But it might still prove that we should agree to make more people and more resources if it’s a package deal.
It does, but by definition.
Let X and Y be populations. Each population has a number of people and an amount of resources. Resources are distributed evenly, so the average utility of a population and each individual’s utility is given by: resources over people. We will say the “standard of living”, the level at which a life is ‘barely worth living’, is a utility of 1. And we will say that Z is when the utility is below the standard of living. These are our definitions.
For numbers, let’s say X and Y start out with 100 people and 500 resources, giving each a utility of 5. This is good! In X, we will perform the false method: simply adding people. In one step, we go to 105 people (utility 4.7, still good), then 110 (utility 4.5) and in 80 steps we will have reached our repugnant Z, with 505 people and 500 resources giving us a utility of 0.99. Now in Y, we will perform the strengthened method: absorb a small population with bare minimum living standards, thus bringing everyone down slightly. In one step, we got to 105 people and 505 resources (4.8 utility, still good) then 110 and 510 (4.6, still good) and then Z arrives ….
No, it doesn’t. Utility in Y will asymptotically approach 1 from above and we will never reach Z. Thus, the repugnant conclusion is dead.
You may argue that “just barely above the absolute bare minimum” is not worth living, but you won’t get very far: previously, we defined any life above the minimum standard as worth living. So if you say that, instead, 2 utility is the minimum worth living for, Y will asymptotically approach 2. And you can hardly argue that “just above 2″ isn’t worth living for, because you just said before that 2 is the minimum! So yes, the repugnant conclusion is truly dead.
(An analogy for this population Y is colonising new planets: the older planets will be affluent, but the frontier new colonies will be hardscrabble and just barely worth it. But this is not a repugnant conclusion! This is like Firefly, and that would be badass!)
Or you may argue that comparing our original Y to a Y++ after many steps, it’s obvious that Y is better. But this won’t get you far either, because in what way is Y better than Y++? If you tell me this comparison beforehand, I will no longer desire to add people when it would reverse that comparison, and if you don’t tell me, well, that’s unfair—it’s no surprise that optimising for one criterion might abandon other criteria, especially ones it didn’t know about.
Footnote: I tried this:
b = 500 a = 100 while (b / a) > 1 b += 5 a += 5 end
and it didn’t terminate, thus the student became enlightened.
I dislike this post. I don’t mean this to be a personal attack and I don’t want to come off as hostile, but I do want to make my objections known. I am choosing to state my reasons in lieu of downvoting.
First, “It does, but by definition.” is clearly false, otherwise you wouldn’t spend 6 paragraphs explaining it. This is something of a pet peeve of mine from grading homework, but whatever, it’s not important.
More importantly, its not really addressing the problems being discussed here. The discussion is whether 100 people at 500 resources is better than your asymptotically-worthless massive population, which is something that you don’t mention at all. Instead, you argue that if we have N+400 resources and N people and each person needs 1 resource to barely survive, then everyone survives when resources are evenly distributed, no matter what N you pick. Okay, but the conclusion is somehow “the repugnant conclusion is dead”? To be honest, I thought you were trying to argue in favor of the repugnant conclusion, at least in the specialized case of a universe that offers you N resources for every additional N people. But the only conclusion I see you really reaching is that a lot of people at a better-than-dead state is better than a world where there aren’t people—this doesn’t strike me as very exciting.
It seems fairly clear to me that one way in which Y is better than Y+ is that Y has greater average utility.
That said, I think most of my dislike for this post is caused by the tone and manner of expression. It was fairly disorganized and overly long. The tone was demeaning and combative: assuming the reader will disagree with basic premises and the use of phrases like “thus the student became enlightened”. Note how the top-level post gives the opposing voice to a fictional character rather than forcing it upon the reader—this is a much friendlier approach.
Lastly, can you tell me where you bought your Halting Machine? I wouldn’t mind one for myself… ;)
It seems fairly clear to me that one way in which Y is better than Y+ is that Y has greater average utility.
Yeah, on reflection the post is very unclear. I agree with the quoted sentiment, but the point I should have made was that we get to Y+ by a process that reduces average utility (redistributing resources evenly), so it doesn’t seem surprising or confusing that Y has greater average utility.
It does, but by definition.
Let X and Y be populations. Each population has a number of people and an amount of resources. Resources are distributed evenly, so the average utility of a population and each individual’s utility is given by: resources over people. We will say the “standard of living”, the level at which a life is ‘barely worth living’, is a utility of 1. And we will say that Z is when the utility is below the standard of living. These are our definitions.
For numbers, let’s say X and Y start out with 100 people and 500 resources, giving each a utility of 5. This is good!
In X, we will perform the false method: simply adding people. In one step, we go to 105 people (utility 4.7, still good), then 110 (utility 4.5) and in 80 steps we will have reached our repugnant Z, with 505 people and 500 resources giving us a utility of 0.99.
Now in Y, we will perform the strengthened method: absorb a small population with bare minimum living standards, thus bringing everyone down slightly. In one step, we got to 105 people and 505 resources (4.8 utility, still good) then 110 and 510 (4.6, still good) and then Z arrives ….
No, it doesn’t. Utility in Y will asymptotically approach 1 from above and we will never reach Z. Thus, the repugnant conclusion is dead.
You may argue that “just barely above the absolute bare minimum” is not worth living, but you won’t get very far: previously, we defined any life above the minimum standard as worth living. So if you say that, instead, 2 utility is the minimum worth living for, Y will asymptotically approach 2. And you can hardly argue that “just above 2″ isn’t worth living for, because you just said before that 2 is the minimum! So yes, the repugnant conclusion is truly dead.
(An analogy for this population Y is colonising new planets: the older planets will be affluent, but the frontier new colonies will be hardscrabble and just barely worth it. But this is not a repugnant conclusion! This is like Firefly, and that would be badass!)
Or you may argue that comparing our original Y to a Y++ after many steps, it’s obvious that Y is better. But this won’t get you far either, because in what way is Y better than Y++? If you tell me this comparison beforehand, I will no longer desire to add people when it would reverse that comparison, and if you don’t tell me, well, that’s unfair—it’s no surprise that optimising for one criterion might abandon other criteria, especially ones it didn’t know about.
Footnote:
I tried this:
and it didn’t terminate, thus the student became enlightened.
I used almost this exact line in a discussion with my girlfriend about a week ago (talking about Everything Matters!.
I dislike this post. I don’t mean this to be a personal attack and I don’t want to come off as hostile, but I do want to make my objections known. I am choosing to state my reasons in lieu of downvoting.
First, “It does, but by definition.” is clearly false, otherwise you wouldn’t spend 6 paragraphs explaining it. This is something of a pet peeve of mine from grading homework, but whatever, it’s not important.
More importantly, its not really addressing the problems being discussed here. The discussion is whether 100 people at 500 resources is better than your asymptotically-worthless massive population, which is something that you don’t mention at all. Instead, you argue that if we have N+400 resources and N people and each person needs 1 resource to barely survive, then everyone survives when resources are evenly distributed, no matter what N you pick. Okay, but the conclusion is somehow “the repugnant conclusion is dead”? To be honest, I thought you were trying to argue in favor of the repugnant conclusion, at least in the specialized case of a universe that offers you N resources for every additional N people. But the only conclusion I see you really reaching is that a lot of people at a better-than-dead state is better than a world where there aren’t people—this doesn’t strike me as very exciting.
It seems fairly clear to me that one way in which Y is better than Y+ is that Y has greater average utility.
That said, I think most of my dislike for this post is caused by the tone and manner of expression. It was fairly disorganized and overly long. The tone was demeaning and combative: assuming the reader will disagree with basic premises and the use of phrases like “thus the student became enlightened”. Note how the top-level post gives the opposing voice to a fictional character rather than forcing it upon the reader—this is a much friendlier approach.
Lastly, can you tell me where you bought your Halting Machine? I wouldn’t mind one for myself… ;)
Yeah, on reflection the post is very unclear. I agree with the quoted sentiment, but the point I should have made was that we get to Y+ by a process that reduces average utility (redistributing resources evenly), so it doesn’t seem surprising or confusing that Y has greater average utility.