In case anyone is interested, Rob Wiblin will be interviewing Tarsney on the 80,000 Hours podcast next week. Rob is accepting question suggestions on Facebook (I think you can submit questions to Rob on Twitter or by email too).

tl;dr: Tarsney seems to me to understate the likelihood that accounting for non-human animals would substantially affect the case for longtermism.

Tarsney includes a helpful appendix listing the simplifications made in his model/paper, and the rationales for these simplifications. Here's a passage from that:

Simplification: The model ignores effects on the welfare of beings other than Homo sapiens and our “descendants”. 

Rationale: (1) The sign and magnitude of the effects of paradigmatic longtermist interventions on the welfare of non-human animals (or their far-future counterparts) are very unclear. (2) Dropping this simplification seems unlikely to change our quantitative results by more than 1–2 orders of magnitude (though this is far from obvious), and so unlikely to affect our qualitative conclusions.

I appreciate Tarsney's caveat that "this is far from obvious", and, given that caveat, I don't strongly disagree with this sentence. But it seems quite plausible to me[1] that considering those effects would strengthen or weaken the case for paradigmatic longtermist interventions by more than 1-2 orders of magnitude, or even that it would flip the sign of the expected value of those interventions. 

Relatedly, I also think that considering those effects should plausibly change which longtermist interventions we support (not just whether we support them vs non-longtermist interventions).

(I'm not sure how likely I see these things as, so maybe I actually agree with Tarsney that this "seems unlikely [but with that being far from obvious]".)

See also Non-Humans and the Long-Term Future.

[1] We could operationalise "it seems quite plausible to me that X" as something like "there's at least a 20% chance that I would think X if I spent another 100 hours of thinking about the topic".

tl;dr: Tarsney writes "resources committed at earlier time should have greater impact, all else being equal". I think that this is misleading and an oversimplification. See Crucial questions about optimal timing of work and donations and other posts tagged Timing of Philanthropy. 

(But that claim was not necessary for any of Tarsney's arguments; he just gave it as one reason why the actual case for longtermism might be stronger than his deliberately conservative estimates suggest.)

Context and explanation:

A core part of Tarsney's model is - roughly speaking - the amount by which spending $1 million on mitigating existential risks changes the probability of being in the target state at a given time, relative to the probability that would occur if the short-termist intervention was used. This parameter is represented by p. The target state means something like "The accessible region of the Universe contains an intelligent civilization”.

Tarsney makes:

a lower-bound estimate [of p] based on the details of our working example, that is almost certainly far too pessimistic, but nevertheless informative.

The estimate proceeds in two stages: First, how much could humanity as a whole change the probability of [the target state at a particular time]
(i.e., roughly, the probability that we survive the next thousand years), relative to the status quo, if we committed all our collective time and resources solely to this objective for the next thousand years? “One percent” seems like a very safe lower bound here (remembering that we are dealing with epistemic probabilities rather than objective chances). Now, if we assume that each unit of time and resources makes the same marginal contribution to increasing the probability of [the target state at that time], we can calculate p simply by computing the fraction of humanity’s resources over the next thousand years that can be bought for 1 million, and multiplying it by 0.01. This yields p [roughly equal to 10 to the power of negative 14].

Tarsney writes that "This is an extremely conservative lower bound", and that "I think it would be justifiable to adjust p upward from this lower-bound estimate by a several-order-of-magnitude “fudge factor”, if we were so inclined" (though he doesn't do this for his paper). He gives two reasons for this. 

The first has to do with diminishing marginal returns and the fact that we'll by default spend far less than all our collective time and resources over the next 1000 years to reducing existential risk. Thus, spending an extra $1 million on the current margin will probably achieve far more than one would expect by "simply by computing the fraction of humanity’s resources over the next thousand years that can be bought for 1 million". This argument makes sense to me, and I do think it suggests Tarsney's estimate for p is a very conservative one (as he intends).

But then he writes:

Second, resources committed at [an] earlier time should have greater impact, all else being equal. (If nothing else, this is true because resources that might be committed to existential risk mitigation, say, 500 years from now can do nothing to prevent any of the existential catastrophes that might occur in the next 500 years, while resources committed today are potentially impactful any time in the next thousand years.)

It's definitely true that there are many reasons why resources committed at an earlier time could have a greater impact. And the reason Tarsney raises is a valid one; we could describe this as discounting for the possibility that the later use of resources would be "too late". This is an extreme example of how we might miss "windows of opportunity" if we wait too long.

But there are also many reasons why resources committed at a later time could have a greater impact. This is especially true if we don't count resources as committed to a problem when they're used in an investment-like way in order to generate more resources that can be committed later, but it's even true if we do count resources as already committed to a problem when they're "merely invested". 

In particular, it's possible that "leverage over the future" (or hingyness, pivotality, etc.) will increase in future. This could occur if:

• We know more in future about what we should do
• Longtermist priorities become more neglected in future
• Windows of opportunity that aren't currently open become open in future
  • E.g., there could be a future point at which important global governance institutions are being set up or policy frameworks for a currently unforeseen technology are being set

(For explanation and discussion of the above points, see here.) 

Of course, the opposite effects could also occur. My point is merely that "resources committed at [an] earlier time should have greater impact, all else being equal" seems to be either false or misleading.

(I think it'd be reasonable for Tarsney to merely claim that his all-things-considered view is that resources committed at an earlier time will in practice probably have a greater impact. But this more uncertain stance would then weaken the case for a several-order-of-magnitude upwards adjustment of p.)

A final quick thing that came to mind: I think that Ord's concept of existential security could be represented in Tarsney's models as the value of r  asymptotically decreasing towards 0 over time. I'd be interested to hear people's thoughts on whether that seems accurate and, if so:

• how accounting for various likelihoods of existential security could affect Tarsney's models conclusions
• how considering Tarsney's models could affect Ord's conclusions

(I haven't tried to think this through myself yet.)

I think it'd be interesting to run a sensitivity analysis on Tarsney's model(s), and to think about the value of information we'd get from further investigation of: 

• how likely the future is to resemble Tarsney's cubic growth model vs his steady model
• whether there are other models that are substantially likely, whether the model structures should be changed
• what the most reasonable distribution for each parameter is. 

It seems like the value of information from that might be very high, at least if we think we don't want to accept fanaticism. This is because Tarsney's paper suggests reasonable empirical views could either support the case for longtermism without requiring fanaticism or only support the case for longtermism if we accept fanaticism. So further research on these models, alternative models, and these parameters could perhaps give us a much better sense of how robust the case for longtermism is.

To some extent, this comment can be boiled down to something that was obvious already: "The case for longtermism seems plausible but uncertain, and whether it's true seems very decision-relevant, so maybe investigating whether it's true would be really valuable." But I think Tarsney's paper highlights specific points to look into, and that it would allow for (rough) quantitative estimates of the value of information to be gained by investigating each point. 

For a quick and non-quantitative example, it seems that the probability of interstellar settlement has a very large bearing on the results of the model, and it also seems like we should be quite uncertain about that probability.

Some caveats to that:

• I'm not sure how tractable these investigations would be.
  • But note that it could be useful just to become somewhat less uncertain than we currently are, even if we still remain quite uncertainty.
• Tarsney's models focus on a particular working example of a longtermist intervention/priority (increasing the chance that there's an intelligent civilization at any given time point). As discussed in other comments here, how good the success of that intervention would be depends on other things not modelled by Tarsney (essentially, what that civilization does with the accessible universe), and there are many other interventions/priorities we might focus on. 
  • So ideally we'd run the sensitivity analysis and value of information calculations on either a more general version of the models or on a set of models that collectively represent various major possible priorities.
• Tarsney's models make various ethical and decision-theoretic assumptions that are conducive to longtermism. An ideal version of the sensitivity analysis and value of information calculations might also allow for investigation of what happens if these assumptions are relaxed. 
  • But that might become unwieldy. 

Thanks for posting this! Your linkpost actually got me to watch the talk for the first time, even though I was aware of this paper for a while.

I think some variant of the cubic growth model could be useful for figuring out whether trying to reduce x-risk is better than trying to make durable changes to the long-term "trajectory" of the social welfare curve. I spent some time a few months ago trying to address this by modeling the trajectory of humanity, so I appreciate this paper for proposing even a simpler toy model.

I have rough thoughts about how the utility from economic growth could be incorporated: Assume that each star system has a growth rate $g$ that the residents of that star system can influence (e.g. through policy). The economy of each star system tends to grow exponentially, but GDP per capita has logarithmic utility, so the utility of the star system $u_s\left(t\right)$ grows roughly linearly.

If the economy of each star system starts at a steady state, then grows exponentially at $g$ starting at time $t_0$, the time at which humanity arrives at the star system, we get $u_s\left(t\right)=u_0+max(0,g(t-t_0\left)\right)$. If the star system's GDP is capped at $\exp \left(u_{max}\right)$, then we get $u_s\left(t\right)=u_0+min(max(0,g(t-t_0)),u_{max})$.

To incorporate economic growth into the trajectory model used in the paper, we can replace $n(s\cdot (t-t_{\ell }\left)\right)$ with the cross-correlation of $u_s\left(t\right)$ and $n(s\cdot (t-t_{\ell }\left)\right)$ (this assumes that all star systems have the same growth rate). Since $u_s\left(t\right)$ is piecewise linear and $n(s\cdot (t-t_{\ell }\left)\right)$ is cubic, the cross-correlation is piecewise quintic (it's the integral of a cubic function times a linear function). My gut tells me that having a piecewise quintic term in the trajectory function instead of a cubic term isn't going to change much about the implications of the model.

Note: I realize that by using GDP per capita, I'm leaving out the population of each star system. This would result in multiplying $u_s\left(t\right)$ by a function that models the population over time, starting at time $t_0$.