"Let me give a more concrete example."

Ah, I understand now. Certainly then there is ambiguity that needs to be sorted out. I'd like to say again that this is not something the original theory was designed to handle. Everything I've been saying in these comments is off the cuff rather than premeditated - it's not surprising that there are flaws in the fixes I've suggested. It's certainly not surprising that the ad hoc fixes don't solve every conceivable problem. And again, it would appear to me that there are plenty of plausible solutions. I guess really that I just need to spend some time evaluating which would be best and then tidy it up in a new post.

"No, they wouldn't, because the people in (B) are different to the people in (C). You can assert that you treat them the same, but you can't assert that they are the same. The (B) scenario with different people and the (B) scenario with the same people are both distinct, possible, outcomes, and your theory needs to handle them both. It can give the same answer to both, that's fine, but part of the set up of my hypothetical scenario is that the people are different."

Then yes, as I did say in the rather lengthy explanation I gave:

"The route of disappearing 1000 people and replacing them with 1000 new people is one of the worse routes."

If you insist that we must get rid of 1000 people and replace them with 1000 different people, then sure, (B) is worse than (C). So now I will remind myself what your objection regarding this was in an earlier comment.

I'll try explaining again briefly. With this theory, don't think of the (B),(C) etc. as populations but rather as "distributions" the status quo population could take. Thus, as I said:

"(B) is a hypothetical which may be achieved by any route. Whether the resulting people of (B)  in the hypothetical are real or imaginary depends on which route you take."

When a population is not the status quo, it is simply representing a population distribution that you can get to. Whichever population is not the status quo is considered in an abstract, hypothetical sense.

Now you wish to specifically consider the case where (with status quo (C)), everyone in (B) is specified to be different to the people in (C). I stress that this is not the usual sense in which comparisons are made in the theory; it is much more specific. Again, if one insists on this, then since we have to disappear 1000 people to get to (B), (B) is worse.

Your issue with this is that: "the people in (B) would not want to move to (C), and vice versa, because that would mean they no longer exist. But your theory now gives a strong recommendation for one over the other anyway."

Now I hope the explanation is fully clear. The distribution of (B) is preferable to people in (C) (i.e. with (C) as the status quo), but if you insist that the only routes to (C) involve getting rid of most of the population and replacing them with 1000 non-identical people, then this is not preferable. When (A) is the status quo, yes, we have a strong preference for (B) over (C) because we don't have to lose 1000 people, and I don't see the problem with considering people with equal welfare who (in the status quo of (A)) are imaginary or "effectively real" as identical. In line with a person-affecting outlook, I give more priority to real people than imaginary or effectively real people -- I only respect the non-identity of real people. And just to add, viewing people as effectively real is not to say that they are really real (since they don't exist yet, even if they are mathematically expected to); it's only been a way to balance the books for forced decisions.

The outcome is still, as far as I can see, consistent with transitivity and my already-avowed rejection of an objective ordering.

"You can assert that you consider the 1000 people in (B) and (C) to be identical, for the purposes of applying your theory. That does avoid the non-identity problem in this case. But the fact is that they are not the same people. They have different hopes, dreams, personalities, memories, genders, etc."

But you stated that they don't exist yet (that they are "created"). Thus, we have no empirical knowledge of their hopes and dreams, so the most sensible prior seems to be that they are all identical. I apologise if I am coming across as obtuse, but I really do not see how non-identity causes issues here. 

"The people in (B) would not want to move to (C), and vice versa, because that would mean they no longer exist."

Sorry, but this is quite incorrect. The people in (C) would want to move to (B). Bear in mind that when we are evaluating this decision, we now set (C) as the status quo. So the 1000 people at welfare $\epsilon$ are considered to be wholly real. If you stipulate that in going to (B), these 1000 people are to be eradicated then replaced with (imaginary) people at high welfare, then naturally the people of (C) should say no.

However, if you instead take the more reasonable route of getting from (C) to (B) via raising the real welfare of the 1000 and slightly reducing the welfare of one person, then clearly (B) is better than (C).

I think I realise what the issue may be here. When I say "going from (C) to (B)" or similar, I do not mean that (C),(B) are existent populations and (C) is suddenly becoming (B). That way, we certainly do run into issues of non-identity. Rather, (C) is a status quo and (B) is a hypothetical which may be achieved by any route. Whether the resulting people of (B)  in the hypothetical are real or imaginary depends on which route you take. Naturally, the best routes involve eradicating as few real people as possible. In this instance, we can get from (C) to (B) without getting rid of anyone. The route of disappearing 1000 people and replacing them with 1000 new people is one of the worse routes. And in the original post, in one of the examples, to get from one population to the other, it was necessary to get rid of real people, with only imaginary gain. Hence, there could not exist  an acceptable route to the second population  -- one better than remaining at the status quo.

I appreciate now that this may have been unclear. However, I did not fully explain this because the idea of one existent population "becoming" (indeed, how?) another existent population is surely impossible and therefore not worth consideration.

"There are also technical problems with how you'd actually apply this logic to more complicated situations where the number of future people differs. Suppose that 1000 extra people are created in (B), but 2000 extra people are created in (C), with varying levels of welfare. How do you apply your theory then? You now need 1000 of the 2000 people in (C) to be considered 'effectively real', to continue avoiding non-identity problem like conclusions, but which 1000? How do you pick? Different choices of the way you decide to pick will give you very different answers, and again your theory is becoming more impersonal, and losing more of its initial intuitive appeal."

I would say exactly the same for this. If these people are being freshly created, then I don't see the harm in treating them as identical. If a person decided not to have a child with their partner today, but rather tomorrow, then indeed, they will almost certainly produce a different child. But the hypothetical child of today is not exactly going to complain if they were never created. That is the reasoning guiding my thought, on the intuitive level.

And given that this calculus works solely by considering welfare, naturally, it is reductive, as is every utilitarian calculus which only considers welfare. Isn't the very idea of reducing people to their welfare impersonal?

"0.1% chance of (A), 99.9% chance of (B)

0.1000001% chance of (A), 99.9% chance of (C)."

Well, it would seem to me this is perfect for an application of the concept of expectation. Taking the expected value, then in both cases ~999 people become effectively real and the same conclusion is reached.

If the odds in the second scenario were 50-50, then the expected value is that 500 people are effectively real (since 999 are expected in the first scenario, 500 in the second scenario and we have to pick one; we take the minimum). Then, the evaluation changes. Of course, this implies there is a critical point where if the chance of (C) in the second option is sufficiently low, then both options are equally good, from the perspective of (A).

The natural question then, which I also ask myself, is what if there were hundreds of scenarios, and in at least one scenario there were no people created. Then, supposedly no one is effectively real. But actually, I'm not sure this is a problem. More thinking will be required here to see whether I am right or wrong.

I do very much appreciate your criticism. Equally, it is quite striking to me that whenever you have pointed out an error, it has immediately seemed clear to me what the solution would be. Certainly, this discussion has been very productive in that way and rounded out this model a bit more. I expect I will write it all up, hopefully with some further improvements, in another post some time in the future.

Sorry, I misread (B) and (C). You are correct that, as written in the post, (C) would  then be the better choice.

However, continuing with what I meant to imply when I realised this was a forced decision, we can note that whichever of (B),(C) is picked, 1000 people will come into existence with certainty. Thus, in this case, I would argue they are effectively real. This is contrasted with the case in which the decision is not forced -- then, there are no 1000 new people necessarily coming into existence, and as you correctly interpreted, the status quo is preferable (since the status quo (A) is actually an option this time).

Regarding non-identity, I would consider these 1000 new people in either (B),(C) to be identical. I am not entirely sure how non-identity is an issue here.

I am still not quite sure what you mean by uncertainty, but I feel that the above patches up (or more accurately, correctly generalises) the model at least with regards to the example you gave.  I'll try to think of counterexamples myself.

By the way, this would also be my answer to Parfit's "depletion" problem, which I briefly glanced over. There is no way to stop hundreds of millions of people continuing to come into existence without dramatically reducing welfare (a few nuclear blasts might stop population growth but at quite a cost to welfare). Thus, these people are effectively real. Hence, if the current generation depleted everything, this would necessarily cause a massive loss of welfare to a population which may not exist yet, but are nevertheless effectively real. So we shouldn't do that. (That doesn't rule out a 'slower depletion', but I think that's fine.)

"From your reply it sounds like you're coming up with a different answer when comparing (B) to (C), because both ways round the 1000 people are always considered imaginary, as they don't literally exist in the status quo? Is that right?"

If the status quo is A, then with my methodology, you cannot compare B and C directly, and I don't think this is a problem. As I said previously, "... in particular, if you are a member of A, it's not relevant that the population of Z disagree which is better". Similarly, I don't think it's necessary that the people of A can compare B and C directly. The issue is that some of your comparisons do not have (A) as the status quo.

To fully clarify, if you are a member of X (or equivalently, X is your status quo), then you can only consider comparisons between X and other populations. You might find that B is better than X and C is not better than X. Even then, you could not objectively say B is better than C because you are working from your subjective viewpoint as a member of X. In my methodology, there is no "objective ordering" (which is what I perhaps inaccurately was referring to as a total ordering).

Thus, 

"(A) is not better than (B) or (C) because to change (B) or (C) to (A) would cause 1000 people to disappear (which is a lot of negative real welfare)."

is true if you take the status quos to be (B),(C) respectively - but this is not our status quo. (Similarly for the third bullet point.)

"Neither (B) nor (C) are better than (A), because an instantaneous change from (A) to (B) or (C) would reduce real welfare (of the one already existing person)."

This is true from our viewpoint as a member of A. Hence, if we are forced to go from A to one of B or C, then it's always a bad thing. We minimise our loss of welfare according to the methodology and pick B, the 'least worst' option.

"Or are you saying that your theory tells us not to transform ourselves to world Z? Because we should only ever do anything that will make things actually better?"

Yes - and the previous description you gave is not what I intended.

"If so, how would your approach handle uncertainty? What probability of a world Z should we be willing to risk in order to improve a small amount of real welfare?"

This is a reasonable question, but I do not think this is a major issue so I will not necessarily answer it now.

"And there's another way in which your approach still contains some form of the repugnant conclusion. If a population stopped dealing in hypotheticals and actually started taking actions, so that these imaginary people became real, then you could imagine a population going through all the steps of the repugnant conclusion argument process, thinking they were making improvements on the status quo each time, and finding themselves ultimately ending up at Z. In fact it can happen in just two steps, if the population of B is made large enough, with small enough welfare."

This is true, and I noticed this myself. However, actually, this comes from the assumption that more net imaginary welfare is always a good thing, which was one of the "WLOG" assumptions I made not needed for the refutation of the Repugnant Conclusion. If we instead take an averaging or more egalitarian approach with imaginary welfare, I think the problem doesn't have to appear. 

For instance, suppose we now stipulate that any decision (given the constraints on real welfare) that has average welfare for the imaginary population at least equal to the average of the real population is better than any decision without this property, then the problem is gone. (Remark: we still do need the real/imaginary divide here to avoid the Repugnant Conclusion.)

This may seem rather ad hoc, and it is, but it could be framed as, "A priority is that the average welfare of future populations is at least as good as it is now", which seems reasonable.

[Edit: actually, I think this doesn't entirely work in that if you are forced to pick between two populations, as in your other example, you may get the same scenario as you describe. 

Edit 2: Equally, if you are "forced" to make a decision, then perhaps those some of those people should be considered as real in a sense since people are definitely coming into existence, one way or another. I think it's definitely important to note that the idea was designed to work for unforced decisions so I reckon it's likely that assuming "forced populations" are imaginary is not the correct generalisation.]

As I say, I had noticed this particular issue myself (when I first wrote this post, in fact). I don't deny that the construction, in its current state, is flawed. However, to me, these flaws seem generally less severe and more tractable  (Would you disagree? Just curious.) - and so, I haven't spent much time thinking about them. 

(Even the "Axiom of Comparison", which I say is the most important part of the construction, may not be exactly the right approach. But I believe it's on the right lines.)

I'm afraid I don't understand this. In my framework, future people are imaginary, whether they are expected to come into existence with the status quo or not. Thus, they only contribute (negative) real welfare if they are brought into the world with negative welfare. I don't see why this would be true for almost all decisions, let alone most. It seems to me that the non-identity problem is completely independent of this. Either way, I am treating all future, or more generally imaginary, people as identical.

"That means every decision you could take will reduce real welfare, and so under this approach no decision can be be better than any other, which seems like a problem!"

As I say, I believe the premise to be false (I may have of course misunderstood), but nevertheless, in this case, you would take the decision that minimises the loss of real welfare and maximises imaginary welfare (I'll assume the infima and suprema are part of the decision space, since this isn't analysis). Then, such a decision is better than every other. I don't understand why the premise would lead to no decision being better than any other.

Hi, Toby. One of the core arguments here, which perhaps I didn't fully  illuminate, is that (I believe that) the "better than" operation is fundamentally unsuitable for population ethics.

If you are a member of A, then Z is not better than A. So Z is worse than A but only if you are a member of A. If you are a member of Z, you will find that A is not better than Z. So, sure, A is worse than Z  but only if you are a member of Z.  In other words, my population ethics depends on the population.

In particular, if you are a member of A, it's not relevant that the population of Z disagree which is better. Indeed, why would you care? The fallacy that every argument re: Repugnant Conclusion commits is assuming that we require a total ordering of populations' goodness. This is a complete red herring. We don't. Doesn't it suffice to know what is best for your particular population? Isn't that the purpose of population ethics? I argue that the Repugnant Conclusion is merely the result of an unjustified fixation on a meaningless mathematical ideal (total ordering).

I said something similar in my reply to Max Daniel's comment; I am not sure if I phrased it better here or there. If this idea was not clear in the post (or even in this reply), I would appreciate any feedback on how to make it more apparent.

I'll give my immediate thoughts.

I agree that the theory experiences significant flaws akin to those of negative utilitarianism. However, something else that perhaps I understated is that the fleshed-out theory was only one example to demonstrate how the Axiom of Comparison could be deployed.  With the axiom in hand, I imagine that better theories could be developed which avoid your compelling example with Bezos (and the Repugnant Conclusion). I would point out that most of the flaws you point out are not results of the axiom itself.

In fact, off the top of my head. If I now said that real people gaining welfare above 0 still counts as real welfare, I think that the Repugnant Conclusion and Bezos are avoided.

I am not sure why the "it is too implausible" defence is not convincing. The Repugnant Conclusion is not implausible to me - one can imagine that, if we accepted it, we might direct the development of civilisation from A to Z. Isn't it much more unlikely that we possess an ability to do exactly one of <improve the welfare of many happy people>  and <improve the welfare of one unhappy person a bit>?

"It also has various other problems that plague lexical and negative-utilitarian theories, such as involving arguably theoretically unfounded discontinuities that lead to counterintuitive results, and being prima facie inconsistent with happiness/suffering and gains/losses tradeoffs we routinely make in our own lives."

I would request some clarification on the above.

"Also, one at least prima facie flaw that you don't discuss at all is that your theory involves incomparability – i.e. there are populations $A$ and $B$ such that neither is better than the other."

I did derive a pair of such populations A,B. If you meant that I did not discuss this further, then I am not sure why it is a problem at all. Suppose that we are population A. Do we truly need a way to assign a welfare score to our population? Isn't our primary (and I'd suggest only) consideration how we might improve? For this latter goal, the theory does produce any comparisons you could ask for.

Edit: I have read through the reasoning again and now it seems to me that the negative utilitarian aspect can indeed be removed (solving Bezos) and without reinstating the Repugnant Conclusion. Naturally, I may be wrong and this may also lead to new flaws. I would be interested to hear your thoughts on this. (The main post has been edited to reflect all new thoughts.)