This is a short follow up to my post on the optimal timing of spending on AGI safety work which, given exact values for the future real interest, diminishing returns and other factors, calculated the optimal spending schedule for AI risk interventions.

This has also been added to the post’s appendix and assumes some familiarity with the post.

Here I consider the most robust spending policies and supposes uncertainty over nearly all parameters in the model^[1] Inputs that are not considered include: historic spending on research and influence, rather than finding the optimal solutions based on point estimates and again find that the community’s current spending rate on AI risk interventions is too low. 

My distributions over the the model parameters imply that

• Of all fixed spending schedules (i.e. to spend X% of your capital per year^[2]), the best strategy is to spend 4-6% per year.
• Of all simple spending schedules that consider two regimes: now until 2030, 2030 onwards, the best strategy is  to spend ~8% per year until 2030, and ~6% afterwards.

I recommend entering your own distributions for the parameters in the Python notebook here^[3]. Further, these preliminary results use few samples: more reliable results would be obtained with more samples (and more computing time).

I allow for post-fire-alarm spending (i.e., we are certain AGI is soon and so can spend some fraction of our capital). Without this feature, the optimal schedules would likely recommend a greater spending rate.

Caption: Fixed spending rate. See here for the distributions of utility for each spending rate.

Caption: Simple  - two regime -  spending rate

Caption: The results from a simple optimiser^[4], when allowing for four spending regimes: 2022-2027, 2027-2032, 2032-2037 and 2037 onwards. This result should not be taken too seriously: more samples should be used, the optimiser runs for a greater number of steps and more intervals used. As with other results, this is contingent on the distributions of parameters.

Some notes

• The system of equations - describing how a funder’s spending on AI risk interventions change the probability of AGI going well - are unchanged from the main model in the post.
• This version of the model randomly generates the real interest, based on user inputs. So, for example, one’s capital can go down.

Caption: An example real interest function $r\left(t\right)$, cherry picked to show how our capital can go down significantly. See here for 100 unbiased samples of $r\left(t\right)$.

Caption: Example probability-of-success functions. The filled circle indicates the current preparedness and probability of success.

Caption: Example competition functions. They all pass through (2022, 1) since the competition function is the relative cost of one unit of influence compared to the current cost. 

This short extension started due to a conversation with David Field and comment from Vasco Grilo; I’m grateful to both for the suggestion.
 

1. ^{^}

    Inputs that are not considered include: historic spending on research and influence, the rate at which the real interest rate changes, the post-fire alarm returns are considered to be the same as the pre-fire alarm returns.

2. ^{^}

   And supposing a 50:50 split between spending on research and influence

3. ^{^}

    This notebook is  less user-friendly than the notebook used in the main optimal spending result (though not un user friendly)  - let me know if improvements to the notebook would be useful for you.

^{^}

The intermediate steps of the optimiser are here.

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My recommendations for small donors

I think there are benefits to thinking about where to give (fun, having engagement with the community, skill building, fuzzies)^[1] but I think that most people shouldn’t think too much about it and - if they are deciding where to give - should do one of the following.

1 Give to the donor lottery

I primarily recommend giving through a donor lottery and then only thinking about where to give in the case you win. There are existing arguments for the donor lottery.

2 Deliberately funge with funders you trust

Alternatively I would recommend deliberately ‘funging’ with other funders (e.g. Open Philanthropy), such as through GiveWell’s Top Charities Fund.

However, if you have empirical or value disagreements with the large funder you funge with or believe they are mistaken, you may be able to do better by doing your own research.^[2] 

3 If you work at an ‘effective’^[3] organisation, take a salary cut

Finally, if you work at an organisation whose mission you believe effective, or is funded by a large funder (see previous point on funging), consider taking a salary cut^[4].

I don’t recommend

(a) Saving now to give later

I would say to just give to the donor lottery and if you win: first, spend some time thinking and decide whether you want to give later. If you conclude yes, give to something like the Patient Philanthropy Fund, set-up some new mechanism for giving later or (as you always can) enter/create a new donor lottery.

(b) Thinking too long about it - unless it's rewarding for you

Where rewarding could be any of: fun, interesting, good for the community, gives fuzzies, builds skills or something else. There’s no obligation at all in working out your own cost effectiveness estimates of charities and choosing the best.

(c) Thinking too much about funging, counterfactuals or Shapley values

My guess is that if everyone does the ‘obvious’ strategy of “donate to the things that look most cost effective^[5]” and you’re broadly on board with the values^[6], empirical beliefs^[7] and donation mindset^[8] of the other donors in the community^[9], it’s not worth considering how counterfactual your donation was or who you’ve funged with.

Thanks to Tom Barnes for comments.

1. ^{^}

   Consider the goal factoring the activity of “doing research about where to give this year”. It’s possible there are distinct tasks that achieve your goals better (e.g. “give to the donor lottery” and “do independent research on X” that better achieve your goals).

2. ^{^}

   For example, I write here how - given Metaculus AGI timelines and a speculative projection of Open Philanthropy’s spending strategy - small donors donations’ can go further when not funging with them.  

3. ^{^}

    A sufficient (but certainly not necessary) condition could be “receives funding from an EA-aligned funded, such as Open Philanthropy” (if you trust the judgement and the share values of the funder)

^{^}

 This is potentially UK specific (I don’t know about other countries) and for people on relatively high salaries (>£50k, the point at which the marginal tax rate is greater than Gift Aid one can claim back).

^{^}

 With the caveat of making sure opportunities doesn’t get overfunded

^{^}

 I’d guess there is a high degree of values overlap in your community: if you donate to a global health organisation and another donor - as a result of your donation - decides to donate elsewhere, it seems reasonably likely they will donate to another global health organisation.

^{^}

 I’d guess this overlap is relatively high for niche EA organisations. I’ve written about how to factor in funging as a result of (implicit) differences of AI timelines. Other such empirical beliefs could include: beliefs about the relative importance of different existential risks among longtermists or the value of some global health interventions (e.g. Strong Minds)

^{^}

 For  particularly public charitable organisations and causes, I’d guess there is less mindset overlap. That is, whether the person you’ve funged with shares the effectiveness mindset (and so their donation may be to a charity you would judge as less cost effectiveness than where you would donate if-accounting-for-funging.

^{^}

 The “community” is roughly the set of people who donate - or would donate - to the charities you are donating to.

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Increasing/decreasing one's AGI timelines decrease/increase the importance ^[1] of non-AGI existential risks because there is more/less time for them to occur^[2].

Further, as time passes and we get closer to AGI, the importance of non-AI x-risk decreases relative to AI x-risk. This is a particular case of the above claim.

1. ^{^}

   but not necessarily tractability & neglectedness

2. ^{^}

   If we think that nuclear/bio/climate/other work becomes irrelevant post-AGI, which seems very plausible to me

Some takes on patient philanthropy

Epistemic status: I’ve done work suggesting that AI risk funders be spending at a higher rate, and I'm confident in this result. The other takes are less informed!

I discuss

• Whether I think we should be spending less now
• Useful definitions of patient philanthropy
• Being specific about empirical beliefs that push for more patience  
• When patient philanthropy is counterfactual
• Opportunities for donation trading between patient and non-patient donors

Whether I think we should be spending less now

In principle I think the effective giving community could be in a situation where we should marginally be saving/investing more than we currently do (being ‘patient’). 

However, I don’t think we’re in such a situation and in fact believe the opposite. My main crux is AI timelines; if I thought that AGI was less likely than not to arrive this century, then I would almost certainly believe that the community should marginally be spending less now. 

Useful definitions of patient philanthropy

I think patient philanthropy could be thought of as saying one of:

1. The community is spending at the optimal rate  - let’s create a place to save/invest so ensure we don’t (mistakenly) overspend and keep our funds secure.
2. The community is spending above the optimal rate - let’s push for more savings on the margin, and create a place to save/invest and give later

I don’t think we should call (1) patient philanthropy. Large funders (e.g. Open Philanthropy) already do some form of (1) by just not spending all their capital all this year. Doing (1) is instrumentally useful for the community and is necessary in any case where the community is not spending all of its capital this year.

I like (2) a lot more. This definition is relative to the community’s current spending rate and could be intuitively ‘impatient’. Throughout, I’ll use ‘patient’ to refer to (2): thinking the community’s current spending rate is too high (and so we do better by saving more now and spending later). 

As an aside, thinking that the most ‘influential’ time ahead is not equivalent to being patient. Non-patient funders can also think this but believe their last spending this year goes further than in any other year.

A potential third definition could be something like “patience is spending 0 to ~2% per year” but I don’t think it is useful to discuss.  

Differences in beliefs between funders driving patience

Of course, the large funders and the patient philanthropist may have different beliefs that lead them to disagree on the community’s optimal spending rate. If I believes one of the following, I’d like decrease my guess of the community’s optimal spending rate (and becoming more patient):

• Thinking that there are not good opportunities to spend lots on now (i.e. higher diminishing returns to spending)
• Thinking that TAI / AGI is further away.
• Thinking that the rate of non-AI global catastrophic risk (e.g. nuclear war, biorisk) is lower
• Thinking that there’ll be great spending opportunities in the run-up to AGI
• Thinking that capital will be useful post-AGI
• Thinking that the existing large funders’s capital is less secure or the large funders’ future effective giving less likely for other reasons 

Since it seems likely that there are multiple points of disagreement leading to different spending rates, ‘‘patient philanthropy’ may be a useful term for the cluster of empirical beliefs that imply the community should be spending less. However, it seems better to be more specific about which particular beliefs are driving this the most.

For example “AI skeptical patient philanthropists” and “better-AI-opportunities-now patient philanthropists” may agree that the community’s current spending rate is too high, but disagree on the optimal (rate of) future spending.

When patient philanthropy is counterfactual 

Patient philanthropists can be considered as funders with a very high ‘bar’. That is, they will only spend down on opportunities better than $x$ utils per $ and if none currently exist, they will wait.

Non-patient philanthropists also operate similarly but with a lower bar $y<x$. While the non-patient philanthropist has funds (and funds anything above $x$ utils per dollar, including the opportunities that the patient philanthropist would otherwise fund) the patient philanthropist spends nothing. The patient philanthropist reasons that the counterfactual value of funding something the non-patient philanthropist would fund is zero and so chooses to save.

In this setup, the patient philanthropist is looking to fund and take credit for the ‘best’ opportunities and - while the large funder is around - the patient philanthropist is just funging with them. Once the large funder runs out of funds, the patient philanthropist’s funding is counterfactual.^[1]

If the large funder and patient philanthropist have differences in values or empirical beliefs, it is unsurprising they have different guesses of the optimal spending rate and 'bar'. 

However, this should not happen with value and belief-aligned funders and patient philanthropists; if the funder is acting 'rationally' and spending at the optimal rate, then (by definition) there are no type-2 patient patient philanthropists that have the same beliefs. 

Opportunities for donation trading between patient and non-patient small donors

There are some opportunities for trade between patient philanthropists and non-patient philanthropists, similar to how people can bet on AI timelines. 

Let’s say Alice pledges to give $$a$/year from her income and thinks that the community should be spending more now. Let’s say that Bob thinks the community should be spending less and and saves $$b$/year from his income in order to give it away later. There’s likely an agreement possible (dependent on many factors) where they both benefit. A simple setup could involve:

• Bob, for the next $c$ years gives away their $$b$/year to Alice’s choice of giving opportunity
• Alice, after $c$ years, giving $$a$/year to Bob’s preferred method of investing/saving or giving 

This example closely follows similar setups suggested for betting on AI timelines.  

1. ^{^}

    Unless the amazing opportunity of$z$ utils/$ appears just after the large funder runs out of funds. Where ‘just after’ is the time that the large funder would have kept going with their existing spending strategy of funding everything about $x$ utils/$ by using the patient philanthropist’s funds. 

Anthropics: my understanding/explanation and takes

In this first comment, I stick with the explanations. In  sub-comments, I'll give my own takes

Setup

We need the following  ingredients

• A non-anthropic prior over worlds $W_1,...,W_n$ where $\sum P\left(W_i\right)=1$ ^[1]
• A set $O_i$ of all the observers in $W_i$ for each $i$.
• A subset of observers  $Y_i\subseteq O_i$ of observers  in each world $W_i$ for each $i$ that contain your exact current observer moment
  • Note it's possible to have some $Y_i$ empty - worlds in your non-anthropic prior where there are zero instances of your current observer moment
• A reference class (you can choose!)  $R=(R_1,...,R_n)$ where $R_i\subseteq O_i$. I call  $R_i$  the  reference set for world $i$ which  is a subset of the observers in that world.
  • Generally one picks a 'rule' to generate the $R_i$ systematically 
    • For example "human observers" or  "human observers not in simulations".
  • All anthropic theories technically use a reference class (even the self-indication assumption)
  • Generally one chooses the reference class to contain all of the you-observer moments (i.e. $Y_i\subseteq R_i$ for all $i$)

And finally, we need a choice of anthropic theory. On observation $E$ (that you are your exact current observer moment), the anthropic differ by the likelihood $P\left(E|W\right)$.

Self-indication assumption (SIA)

Bostrom gives the definition of something like

All other things equal, one should reason as if they are randomly selected from the set of all possible observer moments [in your reference class].

This can be formalised as 

$P_{SIA,R}\left(E|W_i\right)=\frac{|R_i\cap Y_i|}{{\sum }_i|R_i|}\propto |R_i\cap Y_i|$

Note that

• The denominator  - which is  the total number of observers in all possible worlds that are in our reference class - is independent of $i$, so we can ignore it when doing the update since it cancels out when normalising.
• The standard approach of SIA is to take the reference class equal to be all observers, that is $R_i=O_i$ for all $i$. In this case, the the update is proportional to $|Y_i|$
  • This is true for any reference class with $Y_i\subseteq R_i$ (i.e. our reference class does not exclude any instances of our exact current observer moment). 

Heuristically we can describe SIA as updating towards worlds in direct proportion to the number of instances of  "you"  that there are. 

Updating with SIA has the effect of

• Updating towards worlds that are multiverses
• Probably thinking there are many simulated copies of you 
• Probably thinking there are aliens (supposing that the process that leads to humans and aliens is the same, we update towards this process being easier).
• (The standard definition) breaking when you have a world with infinite instances of your exact current observer moment.

Self-sampling assumption (SSA) ^[2]

Bostrom again, 

All other things equal, one should reason as if they are randomly selected from the set of all actually existent observer moments in their reference class

This can be formalised as 

$P_{SSA,R}\left(E|W_i\right)=\frac{|R_i\cap Y_i|}{|R_i|}$

Note that

• The denominator - which is the total number of observers in the reference set in world $i$ - is not independent of i so does not  cancel out when normalising our update
• In the case that one takes a reference class to include all exact copies of ones' current observer moment (i.e. $Y_i\subseteq R_i$), we have the expression simplify to $\frac{Y_i}{R_i}$.^[3]

Heuristically we can describe SSA as updating towards worlds in direct proportion to how relatively common instances of  "you" are in the reference class in the world.

Minimal reference class SSA

This is a special case of SSA, where one takes the minimal reference class that contains the exact copies of your exact observer moment. That is, take $R_i=Y_i$ for every $i$.  This means for any evidence you receive, ruling out worlds that do not contain a copy of you that has this same evidence.

Note that the formula for this update becomes $|Y_i|/|Y_i|$ - for worlds where there is at least one copy of us, the likelihood is 1 and is otherwise 0.^[4] 

Updating with SSA has the effect of 

• Updating towards worlds that are small but just contain copies of you (in the reference class)
• For non-minimal reference classes, believing in a ‘Doomsday’ (i.e. updating to worlds with fewer (future) observers in your reference class, since in those worlds your observations are more common in the reference set). 
• Having generally weaker updates than SIA - the likelihoods are always in [0,1].

Both SIA and SSA

• Update towards worlds where you are more 'special',^[5] for example updating towards "now" being an interesting time for simulations to be run.
• Can be extended to worlds containing infinite observers
• (In my mind) are valid 'interpretations' of what we want 'probability' to mean, but not how I think we should do things. 
• Can be Dutch-booked if paired with the wrong decision theory^[6]

1. ^{^}

   One could also easily write this in a continuous case

2. ^{^}

   Strictly, this is the strong  self-sampling assumption in Bostrom's original terminology (the difference being the use of observer moments, rather than observers)

3. ^{^}

   One may choose not to do this, for example, by excluding simulated copies of oneself or Boltzmann brain copies of oneself.

^{^}

The formal definition I gave for SSA  is only for cases where the reference set is non-empty, so there's not something weird going on where we're deciding 0/0 to equal 0.

^{^}

In SIA, being 'special' is being common and appearing often. In SSA, being 'special' is appearing often relative to other observers

^{^}

Spoilers: using SIA with a decision theory that supposes you can 'control' all instances of you (e.g. evidential like theories, or functional-like theories)  is Dutch-bookable. This is also the case for non-minimal reference class SSA with a decision theory that supposes you only control a single instance of you (e.g. causal decision theory).

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A diagram to show possible definitions of existential risks (x-risks) and suffering risks (s-risks)

The (expected) value & disvalue of the entire world’s past and future can be placed on the below axes (assuming both are finite).

By these  definitions:

• Some x-risks are s-risks
• Not all s-risks are x-risks

I've been building a model to calculate the optimal spending schedule on AGI safety and am looking for volunteers to run user experience testing.
 

Let me know via DM on the forum or email if you're interested  :-) 

 The only requirements are (1) to be happy to call & share your screen for ~20 to ~60 minutes while you use the model  (a Colab notebook which runs in your browser) and (2) some interest in AI safety strategy (but certainly no expertise necessary)

 

I highly recommend Nick Bostrom's  working paper Base Camp for Mt. Ethics.

Some excerpts on the idea of the cosmic host that I liked most:

34. At the highest level might be some normative structure established by what we may term the cosmic host. This refers to the entity or set of entities whose preferences and concordats dominate at the largest scale, i.e. that of the cosmos (by which I mean to include the multiverse and whatever else is contained in the totality of existence). It might conceivably consist of, for example, galactic civilizations, simulators, superintelligences, or a divine being or beings.

39. One might think that we could have no clue as to what the cosmic norms are, but in fact we can make at least some guesses: 

a. We should refrain from harming or disrespecting local instances of things that the cosmic host is likely to care about.

b. We should facilitate positive-sum cooperation, and do our bit to uphold the cosmic normative order and nudge it in positive directions.

c. We should contribute public goods to the cosmic resource pool, by securing resources and (later) placing them under the control of cosmic norms. Prevent xrisk and build AI?

d. We should be modest, willing to listen and learn. We should not too headstrongly insist on having too much our way. Instead, we should be compliant, peace-loving, industrious, and humble vis-a-vis the cosmic host.

41. Maybe this could itself be part of an alignment goal: to build our AI such that it wants to be a good cosmic citizen and comply with celestial morality.

a. We may also want it to cherish its parents and look after us in our old age. But a little might go a long way in that regard.

Suppose you think only suffering counts* (absolute negative utilitarian), then the 'negative totalism' population axiology seems pretty reasonable to me.

The axiology does entail the 'Omela Conclusion' (OC), an analogue of the Repugnant Conclusion (RC), which states that for any state of affairs there is a better state in which a single life is hellish and everyone else's life is free from suffering. As a form of totalism, the axiology does not lead to an analogue of the sadistic conclusion  and is non-anti-egalitarian.

The OC (supposing absolute negative utilitarianism) seems more palatable to me than the RC (supposing classical utilitarianism). I'm curious to what extent, if at all, this intuition is shared.

Further, given a (debatable) meta-intuition for robustness of one's ethical theory, does such a preference suggest one should update slightly towards absolute negative utilitarianism or vice versa?

*or that individual utility is bounded above by 0

Using  goal factoring on tasks with ugh fields

Summary: Goal factor ugh tasks (listing the reasons for completing the task) and then generate multiple tasks that achieve each subgoal.

Example: email

 I sometimes am slow to reply to email and develop an ugh-field around doing it. Goal factoring "reply to the email" into

• complete sender's request
• be polite to the sender (i.e. don't take ages to respond)

one can see that the first sub-goal may take some time (and maybe is the initial reason for not doing it straight away), the second sub-goal is easy! One can send an email saying you'll get back to them soon. [Of course, make sure you eventually fulfil the request, and potentially set a reminder to send a polite follow-up email if you're delayed longer!