The birth penalty fixes a lot of unintuitive products of the classic total uti. For example, if you treat every "new" person as catching up to the penalty (which can only be achieved if you at least live with minimal acceptable happiness for your entire life, aka h0), then killing a person and replacing him with someone of equal happiness is bad. Cause the penalty that was not yet caught up with in the killed person remains as a negative quantity in the total utility, a debt, if you will. In total uti, this doesn't apply and it logically follows that there's nothing wrong with killing a person and replacing him with a new person of equal happiness, which is unintuitive.

"I'm also very unsure about the assertion that "happy to exist" and "prefer not to die now" is an important difference [...]" - this is important because there are people that feel they are not happy with existence, and would rather to not have been born at all, but don't want to die now that they do in fact exist. If you don't have this difference you can't capture that intuition. I'm not sure how the N unhappy years argument is relevant to this or how it renders the difference moot. In particular:

" "prefer to continue to live from this point" is equal to "happy to come into existence at this point" "

is in fact false, for a significant amount of people.

Can you give a narrative summary of this theory?

I did not create this theory from a particular narrative, I just looked for a mathematical model that fits certain special cases, which is a fine method in my book. But, if you wish, we can probably think of the $-u_0$ term as an extra penalty for death and the age-dependent term as "being tired of life".

I'm having trouble understanding what those constants actually mean WRT ethical decisions about creating and terminating lives, and especially in comparing lives (when is it better to destroy one life in order to create two different ones, and/or when is it better to reduce h for some time in a life in order to increase h in another (or to bring another into existence).

I'm not sure I understand the question. For any case you can do the math and see what the model says. I already gave some examples in which you can see what the constants do.

...Why isn't that already included in h(t)?

Like I said in the text, the age-dependent penalty can be included in h(t) if you wish. Then we get a model in which there is no age-dependent penalty but there is still the death penalty (no pun intended). Looking from this angle, we get a repugnant conclusion with many very long-lived people who only barely prefer life to death. But, the separation of "effective happiness" into "quality of life" and "age-dependent penalty" paints a new picture of what such people look like. The reason they only barely prefer life to death is not because they are suffering so much. It is because they lived for very long and are sort of very sated with life.

At any point in time, "prefer to continue to live from this point" is equal to "happy to come into existence at this point", right?

No. Many people have the opposite intuition, especially people whose life is actually bad.

I'm not sure that $h_0$ should be interpreted as "ordinary happiness", at least that's not how I described it. Regarding ${\tau }_0$, human preferences are the product of evolution plus maybe to some extent culture. So, it should not be surprising if some of the parameters come either from the ancestral environment in which evolution happened or from the "memetically ancestral" environment in which the culture evolved. And, I am talking about a model of (modern?) human preferences, not about some kind of objective morality (which doesn't exist).

Excellent question! I think that my actual preferences are some combination of selfish and altruistic (and the same is probably true of most people), and DNT only tries to capture the altruistic part. It is therefore interesting to try writing down a model of how selfish utility aggregates with altruistic utility. A simple "agnostic" formula such as a linear combination with fixed coefficients works poorly, because for any given coefficients it's easy to come up with a hypothetical where it's either way too selfish or way too altruistic.

I think that it's more reasonable to model this aggregation as bargaining between two imaginary agents: a selfish agent that only values you and people close to you, and an altruistic agent with impartial (DNT-ish) preferences. This bargaining can work, for example, according to the Kalai-Smorodinksy solution, with the disagreement point being "purely selfish optimization with probability $p$ and purely altruistic optimization with probability $1-p$", where $p$ is a parameter reflecting your personal level of altruism. Of course, the result of bargaining can be expressed as a single "effective" utility function, which is just a linear combination between the two, but the coefficients depend on the prior and strategy space.

It's interesting to speculate about the relation between this model and multiagent models of the mind [? · GW].

Something of the same nature should apply when a group of people act cooperatively. In this case we can imagine bargaining between an agent that only cares about this group and an impartial agent. Even if the group includes all living people, the two agents will be different since the second assigns value to animals and future people as well.

Of course time discounting can make things look different, but I see no moral justification to discount based on time.

Actually I think time discount is justified and necessary. Without time discount, you get a divergent integral over time and utility is undefined. Another question is, what kind of time discount exactly. One possibility I find alluring is using the minimax-regret decision rule for exponential time discount with a half-life that is allowed to vary between something of the order of ${\tau }_0$ to $\infty$.

If I'm running a simulation of a bunch of happy humans, it's entirely possible for me to completely avoid your penalty term just by turning the simulation off and on again every so often to reset all of the penalty terms.

No. First of all, if each new instance is considered a new person then the result of turning off and back on would be negative because of the $-u_0$ term. Assuming $u_0\ge h_0{\tau }_0$ (like I suggest in the text) means the loss from $-u_0$ is always greater than the gain from avoiding the age-dependent penalty.

Second, like I said in the text, I'm talking about an approximate model, not the One True Formula of morality. This model has limited scope, and so far I haven't included any treatment of personal identity shenanigans in it. However, now that you got me thinking about it, one way to extend it that seems attractive is:

• Consider the $-u_0$ term as associated with the death of a person. There can be partial death which gives a partial penalty if the person is not entirely lost. If the person is of age $\tau$ at the time of death, and ey have a surviving clone that split off when the person was of age ${\tau }_1$, then it only counts as $\frac{\tau -{\tau }_1}{\tau }$ of a death so the penalty is only $-\frac{\tau -{\tau }_1}{\tau }{u}_0$. If the person dies but is resurrected in the future, then we can think of death as producing a $-u_0$ penalty and resurrection as producing a $+u_0$ reward. This is important if we have time discount and there is a large time difference. Imperfect resurrection will produce only a partial resurrection reward. You cannot fully resurrect the same person twice, but a good resurrection following a bad resurrection awards you the difference. No sequence of resurrections can sum to more than 1, and a finite sequence will sum to strictly less than 1 unless at least one of them is perfect. Having amnesia can be counted as dying with a living clone or as dying fully with a simultaneous partial resurrection, which amounts to the same.

• Consider the age-dependent penalty as referring to the subjective age of a person. If you clone a person, the age counter of each continues from the same point. This is consistent with interpreting it as a relation between "true happiness" and "quality of life".

I think that this extension avoids the repugnant conclusion as well as the original, but it would be nice to have a formal proof of this.

The penalty doesn't reset when you create a new human. You are left with the negative value that the killed human left behind, and the new one starts off with a fresh amount of -u0[new person] to compensate for. If the original human would have been left alive, he would have compensated for his own, original -u0[original person], and the entire system would have produced a higher value.

To the contrary- turning the simulation on adds up all the -u_0 terms for all of the moral patients in the simulation, meaning that the first tick of the simulation is hugely negative.

I don't share the opinion that numbers are moral patients within a context where they are visible as numbers, because I don't think it's supererogatory or required to run DFEDIT and set every dwarf's happiness value to MAXINT, and in any context where "I" am visible to an entity running a simulation of me as a number or analogous concept, changing the value which corresponds with what "I" "call" "my happiness" within that simulation is not a thing that can be understood in any context that I have access to.

I think another good way to look at u0 that compliments yours is to look at it as the "penalty for dying with many preferences left unsatisfied."  Pretty much everyone dies with some things that they wanted to do left undone.  I think most people have a strong moral intuition that being unable to fulfill major life desires and projects is tragic, and think a major reason death is bad is that it makes us unable to do even more of what we want to do with our lives. I think we could have u0 represent that intuition.

If we go back to Peter Singer's original formulation of this topic, we can think of unsatisfied preferences as "debts" that are unpaid.  So if we have a choice between creating two people who live x years, or 1 person who lives 2x years, assuming their total lifetime happiness is otherwise the same, we should prefer the one person for 2x years. This is because the two people living x years generate the same amount of happiness, but twice the amount of "debt" from unfulfilled preferences.  Everyone will die with some unfulfilled preferences because everyone will always want more, and that's fine and part of being human [LW · GW].

Obviously we need to calibrate this idea delicately in order to avoid any counterintuitive conclusions.  If we treat creating a preference as  a "debt" and satisfying it as merely "paying the debt" to "break even" then we get anti-natalism. We need to treat the "debt" that creating a preference generates as an "investment" that can "pay off" by creating tremendous happiness/life satisfaction when it is satisfied, but occasionally fails to "pay off" if its satisfaction is thwarted by death or something else. 

I think that this approach could also address Isnasene's question below of figuring out the -u0 penatly for nonhuman animals.  Drawing from Singer again, since nonhuman animals are not mentally capable of having complex preferences for the future, they generate a smaller u0 penalty. The preferences that they die without having satisfied are not as strong or complex.  This fits nicely with the human intuition that animals are more "replaceable" than humans and are of lesser (although nonzero) moral value. It also fits the intuition that animals with more advanced, human-like minds are of greater moral value. 

Using that approach for animals also underscores the importance of treating creating preferences as an "investment" that can "pay off."  Otherwise it generates the counterintuitive conclusion that we should often favor creating animals over humans, since they have a lower u0 penalty.  Treating complex preference creation as an "investment" means that humans are capable of generating far greater happiness/satisfaction than animals, which more than outweighs our greater u0 penalty.

We would also need some sort of way to avoid incentivizing the creation of intelligent creatures with weird preferences that are extremely easy to satisfy, or a strong preference for living a short life as an end in itself. This is a problem pretty much all forms of utilitarianism suffer from.  I'm comfortable with just adding some kind of hack massively penalizing the creation of creatures with preferences that do not somehow fit with some broad human idea of eudaimonia. 

I took a crack at figuring it out here. [LW(p) · GW(p)]

I basically take a similar approach to you. I give animals a smaller -u0 penalty if they are less self-aware and less capable of forming the sort of complex eudaimonic preferences that human beings can. I also treat complex eudaimonic preferences as generating greater moral value when satisfied in order to avoid incentivizing creating animals over creating humans.

h(t) already accounts for boredom and 'tired of life' effects.

See my reply to Dagon [LW(p) · GW(p)].

Note that 'dying sucks' is already included in h(t), because h(dying) is expected to be very negative.

If really you want, you can reinterpret $-u_0$ as some negative spike in $h\left(t\right)$ at the time of death, that occurs even if the person died instantly without any awareness of death. I think that maybe my use of the word "happiness" was confusing due to the nebulous nature of this concept and instead I should have talked about something like "quality of life" or "quality of experience" (still nebulous but a little less so, maybe).

There is no protection against utility monsters, people who have h(t) so high that their existence and increasing their h dominates every other consideration. If that is patched to cap the amount of utility that any one individual can have, there is no protection against utility monster colonies, such that each member of the colony has maximum h(t) and the colony is so numerous that its collective utility dominates every other consideration.

I only intended to address particular issues, not give a full theory of ethics (something that is completely infeasible anyway). I think $h$ is already bounded (ofc we cannot verify this without having a definition of $h$ in terms of something else, which is entirely out of scope here). Regarding the "utility monster colony" I don't see it as a problem at all. It's just saying "the concerns of a large population dominate the concerns of a small population" which is fine and standard in utilitarianism. The words "utility monster" are not doing any work here.

A better utilitarianism model might include a weight factor for 'how much' of a moral patient an entity is.

I agree something like this should be the case, like I said I had no intention to address everything.

Specifically, while in the preferred world the huge population is glad to have been born, you're still left with a horribly suffering population.

This conclusion seems absolutely fine to me. The above-$h_0$ population has positive value that is greater than the negative value of the horribly suffering population. If someone's intuition is against that, I suppose it's a situation similar to torture vs. dust specks [LW · GW]: failure to accept that a very bad thing can be compensated by a lot of small good things. I know that, purely selfishly, I would prefer a small improvement with high probability over something terrible with sufficiently tiny probability. Scaling that to a population, we go from probabilities to quantities.

With fixed, limited energy, killing-and-replacing-by-an-equivalent is already going to be a slight negative: you've wasted energy to accomplish an otherwise morally neutral act. It's not clear to me that it needs to be more negative than that (maybe).

I strongly disagree (it is not morally neutral at all) but now sure how to convince you if you don't already have this intuition.

Sure