Multiplier Isn’t Reason Not To Wait

On the issue of whether to help now vs. later, many reasonable arguments have been collected on both sides. For example, positive interest rates argue for helping later, while declining need due to rising wealth argues for helping now. But I keep hearing one kind of argument I think is unreasonable, that doing stuff has good side effects:

Donating to organizations (especially those that focus on influencing people) can help them reach more people and raise even more money. (more)

Giving can send a social signal, which is useful for encouraging more giving, building communities, demonstrating our generosity, and coordinating with charities. (more)

Influencing people to become effective altruists is a pretty high value strategy for improving the world. … You can do more good with time in the present than you can with time in the future. If you spend the next 2 years doing something at least as good as influencing people to become effective altruists, then these 2 years will plausibly be more valuable than all of the rest of your life. (more)

Yes doing things now can have good side effects, but unless something changes in the side-effect processes, doing things later should have exactly the same sort of side effects. And because of positive interest rates, you can do more later, and thus induce more of those good side effects. (Also, almost everyone can trade time for money, and so convert money or time now into more money or time later.)

For example, if you can earn 7% interest you can convert $1 now into $2 a decade from now. Yes, that $1 now might lend respectability now, induce others to copy your act soon, and induce learning by the charity and its observers. But that $2 in a decade should be able to induce twice as much of all those benefits, just delayed by a decade.

In math terms, good side effects are multipliers, which multiply the gains from your good act. But multipliers are just not good reasons to prefer $1 over $2, if both of them will get the same multiplier. If the multiplier is M, you’d just be preferring $1M to $2M.

Now it does seem that many people are arguing that these side-effect processes are in fact changing, and changing a lot. They suggest that that if you work with or donate to them or their friends, then these efforts today can produce huge gains in inducing others to copy you, or in learning better how to do things, gains that won’t be available in the future. Because they and you and now are special.

I think one should in general be rather suspicious of investing or donating to groups on the basis that they, or you, or now, is special. Better to just do what would be good even if you aren’t special. Because usually, you aren’t.

Now one very believable way in which you might be special now is that you might be at a particular age. But the objectively best age to help is probably when you have peak abilities and resources, around age 40 or 60. If you are near your peak age, then, yes, maybe you should help now. If you are younger though, you should probably wait.

Added 14Apr: Every generation has new groups with seemingly newly urgent or valuable causes. So you need some concrete evidence to believe that your new cause is especially good relative to the others. I am not at all persuaded that today is very special just because some people throw around the phrase “effective altruism.”

Added 19Apr: Since my point doesn’t seem to get through just using simple words, here is a more formal math explanation:

Without loss of generality, we can define help x so that it is time-independent, i.e., so that x gives the same amount of direct help no matter the time t it is given. Also, assume that the process by which direct help x at time t results in indirect help at later times is stationary. That is, for every small x spent at time t, a distribution of gains are produced at later delays s according to the same function f(s). Thus the total help resulting from direct help x at time t is x*(1+Integral_t^Infty f(u-t)*du) = x*(1+Integral_0^Infty f(s)*ds. So if this integral is finite, then direct help x induces a constant indirect help multiplier M = 1+Integral_0^Infty f(s)*ds.

One might define a rate of return r for this indirect help as the r that solves the equation 1 = Integral_0^+Infty exp(-r*s)*f(s)*ds. And this rate of return r might in fact be huge. But note that regardless of the return r one calculates from a formula like this, one always gives more total help by choosing a larger amount of direct help x. So if you can give more direct help by helping later, you should.

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  • TaymonBeal

    What if positive side-effects don’t take the form of linear multipliers? It seems to me that many such effects (such as sending a social signal by publicly donating to a charity) should scale less than linearly with the amount of money donated; if I doubled my donation, I would not expect the amount of money donated by others as a result to double. If this is the case, then it does more good to donate regularly.

    • Do you have data on how people are influenced by the number of other donors, vs just the total amount donated? Do most people even know the number of donors?

      • sanxiyn

        This would be interesting to find out from Kickstarter. Kickstarter shows both the number of donors and the amount donated.

  • It seems the difference might be whether the “multiplier” is a one-time gain, vs. some chance of changing the overall growth rate in society. Imagine that altruism is a virus (“meme”), and our goal is to spread the infection. The point is that if you convince someone else to become an altruist, then they on their own may later also convince others.

    So then the question becomes: how does the growth rate of meme propagation compare with the growth rate of financial investments? Those different growth rates would be what determines whether it is more effective to donate now (and thus perhaps have a larger base of altruists from which to grow in the future), vs. invest financially now, and donate a larger amount in the future, but at the cost of society having less time to compound the effect of your donation.

    (All that said, I’m actually skeptical that encouraging more charity in fact makes the world a better place. But I appreciate that such a distinction isn’t the point of this post.)

    • If the ease of meme propagation doesn’t change over time then there will be memes in the future one could promote later with the same ease.

  • John_Maxwell_IV

    It seems to me that you’ve missed something huge here. Investing money produces exponential growth because the money you gain through investment can be reinvested, producing a virtuous cycle. Money is not the only resource that works this way. If an average EA who works on spreading EA memes full-time is able to create an expected 0.1 EA per month, and some of those EAs themselves work to spread EA memes and create new EAs at the same rate, that’s also exponential growth. The EA movement currently has a doubling time much quicker than the economy as a whole, so it seems pretty obvious that investing resources to sustain that doubling time is a better idea than investing resources in the far-slower-growing economy.

    In general, I suspect that investing in the economy should be one of the slowest exponential growth options available out of all the ways to invest in improving society, since we have many highly-paid, intelligent hedge fund managers who are picking all of the low-hanging fruit in terms of traditional financial investments. There are lots of smart people working on finding the next Google and far fewer working on finding the next Wikipedia. If you want to invest in society as a whole instead of making money for yourself, you should be looking at opportunities where you’ll have a hard time capturing even a fraction of the value you create.

    • Today one could work to recruit folks to some fast growing group of today, and in a decade there will be other fast growing groups for which one could recruit. This doesn’t make today special, unless the groups of today are special.

      • John_Maxwell_IV

        OK, let’s make my model just a bit more sophisticated: whenever a new EA gets recruited, there’s half a chance they work on spreading EA ideas (thus creating more EAs) and half a chance they follow your advice and invest their earnings in the Grand EA Endowment Fund, to be carefully managed so that it grows exponentially until the heat death of the universe. That provides a trivial reason why spreading EA ideas is more valuable now than it is in the future: contributions to the Grand EA Endowment Fund are more valuable now because of the time value of money. A dollar added to the GEEF now will be worth more than $1 in 2100, so we strongly prefer to have dollars added to the fund now. And hence we strongly prefer to create EAs now.

        Let’s take this argument further. Exponential growth is what happens when the growth in a quantity is proportionate to the quantity itself. (Mathematically, the derivative of an exponential is going to be a constant number times the exponential. Intuitively, think of a population of rabbits: the more rabbits you have, the faster the number of rabbits you have grows.) You could think of the size of the economy as a measure of the capabilities of humanity. The reason the economy grows exponentially is because the more capable humanity is, the faster we are at gaining new capabilities for ourselves. So to the extent that giving to EA causes advances humanity’s capabilities as a whole (“flow-through effects”), we’d prefer to give sooner rather than give later. Also to the extent that giving to EA causes reduce existential risk (not immediately sure how best to model this).

        I think if you examined many EA causes in detail you’d see *some* reason why we’d prefer to work on the cause sooner rather than later. For example, the sooner we have artificial meat that tastes as good as natural meat, the sooner people will stop killing animals in order to eat meat. Etc. It’s a rare cause where people will shrug their shoulders and say “well, we could solve this problem now, or we could put off solving it a century or two with no ill effects”. It’s possible that you’re right and saving money is the way to go, but it would take a much better researched and more mathematically sophisticated argument to convince me.

      • Owen Cotton-Barratt

        One plausible way in which they might be special is that I may today be able to spend money to generate more money which, although held by other people, is close to as valuable for me as money I hold myself, and likely to remain so in the future. The difference from many groups is that there is more of a tie by what is ultimately valued than a tie by agreement about what the next step should be.

        It’s a bit hard to work out what the rate of return is here, particularly as it may simultaneously be using up the resource of ‘people who can easily be recruited to the movement’.

      • When someone asks you to show that X is different from Y, it isn’t enough to describe features of X. You have to compare those to features of Y.

      • Owen Cotton-Barratt

        I did — perhaps rather obliquely, but I don’t think this is the place to go into a long discussion of it. I said:

        >The difference from many groups is that there is more of a tie by what is ultimately valued than a tie by agreement about what the next step should be.

        Many fast-growing groups coalesce around the idea that we should be doing X now. If I agree with such people, I’m still not so confident that I’ll agree with whatever they think is a high priority in 30 years time. So I’m less willing to expend my own resources for increased resources for the group. For a group which is more centred around shared values and an openness to finding the right routes towards those values, I have higher confidence.

        How often do you think groups of the latter type arise? I’m not sure, but I think this is a much more relevant question than “how often do fast growing groups arise?”

      • OK, you have at least identified something concrete that you believe is different now. I’m skeptical that this is in fact different now, however. I expect this group to fragment soon around their different favored routes.

      • Owen Cotton-Barratt

        Yes, this is a concern. I think trying to understand how much this will happen, and whether we can do anything to guard against it, is an important question.

    • Vaniver

      “It seems to me that you’ve missed something huge here. Investing money produces exponential growth because the money you gain through investment can be reinvested, producing a virtuous cycle.”

      Yeah, this is the exponential growth he’s talking about. You need to make the argument that EA represents a better growth opportunity than normal investments- perhaps that’s true, but it’s not obvious that it’s true. What interest rate do you expect on EA growth?

      • John_Maxwell_IV

        A crude way to look at the growth of the EA movement is to look at Givewell’s annual money moved: I’m not sure what the best way to think about Good Ventures is, but even if you restrict yourself to non-Good Ventures donations, Givewell’s money moved is growing way faster than the economy on a percentage basis.

        Another crude way to look at the growth of the EA movement is to look at the EA facebook group: It has 2,708 members, 61 of which have been added in the last week. That’s 2% week-over-week growth, which translates to 2-3x annualized growth.

        Hence my statement: “The EA movement currently has a doubling time much quicker than the economy as a whole”.

      • There have always been fast growing groups, and there always will. That doesn’t make today special.

      • John_Maxwell_IV

        “The stock market will always be growing quickly. That doesn’t make today special.” Time value of money is better studied by economists, but really most everything is more valuable sooner rather than later.

  • Owen Cotton-Barratt

    I have a lot of sympathy for scepticism that our opportunities now are special. However, we should also be aware that special opportunities sometimes do arise. And the downside cost of investing in an opportunity which turns out not to be special is probably smaller than the upside cost of correctly identifying one that is.

    So we don’t need anything like certainty that ours is a special opportunity for it to be worth acting on. What we do need is for it to reach a certain threshold of plausibility. And we should put a fair amount of effort into working out just how plausible it is that we have a special opportunity. We should for example look historically to see how often opportunities arise which seem comparably good. We are unlikely to be able to show conclusively that the opportunity is definitely special until it no longer exists, but we might find reasons to think that it definitely isn’t special, which would sway us.

    • Forgoing a doubling or quadrupling of your gains can’t be a small opportunity cost unless you think you might gain even more from your special current chance. That raises the bar a lot on just how special that chance must be.

      • Owen Cotton-Barratt

        Yes, this is right and can be underappreciated (although quadrupling sounds optimistic to me: the value of investment is only appreciating at the rate at which interest rates beat the general rate of social return).

      • Even if the “social return” is a higher *rate* of return, it still might be a finite amount, in that it runs out within a finite time. In that case, you’d still get more total by waiting and triggering that process later.

      • Owen Cotton-Barratt

        This could be the case, but conventional wisdom seems to be that after the benefits have diffused through the economy, they continue to compound at the rate of economic growth, and this will be positive.

      • Many ways to help people in need don’t contribute much to economic growth at all. Such as hospice care.

      • Owen Cotton-Barratt

        Yep. I think we agree on a lot. I would be interested in having a conversation with you sometime to pinpoint where the disagreements are coming from, but this isn’t the right medium for it.


    Isn’t it possible, or even likely that the recipient will also get a 7% interest rate, or even more when are more growth opportunities in their environment (for example a third world country that merely has to adopt existing technology to achieve phenomenal growth vs. a developed country that would have to invent and adopt new technology which is far more expensive/difficult)?

    In any case it’s a pointless argument which lends itself easily to those who really do not want to give but just say they do. There will always be future interest accumulation, basing your giving on that would keep you from giving until the end of time and then you’ve helped no one. The exception is if you expect a particularly high interest rate for a limited amount of time.

  • Lord

    One can’t emphasize interest rates without considering discount rates. What is the real value, real in the sense of proportional claim on assets and resources of society, of $1 now vs $2 in the future. In the absence of any specific information to the contrary, the value of $1 now should be assumed to be identical to the value of $2 in the future and the assumed discount rate should equal the interest rate. Money is sterile and produces nothing of itself. It is only money invested in real concrete projects that is capable of producing a real return. The hazard is money only measures markets which can shortchange non market investments even if these can provide vastly better returns than market ones though not necessarily private ones.

    • If you just care less about need helped in the future, that is a lot like declining need, and yes can be a reason for you not to wait.

      • Lord

        This doesn’t have to mean caring less, only caring equally making one ambivalent about when to act. One may consider one will be in a better position to act in the future even one doesn’t think ones actions will amount to any more, just that one may have better knowledge and do so more efficiently.

        This is mainly about how to compare value today with value in the future, real (absolute inflation adjusted) or real real (relative proportional wealth). One could also compare capital with income, instead of a one time gift, the establishment of a fund providing an income for giving. Capital can do a lot more now while income can do a lot more over time. The latter may impose higher management and overhead costs though so may only make sense with large sums.

  • There’s a lot going on in a proper modeling of this question. One element that people are leaving out: Are the societies EA targets Malthusian or Simon?

    A Simon (Simonian?) can point to social returns and expect the benefits to keep growing. Save a baby, and he might grow up to become a fisherman who will make food cheaper for his area. That’s not a one-time “multiple,” that’s a growth in goodness that should be discounted if it’s pushed into the future like any other asset. If the social return is larger than the expected financial return, then you should act now.

    A Malthusian would be far more dismal. Save a baby, and he will consume more fish throughout his entire life. Acting charitably gives you a hedonic rush, increases total utility and decreases average utility. Even if you see believe this is good in your interpretation of the Mere Addition Paradox, there’s no reason to cause this change now rather than later. “Multiple” is an accurate description of the social return.

    Personally, I think the Simon story is only true in countries with strong institutions. I am optimistic that my financial return rate (which includes my small business) will beat the social return rate even in those countries.

    I agree that insufficient skepticism is given to EA claims, but I think there’s plausible beliefs that could potentially justify acting now.

    • Even if benefits keep growing, they might grow slower than do financial returns. That is, it might be that r > g. In this case you’d get more by first investing, then donating.

      • Absolutely. That’s the strategy I’m using.

        Or, at least that’s what I tell myself on April 14th when I’m filling out my taxes and notice I didn’t donate much. Well timed post.

      • IMASBA

        But when do you donate then, when you’re on your deathbed? But wait, why not put it into a fund that can keep collecting interest after your death until the end of time?

        Why would you torment yourself like this instead of just giving now that you know for sure that you have the money (you might be dead tomorrow or get your money stolen or the economy might crash, etc…), unless you really expect an unusual period of high interest rate in the near future?

    • SoerenMind

      About the “Simonian” growth: The multiplier Robin talks about never happens immediately. It is spread out over time, though not infinitely. Most of it may happen early on though.

      It would be a mistake, I think, to assume that because the multiplier may still take effect decades later (the baby becomes a fisherman) that it is actually growing exponentially. Instead it will grow at the speed of economic growth after some time has passed. This point is made in more detail here:

      One thing I do wonder about though is how quickly values and memes such as effective altruism grow. It seems that saying they grow “at the rate of economic growth” is not applicable. Instead, they may, after the multiplier is ‘used up’, end up growing at the speed of population growth. But that’s speculative. I’ve heard Paul Christiano say this at least.

      • Do you mean per capita growth or total growth? This seems like a non-trivial claim.

      • SoerenMind

        Per capita growth, but not entirely sure. Save a baby and you’ve added one life. The economic value of that life will ultimately grow at the rate of per capita growth (in expectation), like with all other lives. Have you read the article I linked to? Which part do you mean is non-trivial?

  • Jess Riedel

    I agree with much of this post. One thing I might take issue with:

    >They suggest that that if you work with or donate to them or their friends, then these efforts today can produce huge gains in inducing others to copy you, … gains that won’t be available in the future. Because they and you and now are special…

    > But the objectively best age to help is probably when you have peak abilities and resources, around age 40 or 60.

    Ages 40-60 might be highest impact for direct action, but for those of us who do not rise to become a public figure, the ability to influence those around us plausibly peaks in our 20s. After this point, other people just won’t change that much. This time period isn’t special historically, it’s just relative to each individual.

    Therefore, it might be best to help when young at a (modest?) level that’s high enough to send a hard-to-fake social signal (in the hopes of influencing young friends) while still saving the bulk of your resources for later. If we’re talking fungible donations, that would mean tapering off giving in your upper 20s and waiting to give everything else away until cognitive decline begins to set in at old age.

    • I know of data on productivity and connections, but not of data on the sort of influence you have in mind. But hard to believe that data isn’t out there somewhere.

  • dc

    But the side effects themselves should grow over time – and likely at the same rate as the market. For an effective donation, you should be indifferent between giving now and giving later. A truly good donation is one carefully chosen such that the side effect / benefits compound at an above-market rate. This is not implausible – a donation that allowed some one to go to college for the first time in their family should have highly positive returns on the benefits / side effects.

  • cinnamon50

    The rational economist, in his majestic math, says that the poor man can equally eat a loaf of bread, or sleep under a bridge, tomorrow as well as today…

    tell you what: you spend 6 months living on min wage, working some cruddy job, you still have the same opinion, thats fine

    • Martin-2

      A poor person might prefer that you give less today than more in ten years. He might also prefer that you give more now than less 10 years ago. Or that you gave more ten years ago than less 20 years ago. I wouldn’t call any of the math here “majestic”.

    • IMASBA

      According to the rational economist a man can go without food one year and just eat a lot the next year…

  • Robert_Easton

    Where can I earn 7% real interest? I’m not even convinced I can earn 0% real interest. When did you stop believing in EMH?

    Anyway that aside, maybe I don’t think today is special. Maybe I think yesterday was better than today. Because the cheapest life that could be saved yesterday was cheaper than today. And the day before yesterday was even better, because the cheapest life I could save then was even cheaper. And tomorrow, the world will be a slightly better place than it is today, and the cheapest life I can save will have gone up in price. My discount rate is determined by how fast I think the lives of the poorest in the world are improving. And currently that’s faster than the measly real interest rates I can earn.

    • You comment on the post without having read its second sentence? That’s where I said declining need is a valid argument. Also, the 7% is just an example, not a prediction.

      • Robert_Easton

        You ask what is special about today; I say today is special compared to tomorrow and yesterday was special compared to today.

        The expected real interest rate decides whether this entire debate is even relevant. Looking at government bonds, I see 0% real interest rates as far as the eye can see. You regularly talk about this topic as if you instead expect 5%+

      • Why should someone intending to donate to charity limit themselves to risk free investment? Altruistically motivated donors should worry little about such risk.

      • Robert_Easton

        The risk free rate is the best estimate I have of future rates of return. Because I believe in EMH and therefore believe the equity premium was just historical accident in the US (and other highly successful countries) in the 20th century. If you want to take the anti-EMH position on that; that’s fine, I know the majority do.

  • Ryan Carey

    If The Haste Consideration, which you cite, is right, then we should time-discount steeply because outreach offers good returns for altruists. The ‘multiplier’ is really understood as a high claimed return. Then, by outreaching, young altruists are investing, just as you say they should.

    • No, rate of return is just a different concept from multiplication.

  • I’ve added a more formal treatment to the post.

  • The math [Added 19Apr] helps, thanks. I think the simple counter is: the integral is (imagined to be) not finite. Assume only EA improves the world. Assume 1% of the current world population acts according to EA. “EA” is a virus (“meme”), which can spread. In steady state, 99% of the population will act according to EA.

    In such a scenario, the sooner to spread the EA meme throughout the population, the longer humanity gets to reap the rewards (until the end of time) for the new behavior.

    What you’re hoping to influence, is the growth rate of the meme spreading. The actual direct “good” is done by the future populations, and its sum is not finite.

    Thus you should act now, rather than later. (At least, depending on the relative growth rates of EA meme spreading, vs. financial returns.)

    (I feel I must re-iterate: I’m not personally convinced that charity makes the world a better place. But again, that hypothetical is assumed in this post.)

  • John_Maxwell_IV

    OK, I looked at your math. Here are my comments. If you’re going to integrate out to time t=infinity, in other words, assume that the universe will have no heat death, then I don’t think “this integral is finite” is a particularly reasonable assumption. And as soon as you integrate the heat death of the universe in to your model, you’ll find that if you delay helping, that gives your aftereffects less time to manifest themselves. So then there’s an actual tradeoff.

    Your argument seems wrong to me because you’re treating the aftereffects as a constant but looking at the multiplier from saving as unbounded. What matters here is (a) what function describes the return on investment from saving your money and (b) what function describes your return on investment from giving (this function is going to be different for each cause). If (b) blows up faster than (a), you’ll want to give right away. If (a) blows up faster than (b), you’ll want to save. If you’re claiming that (b) asymptotically trends towards a constant and (a) does not, that’s a claim you haven’t supported.

    • My argument for finite is given by the link at the word “finite.” The expected effect approaches zero *long* before the heat death of the universe.

      • John_Maxwell_IV

        Thanks, I missed your link. I don’t find it particularly persuasive; it seems like you’re leaning on metaphors pretty heavily. I think I agree with you that Thomas Paine, and other actors in the political realm, can’t generally expect to exert meaningful, deliberate, long-lasting influence. I’m less sure about, say, public intellectuals outside of the political realm. It seems ideas like math and existentialism have permeated the culture for a while now and if nothing else are probably upstream of various effects that are probably truly exponential, like what investors do with their exponentially growing bankrolls. And if you grant the notion of an exponentially growing economy, anything that moves us forward on that exponential even slightly will have an exponential impact in the long run, the math is very simple:

      • It isn’t reasonable to expect that typical actions you take to “help” will increase the exponential economic growth rate. And if we are talking about a temporary bump in growth, the difference between helping now and helping later seems finite.

      • John_Maxwell_IV

        I don’t claim to be able to increase the exponential economic growth rate. I claim to be able to add to humanity’s capacity for doing stuff. And since the growth in humanity’s capacity for doing stuff is proportionate to humanity’s capacity for doing stuff, the capacity addition as a result of my actions grows exponentially in the long haul. Did you read the comment I linked to?

      • Yes I read it. I’m skeptical that you can grow the economy faster via help than the rate that investments grow: