some more people whose lives are barely worth living?

**Alice**: No. Adding lives barely worth living uses the extra resources more efficiently than leaving Parfit's second continent empty for all eternity. But, it's not the most efficient way. Not if you believe that creating new people and enhancing the utility of existing people are _both_ important values.

Let's take population "A+" again. Now imagine that instead of having a population of people with lives barely worth living, the second continent is inhabited by a smaller population with the same very high percentage of resources and utility per person as the population of the first continent. Call it "A++. " Would you say "A++" was better than "A+?"

**Bob**: Sure, definitely.

**Alice**: How about a world where the two continents exist, but the second one was never inhabited? The people of the first continent then discover the second one and use its resources to improve their level of utility.

**Bob**: I'm less sure about that one, but I think it might be better than "A+."

**Alice**: So what Parfit actually proved was: "For every population, A, with a high average level of utility there exists another, better population, B, with more people, _access to more resources_ and a lower average level of utility."

And I can add my own corollary to that: "For every population, B, there exists another, better population, C, that has the _same access to resources_ as B, but a _smaller population and higher average utility._"

**Bob**: Okay, I get it. But how does this relate to my cable TV sales pitch?

**Alice**: Well, my current situation, where I'm spending my money on normal things is analogous to Parfit's population "A." High utility, and very efficient conversion of resources into utility, but not as many resources. We're assuming, of course, that using resources to both create new people and improve the utility of existing people is more morally efficient than doing just one or the other.

The situation where the government gives me $50 to spend on Package A+ is analogous to Parfit's population A+. I have more resources and more utility. But the resources aren't being converted as efficiently as they could be.

The situation where I take the 50% discount and buy Package B is equivalent to Parfit's population B. It's a better situation than A+, but not the most efficient way to use the money.

The situation where I get the $50 from the government to spend on whatever I want is equivalent to _my_ population C. A world with more access to resources than A, but more efficient conversion of resources to utility than A+ or B.

**Bob**: So what would a world where the government kept the money be analogous to?

**Alice**: A world where Parfit's second continent was never settled and remained uninhabited for all eternity, its resources never used by anyone.

**Bob**: I get it. So the Mere Addition Paradox doesn't prove what Parfit thought it did? We don't have any moral obligation to tile the universe with people whose lives are barely worth living?

**Alice**: Nope, we don't. It's more morally efficient to use a large percentage of our resources to enhance the lives of those who already exist.

**Bob**: This sure has been a fun conversation. Would you like to buy a cable package from me? We have some great deals.

**Alice**: NO!

SUMMARY:

My argument is that Parfit’s [Mere Addition Paradox](http://en.wikipedia.org/wiki/Mere_addition_paradox) doesn’t prove what it seems to. The argument behind the Mere Addition Paradox is that you can make the world a better place by the “mere addition” of extra people, even if their lives are barely worth living. In other words : "For every population, A, with a high average level of utility there exists another, better population, B, with more people and a lower average level of utility." This supposedly leads to the Repugnant Conclusion, the belief that a world full of people whose lives are barely worth living is better than a world with a smaller population where the people lead extremely fulfilled and happy lives.

Parfit demonstrates this by moving from world A, consisting of a population full of people with lots of resources and high average utility, and moving to world A+. World A+ has an addition population of people who are isolated from the original population and not even aware of the other’s existence. The extra people live lives just barely worth living. Parfit argues that A+ is a better world than A because everyone in it has lives worth living, and the additional people aren’t hurting anyone by existing because they are isolated from the original population.

Parfit them moves from World A+ to World B, where the populations are merged and share resources. This lowers the standard of living for the original people and raises it for the newer people. Parfit argues that B must be better than A+, because it has higher total utility and equality. He then keeps adding people until he reaches Z, a world where everyones’ lives are barely worth living and the population is vast. He argues that this is a paradox because most people would agree that Z is not a desirable world compared to A.

I argue that the Mere Addition Paradox is a flawed argument because it does not just add people, it also adds resources. The fact that the extra people in A+ do not harm the original people of A by existing indicates that their population must have a decent amount of resources to live on, even if it is not as many per person as the population of A. For this reason what the Mere Addition Paradox proves is not that you can make the world better by adding extra people, but rather that you can make it better by adding extra people and _resources to support them_. I use a series of choices about purchasing cable television packages to illustrate this in concrete terms.

I further argue for a theory of population ethics that values both using resources to create lives worth living, and using resources to enhance the utility of already existing people, and considers the best sort of world to be one where neither of these two values totally dominate the other. By this ethical standard A+ might be better than A because it has more people and resources, even if the average level of utility is lower. However, a world with the same amount of resources as A+, but a lower population and the same, or higher average utility as A is better than A+.

The main unsatisfying thing about my argument is that while it avoids the Repugnant Conclusion in most cases, it might still lead to it, or something close to it, in situations where creating new people and getting new resources are, as [one commenter noted](/r/discussion/lw/dso/the_mere_cable_channel_addition_paradox/73dz), a “package deal.” In other words, a situation where it is impossible to obtain new resources without creating some new people whose utility levels are below average. However, even in this case, my argument holds that the best world of all is one where it would be possible to obtain the resources without creating new people, or creating a smaller amount of people with higher utility.

In other words, the Mere Addition Paradox does not prove that: "For every population, A, with a high average level of utility there exists another, better population, B, with more people and a lower average level of utility." Instead what the Mere Addition Paradox seems to demonstrate is that: "For every population, A, with a high average level of utility there exists another, better population, B, with more people, _access to more resources_ and a lower average level of utility." Furthermore, my own argument demonstrates that: "For every population, B, there exists another, better population, C, which has the _same access to resources_ as B, but a _smaller population and higher average utility._"