Crossposted on LessWrong.

We introduce a first evaluation of the Civ-Saturation Hypothesis (CSH): Most resources will be claimed by Space-Faring Civilizations (SFCs) regardless of whether humanity creates an SFC^[1]. This hypothesis, if significantly true, could have macrostrategic impacts for the longtermist community, as hinted in a previous post. In the literature, we find that as long as we assume some form of EDT (e.g., CDT + controlling exact copies), the Civ-Saturation Hypothesis is 84% or more representative of reality (best guess estimate, 64% using a conservative estimate). These estimates point towards thinking that the Civ-Saturation Hypothesis could indeed be relevant for impartial longtermist EDT believers. We then introduce additional reasons about whether these estimates are underestimating or overestimating the Civ-Saturation of our reachable universe. 

In future posts, we will introduce which macrostrategic updates may be warranted by these results. For now, you can think of the CSH being 84% representative of reality as equivalent to saying that 84% of humanity's SFC resources would be grabbed by other SFCs if humanity's SFC did not come to exist.

How much this information should impact the priority of Extinction-Risks reduction depends on the value produced by other SFCs relative to the value humanity's SFC would produce. In another post, we list some preliminary reasons why we may expect these values to be similar, what we call the Civ-Similarity Hypothesis^[2], and whose starting point is the Mediocrity Principle. 

Sequence: This post is part 5 of a sequence investigating the longtermist implications of alien Space-Faring Civilizations. Each post aims to be standalone. You can find an introduction to the sequence in the following post.

Summary

Through an analysis using both conservative (Finnveden 2019) and best-guess estimates (Cook 2022)^[3], we evaluate the Civ-Saturation Hypothesis^[1] given four sets of beliefs (called ADT implementations^[4]) which guide how to aggregate possible worlds by their Decision Relevance. We focus on two of them: CDT, and the most conservative EDT version (~ CDT + controlling exact copies). Our evaluations aggregate possible worlds using descendant resource-weighting rather than count-weighting, producing more accurate and more conservative estimates of Civ-Saturation (i.e. lower estimates). 

We find that the Civ-Saturation Hypothesis appears mostly incorrect under pure CDT assumptions (thus excluding controlling exact copies), but that it is significantly representative of reality when accounting for evidential correlations^[5]: 64% given a conservative estimate, and 84% or higher given our best guess estimate. This suggests that a majority of humanity's potential SFC resources would be recovered by other SFCs if humanity's SFC did not come to exist.

Additionally, we know a reason why these estimates may slightly or severely understate the reality: Earth may still later create an SFC even if humanity goes extinct without creating one. We list a few other reasons supporting the conservative nature of the conclusion and its robustness (e.g., the conclusion would be even stronger if we had used more uncertain estimates). We list a last argument, the decay of resources, as reducing the validity of our estimates and pushing for lower Civ-Saturation. 

We finally explain technically how to evaluate the correctness of the CSH and how to compute the Marginal Civ-Saturation metrics ($MC{S}_h$, $MC{S}_c$, and $MC{S}_w$), which measure how many marginal resources would be grabbed in different contexts, with $MC{S}_h$ being particularly relevant for making decisions as it measures the marginal resources brought by humanity's SFC existence relative to its potential. 

A first evaluation of the Civ-Saturation Hypothesis

Summarizing necessary concepts

If you are not interested in how the analysis is done, you may want to skip this section and directly look at the results in the next section.

This section summarizes the concepts necessary to technically understand our analysis of the correctness of the Civ-Saturation Hypothesis. 

SFC density estimates. In Space-Faring Civilization density estimates and models - Review, we reviewed existing estimates of Space-Faring Civilization (SFC) density in the universe and concluded that, among available estimates, the most conservative estimate was produced by Finnveden 2019, and our best guess estimate was produced by Cook 2022^[6].

Civ-Saturation metrics. In Formalizing Civ-Saturation Concepts and Metrics, we operationalized what we mean by the Civ-Saturation of a world and illustrated this concept using a simplistic simultaneous appearance displacement model. We created three metrics: the $MC{S}_h$^[7], the $MC{S}_c$^[8], and the $MC{S}_w$^[9]. These metrics express how many marginal resources will be grabbed in different contexts. $MC{S}_h$  is the metric to use to guide our decisions. In the same document, we showed that we can approximate $MC{S}_h$ by the fraction of humanity's SFC resources that would be lost if it did not exist. And that we can approximate the correctness of the Civ-Saturation Hypothesis (CSH) by the fraction of humanity's SFC resources that would NOT be lost if it did not exist.

Weighing possible worlds using different ADT implementations. In Decision-Relevance of worlds and ADT implementations, we described what we mean by ADT implementations and explored the space of possible implementations. Each ADT implementation is linked to a method used to measure the Decision-Relevance Potential (DRP) of possible worlds (a formalized version of the Decision-Worthiness in Cook 2022), which is related to the world-variant-only part of the marginal utility calculation used to make decisions. We described four especially relevant ADT implementations linked to four sets of beliefs we find appealing.

• ADT(no copies, descendant resource-weighted)
  • This ADT implementation is the one we should assume if, for example, we are longtermists and purely CDT believers (and thus we completely ignore the impact of our exact copies).
• ADT(exact copies, descendant resource-weighted)
  • This ADT implementation matches our beliefs if we think most of our impact is evidential and comes from our correlation with our exact copies. In this case, we believe that evidential correlations are “extremely weak” and thus limited to exact copies, but still dominate our evidential impact.
• ADT(approximate copies^[10], descendant resource-weighted)
  • This ADT implementation matches our beliefs if we think we are also significantly correlated with our approximate copies. We define approximate copies as being as similar as possible to us while relaxing the observation that humanity appeared at a specific time. In this case, we believe evidential correlations are “weak” but dominate through approximate copies.
• ADT(Space-Faring Civilization Shapers^[11], descendant resource-weighted)
  • This ADT implementation matches our beliefs if we think we are significantly correlated with all SFC Shapers (e.g., through learning about selection mechanisms reducing the impact-weighted distribution of intelligent agents shaping SFCs). In this case, we believe that evidential correlations are “strong”. SFC Shapers are defined as the smallest group of agents within an Intelligent Civilization that control most of the impact of this civilization on the SFC they could create.

These four ADT implementations perform some anthropic weighting between worlds. They rely on proxies to compute the Decision-Relevance Potential, which uses resource-weighting, contrary to popular anthropic updates, SSA and SIA, whose equivalences, in terms of ADT implementations, use count-weighting. Using resource-weighting, in addition to better approximating the marginal utility brought by each possible world, will also lead us to produce more conservative estimates about how representative of reality the Civ-Saturation Hypothesis (CSH) is.

Evaluations in the literature

Summary

Let’s start by summarizing the final results extracted from the literature. As introduced in the previous section, the correctness of the CSH depends on which beliefs you hold and which ADT implementation you should use to aggregate possible worlds. In the following table, we display the available information for eight ADT implementations {Count-weighted, Resource-weighted} x {No copies, Exact copies, Approximate copies, SFC Shapers}. 

Interpreting these numbers

• When we say that the Civ-Saturating Hypothesis (CSH) is Y% representative of reality, this means that, in expectation over decision-relevance-weighted worlds, other SFCs could reach Y% of the expected resources of humanity's SFC if it does not exist. Informally: Y% of our potential future resources would not be lost if we don't create an SFC.

You can find hints to macrostrategic implications in a previous post. We will develop this later, but for now, we can read our current results as:

• If we think our impact is dominated by our direct impact (e.g., CDT or no evidential correlation), then the CSH is mostly incorrect and can likely be ignored.
• If we think our impact is dominated by our correlation with other agents (e.g., EDT and evidential correlation with our perfect copies), then CHS is likely 84% representative of reality (64% or more with our conservative estimate). This means that humanity's SFC resources would be 84% (or more) recovered by other SFCs if humanity's SFC did not come to exist. Conditional on other SFCs producing similar Expected Utility (EU) than humanity's SFC, this result could further imply that increasing P(humanity creates an SFC), for example, by reducing nuclear or bioweapon X-risks, is 84% (or more) less important than increasing P(alignment^[12] | humanity creates an SFC). We will study this last condition when evaluating the Civ-Similarity Hypothesis^[13] in later posts.

See the appendix for details about these estimates. In the appendix, you can find a more exhaustive table and explanations about how these numbers are extracted from the existing literature of results.

Additional arguments

We may be currently severely underestimating Civ-Saturation around Earth. Our estimates of Civ-Saturation may potentially need to be strongly updated upwards because we are, in our current estimates, ignoring the fact that we don't know if humanity going extinct before creating an SFC would always cause all complex life on Earth to go extinct, and thus if it would remove the potential for Earth to later create SFCs. Earth still has an estimated one to two billion years of remaining habitable time^{[14][15][16][17]}, and thus if the first Intelligent Civilization (IC) from Earth goes extinct without creating an SFC, it does not automatically mean that Earth would NOT generate an SFC later. If life has, as is plausible, a general trend towards higher evolvability^[18][19] and higher intelligence^[20][21][22], then the resources lost by humanity's extinction would only be caused from the delay between the failed creation of an SFC by humanity and the successful creation by one of the subsequent ICs. How long this delay would be is uncertain, as well as its impact. However, there is a chance that this argument alone could make us update strongly towards a more Civ-Saturated universe. Notably, this update may also be significant when our universe is empty of other planets from which SFCs could emerge, as well as when assuming CDT only.

Using more uncertain estimates produces higher Civ-Saturation. In short, the Civ-Saturation Hypothesis is robust to increasing uncertainty. Let's explain why. You may think: "The distribution estimates of the density of Space-Faring Civilizations we are using are overconfident, we should use wider, more uncertain distributions". However, one interesting property of the hypothesis we study is that using more uncertain estimates makes the hypothesis even more likely to be correct. This is true as long as the uncertainty we add to our distribution estimates is fairly distributed over a large interval which includes the density of one SFC per reachable universe. One way to make the Civ-Saturation Hypothesis incorrect is by lowering our uncertainty and learning that there are almost no chances for the universe to be saturated. The second way to make the hypothesis incorrect is to argue that EDT should not be used, or that we are not correlated with any agents in our world.

Being uncertain between CDT and EDT may lead to the same conclusion. The conclusion presented in this post (84+% of the resources would not be lost) assumes using the weakest version of EDT, something like "CDT + we control our exact copies". EDT and CDT are pretty similarly defined^[23]. One way to compare CDT with EDT is that CDT equals EDT while ignoring the information we gain about the causally disconnected states of the world, such as information we gain about past states of the world, or about the actions of correlated agents. Thanks to the similarity between CDT and EDT, even when we are uncertain between which of these theories to use, we may (not fully rigorously) want to aggregate the marginal impact we have under both decision theories to make a choice given our uncertainty between both. When computing our expected impact over these decision theories, we will end up ignoring CDT entirely as long as we think the number of agents correlated with us is much larger than one, which may be the case in an infinite or almost infinite universe^[24][25].

Civ-Saturation is likely higher since we are likely correlated with SFC Shapers, not only with our perfect copies. We know many laws governing human behaviors and shaping moral values. The simple existence of these laws may be enough to make our correlation with SFC Shapers dominate our marginal utility calculations and thus the actions we should take. Our decisions may be dominated by our impact on SFC Shapers given that their number is likely astronomically larger than the number of our exact copies. There is thus a wager on being correlated with SFC Shapers. Let's now assume this correlation dominates our marginal utility calculations, then as illustrated in the figure "Decision-Relevance Potential vs Potential SFC Density for different ADT implementations" found later in this post, high saturation worlds would be more Decision-Relevant than in the current estimate focusing on our correlation with exact copies only. This would cause the Civ-Saturation Hypothesis to plausibly be more than 84% correct.

Accounting for the decay of resources may reduce our current estimates. The current estimates of Civ-Saturation may need to be updated downward if resources decay significantly over time. If humanity does not create an SFC and our potential resources are instead grabbed by other SFCs at a later point in time, these resources will have more time to decay and be lost. To know the strength of this effect, we would need to know (a) how fast resources decay and (b) how much delay there would be between humanity's SFC grabbing resources and another SFC potentially reaching the same resources. We quickly discuss these questions in a footnote^[26]. 

Understanding the process behind these numbers

In this section, we formalize how one would compute the correctness of the CSH. To do that, one would need access to the appearance and propagation models also used to compute the SFC density estimates. This section will give more detail to the people curious to check how the evaluation can be done. We won’t actually run computations.

Computing the correctness over possible worlds

In Formalizing Civ-Saturation Concepts and Metrics, when formulating civ-saturation we assumed a single possible world. However, we are uncertain about which world we are in, and thus, we need to modify how we compute humanity's Marginal Civ-Saturation ($MC{S}_h$) to be able to evaluate the Civ-Saturation Hypothesis (CSH). We keep using total utilitarianism, methodology of ADT, and weight worlds using a Decision-Relevance proxy (DR) given by each of the four ADT implementations presented at the start of the post. Since our goal is to evaluate the CSH, we only track how the SFC Density (D) impacts the DR of worlds. We ignore how other parameters impact our estimates. Formally, in a single world, we had the following. Given $CS\left(D\right)$ the Civ-Saturation, $MC{S}_h\left(D\right)$ humanity's Marginal Civ-Saturation, $R_h\left(D\right)$ the resources grabbed by humanity's SFC in worlds of SFC density D, and $D=D_{\neg h}+D_h$:

$MC{S}_h(D_{\neg h}+D_h)=\frac{1}{R_{\text{h}}}\cdot \frac{\delta R_{\text{h}}(D_{\neg h}+D_h)}{\delta D_h}$ 

$CSHEvaluation=1-|MC{S}_h\left(D\right)|$

Given uncertainty between possible worlds, we now need to weigh worlds by their Decision-Relevance. After aggregating worlds, we will get what we call Anthropically Weighted Expected (AWE) values. Given $P\left(D\right)$ the likelihood of being in a world with SFC density D, $DRP\left(D\right)$ the Decision-Relevance Potential used to weigh groups of possible worlds with SFC density D, we have:

$AWEDR={\int }_{D=0}^{D=+\infty }P\left(D\right)DRP\left(D\right)dD$

$AWEMC{S}_h=\frac{1}{AWEDR}{\int }_{D=0}^{D=+\infty }P\left(D\right)DRP\left(D\right)MC{S}_h\left(D\right)dD$

$CSHEvaluation=1-|AWEMC{S}_h|$

By using this aggregation method, we weight each possible world by their Decision-Relevance. $MC{S}_h$ is unitless and is a metric describing each world in a normalized manner such that aggregating it between worlds will fairly represent each world. Notably the importance of each world, e.g. how much resource we impact in each, is already accounted in the DRP function, such that it is correct to not include it in the $MC{S}_h$ metric.

To compute these evaluations, we need the values of three functions, all varying over groups of possible words with SFC density $D$.

• $P\left(D\right)$, the likelihood distribution over $D$
• $DRP\left(D\right)$, the Decision-Relevance Potential over $D$
• $MC{S}_h\left(D\right)$, humanity's Marginal Civ-Saturation over $D$

As a reminder, the Decision-Relevance (DR) of a world is the multiplication of its likelihood and its DR Potential.

In the following sections, we will present the estimates used to produce the results above, given these four sets of beliefs.

Likelihood distribution over SFC Density

In Space-Faring Civilization density estimates and models - Review, we reviewed existing potential SFC density estimates and concluded that the most conservative yet informed estimate was produced by Finnveden 2019, and that our best guess was Cook 2022. Here are these two distributions, extracted using pixel positions, and converted into the same unit:

Decision-Relevance Potential over SFC Density

We chose to look at four ADT implementations. We describe and then plot below the trends of their respective Decision-Relevance Potential when changing the density of potential SFCs^[27].

Illustration of trends

Description of trends

• ADT(no copies, descendant resource-weighted) - This ADT implementation ignores the impact of our exact copies (e.g., when assuming CDT) or assumes they don’t exist^[28]. The worlds in which our descendants grab the most resources are those in which our SFC is alone. When the density of SFC reaches around one per reachable universe, then the Decision-Relevance Potential of these worlds starts decreasing somewhat linearly with the density.
• ADT(exact copies, descendant resource-weighted) - When accounting for our exact copies, at low densities we expect their number to be proportional to the density of SFCs since we don't have reasons to think their frequency among SFCs would change in function of the density of SFCs. But above the density of one this changes. We know that our exact copies don’t observe alien SFCs. Because of that we should expect our frequency among ICs to decrease when increasing the density of SFCs. In the end, for densities increasing above one the share that our exact copies grab will decrease because of the Fermi Observation.
• ADT(approximate copies, descendant resource-weighted): The amount of resources grabbed by the descendants of our approximate copies increases until all the resources in the world are grabbed. After that point, it stays constant. This assumes the frequency of our approximate copies among Intelligent Civilization stays constant when the density of SFC varies. This is fulfilled by the definition of approximate copies, which specify that they are our copies with just enough relaxation to allow them to have their appearance time randomly sampled, thus removing the update on the Fermi Observation.
• ADT(Space-Faring Civilization Shapers, descendant resource-weighted) - The trend for this ADT implementation is similar to that of the previous one. The amount of resources grabbed by all SFC increases until all resources are grabbed, around a density of one. After that, the amount of resources grabbed is constant.

$MC{S}_h$ over SFC Density

The value of this component depends upon the physical models of SFC appearance and SFC propagation. We won’t describe here the models used by Finnveden 2019 and Cook 2022, nor will we replicate them. You can find a review of existing models and summaries of those used in this two pieces of work in Space-Faring Civilization density estimates and models - Review. You can also find some methods to approximate this value in the appendix of Formalizing Civ-Saturation concepts and metrics.

Context

Evaluating the Existence Neutrality Hypothesis - Introductory Series. This post is part of a series introducing a research project for which I am seeking funding: Evaluating the Existence Neutrality Hypothesis. This project includes evaluating both the Civ-Saturation^[29] and the Civ-Similarity Hypotheses^[2] and their longtermist macrostrategic implications. This introductory series hints at preliminary research results and looks at the tractability of making further progress in evaluating these hypotheses.

Next steps: Evaluating the tractability of the project. In the following two posts, we will introduce content related to the tractability of evaluating the Civ-Similarity Hypothesis^[2]: The Expected Utility efficiency of humanity's future SFC is similar to that of other SFCs. 

Acknowledgements

Thanks to Tristan Cook, and Justis Mills for their excellent feedback on this post and ideas. Note that this research was done under my personal name and that this content is not meant to represent any organization's stance. 

Appendix: 

Full table of results

Extracting results from the literature

In Finnveden 2019 (relevant section), they produce a (conservative) likelihood distribution over SFC densities using a try-once steps appearance model and a greedy propagation model. They then update this likelihood distribution using SIA, equivalent to ADT(exact copies, count-weighted), and later multiply by the fraction of the reachable Universe that one of our exact copy gets. In the end, this is equivalent to using ADT(exact copies, descendant resource-weighted). They then give us an estimate of how much humanity gets from a reachable universe centre on one of our copies (5%) and of how much of that would be lost if we didn’t exist (36%). The second number equals the $MC{S}_h$ aggregated over worlds using ADT(exact copies, resource-weighted), we thus report it in the table, as well as 64% = 100%-36% for the correctness of the CSH. The multiplication of both numbers (5%*36%~1.8%) is maybe equals to the $MC{S}_w$ and this number is a lower bound to the value $MC{S}_h$ could take. For ADT(no copies, count-weighted), we use the distribution before the SIA update and approximate $MC{S}_w$ by the probability  $P(D<3)$ (see more information in a previous post).

In Cook 2022, simulations are built using a sequence of time-dependent steps as appearance model in conjunction to a greedy propagation model. These simulations are used to estimate SFC appearance and propagation dynamics. Anthropic updates are applied, and in particular, their ADT+Total Utilitarian update matches ADT(exact copies, descendant resource-weighted) (first relevant section, and second relevant section). Here are the most relevant results from this work:

The X axis of the bottom plots is equal to the $MC{S}_h$. The Y axis (of all plots), while named “cumulative probability” is actually the “cumulative decision-worthiness” defined in Cook’s post, which is equivalent to our Decision-Relevance we defined in Decision-Relevance of worlds and ADT implementations. The left plot updates on the Fermi-Observation (observable universe-wide, with information traveling at the speed of light $c$) while the right plot updates on observing the absence of aliens on Earth (information and aliens traveling at a speed $v$ lower than $c$). We will use the most conservative update, the Fermi-Observation. From eyeballing the bottom left plot, we can see that the expected $MC{S}_h$ is around 0.18. By using pixel areas to produce the same estimate, I arrive at $MC{S}_h\approx 0.16$, thus CSH would be 84% representative of reality. We keep this last estimate and follow the same process with the graphs for ADT(exact copies, count-weighted), AKA SIA, we get 90% in that case (eyeballing).

Finally, from the top left plot, we can get an estimate of the cumulative Decision-Relevance in Non-Saturated Worlds (SFC Density below 3 as defined in Formalizing Civ-Saturation Concepts and Metrics, and below ~60 after converting into density per observable universe instead of reachable universe). This gives us a good approximation for the cumulative Decision-Relevance of worlds in which (any kind of) MCS is very low: 6% (eyeballing). This approximates the $MC{S}_w$ and is a lower bound for the $MC{S}_h$. We produce a similar estimate with ADT(exact copies, count-weighted) and ADT(no copies, count-weighted) for which we get 0.1% and 50% (eyeballing).