Reasonableness and public goods games

Apr 1 JDN 2458210

There’s a very common economics experiment called a public goods game, often used to study cooperation and altruistic behavior. I’m actually planning on running a variant of such an experiment for my second-year paper.

The game is quite simple, which is part of why it is used so frequently: You are placed into a group of people (usually about four), and given a little bit of money (say $10). Then you are offered a choice: You can keep the money, or you can donate some of it to a group fund. Money in the group fund will be multiplied by some factor (usually about two) and then redistributed evenly to everyone in the group. So for example if you donate $5, that will become $10, split four ways, so you’ll get back $2.50.

Donating more to the group will benefit everyone else, but at a cost to yourself. The game is usually set up so that the best outcome for everyone is if everyone donates the maximum amount, but the best outcome for you, holding everyone else’s choices constant, is to donate nothing and keep it all.

Yet it is a very robust finding that most people do neither of those things. There’s still a good deal of uncertainty surrounding what motivates people to donate what they do, but certain patterns that have emerged:

  1. Most people donate something, but hardly anyone donates everything.
  2. Increasing the multiplier tends to smoothly increase how much people donate.
  3. The number of people in the group isn’t very important, though very small groups (e.g. 2) behave differently from very large groups (e.g. 50).
  4. Letting people talk to each other tends to increase the rate of donations.
  5. Repetition of the game, or experience from previous games, tends to result in decreasing donation over time.
  6. Economists donate less than other people.

Number 6 is unfortunate, but easy to explain: Indoctrination into game theory and neoclassical economics has taught economists that selfish behavior is efficient and optimal, so they behave selfishly.

Number 3 is also fairly easy to explain: Very small groups allow opportunities for punishment and coordination that don’t exist in large groups. Think about how you would respond when faced with 2 defectors in a group of 4 as opposed to 10 defectors in a group of 50. You could punish the 2 by giving less next round; but punishing the 10 would end up punishing 40 others who had contributed like they were supposed to.

Number 4 is a very interesting finding. Game theory says that communication shouldn’t matter, because there is a unique Nash equilibrium: Donate nothing. All the promises in the world can’t change what is the optimal response in the game. But in fact, human beings don’t like to break their promises, and so when you get a bunch of people together and they all agree to donate, most of them will carry through on that agreement most of the time.

Number 5 is on the frontier of research right now. There are various theoretical accounts for why it might occur, but none of the models proposed so far have much predictive power.

But my focus today will be on findings 1 and 2.

If you’re not familiar with the underlying game theory, finding 2 may seem obvious to you: Well, of course if you increase the payoff for donating, people will donate more! It’s precisely that sense of obviousness which I am going to appeal to in a moment.

In fact, the game theory makes a very sharp prediction: For N players, if the multiplier is less than N, you should always contribute nothing. Only if the multiplier becomes larger than N should you donate—and at that point you should donate everything. The game theory prediction is not a smooth increase; it’s all-or-nothing. The only time game theory predicts intermediate amounts is on the knife-edge at exactly equal to N, where each player would be indifferent between donating and not donating.

But it feels reasonable that increasing the multiplier should increase donation, doesn’t it? It’s a “safer bet” in some sense to donate $1 if the payoff to everyone is $3 and the payoff to yourself is $0.75 than if the payoff to everyone is $1.04 and the payoff to yourself is $0.26. The cost-benefit analysis comes out better: In the former case, you can gain up to $2 if everyone donates, but would only lose $0.25 if you donate alone; but in the latter case, you would only gain $0.04 if everyone donates, and would lose $0.74 if you donate alone.

I think this notion of “reasonableness” is a deep principle that underlies a great deal of human thought. This is something that is sorely lacking from artificial intelligence: The same AI that tells you the precise width of the English Channel to the nearest foot may also tell you that the Earth is 14 feet in diameter, because the former was in its database and the latter wasn’t. Yes, WATSON may have won on Jeopardy, but it (he?) also made a nonsensical response to the Final Jeopardy question.

Human beings like to “sanity-check” our results against prior knowledge, making sure that everything fits together. And, of particular note for public goods games, human beings like to “hedge our bets”; we don’t like to over-commit to a single belief in the face of uncertainty.

I think this is what best explains findings 1 and 2. We don’t donate everything, because that requires committing totally to the belief that contributing is always better. We also don’t donate nothing, because that requires committing totally to the belief that contributing is always worse.

And of course we donate more as the payoffs to donating more increase; that also just seems reasonable. If something is better, you do more of it!

These choices could be modeled formally by assigning some sort of probability distribution over other’s choices, but in a rather unconventional way. We can’t simply assume that other people will randomly choose some decision and then optimize accordingly—that just gives you back the game theory prediction. We have to assume that our behavior and the behavior of others is in some sense correlated; if we decide to donate, we reason that others are more likely to donate as well.

Stated like that, this sounds irrational; some economists have taken to calling it “magical thinking”. Yet, as I always like to point out to such economists: On average, people who do that make more money in the games. Economists playing other economists always make very little money in these games, because they turn on each other immediately. So who is “irrational” now?

Indeed, if you ask people to predict how others will behave in these games, they generally do better than the game theory prediction: They say, correctly, that some people will give nothing, most will give something, and hardly any will give everything. The same “reasonableness” that they use to motivate their own decisions, they also accurately apply to forecasting the decisions of others.

Of course, to say that something is “reasonable” may be ultimately to say that it conforms to our heuristics well. To really have a theory, I need to specify exactly what those heuristics are.

“Don’t put all your eggs in one basket” seems to be one, but it’s probably not the only one that matters; my guess is that there are circumstances in which people would actually choose all-or-nothing, like if we said that the multiplier was 0.5 (so everyone giving to the group would make everyone worse off) or 10 (so that giving to the group makes you and everyone else way better off).

“Higher payoffs are better” is probably one as well, but precisely formulating that is actually surprisingly difficult. Higher payoffs for you? For the group? Conditional on what? Do you hold others’ behavior constant, or assume it is somehow affected by your own choices?

And of course, the theory wouldn’t be much good if it only worked on public goods games (though even that would be a substantial advance at this point). We want a theory that explains a broad class of human behavior; we can start with simple economics experiments, but ultimately we want to extend it to real-world choices.

Two terms in marginal utility of wealth

JDN 2457569

This post is going to be a little wonkier than most; I’m actually trying to sort out my thoughts and draw some public comment on a theory that has been dancing around my head for awhile. The original idea of separating terms in marginal utility of wealth was actually suggested by my boyfriend, and from there I’ve been trying to give it some more mathematical precision to see if I can come up with a way to test it experimentally. My thinking is also influenced by a paper Miles Kimball wrote about the distinction between happiness and utility.

There are lots of ways one could conceivably spend money—everything from watching football games to buying refrigerators to building museums to inventing vaccines. But insofar as we are rational (and we are after all about 90% rational), we’re going to try to spend our money in such a way that its marginal utility is approximately equal across various activities. You’ll buy one refrigerator, maybe two, but not seven, because the marginal utility of refrigerators drops off pretty fast; instead you’ll spend that money elsewhere. You probably won’t buy a house that’s twice as large if it means you can’t afford groceries anymore. I don’t think our spending is truly optimal at maximizing utility, but I think it’s fairly good.

Therefore, it doesn’t make much sense to break down marginal utility of wealth into all these different categories—cars, refrigerators, football games, shoes, and so on—because we already do a fairly good job of equalizing marginal utility across all those different categories. I could see breaking it down into a few specific categories, such as food, housing, transportation, medicine, and entertainment (and this definitely seems useful for making your own household budget); but even then, I don’t get the impression that most people routinely spend too much on one of these categories and not enough on the others.

However, I can think of two quite different fundamental motives behind spending money, which I think are distinct enough to be worth separating.

One way to spend money is on yourself, raising your own standard of living, making yourself more comfortable. This would include both football games and refrigerators, really anything that makes your life better. We could call this the consumption motive, or maybe simply the self-directed motive.

The other way is to spend it on other people, which, depending on your personality can take either the form of philanthropy to help others, or as a means of self-aggrandizement to raise your own relative status. It’s also possible to do both at the same time in various combinations; while the Gates Foundation is almost entirely philanthropic and Trump Tower is almost entirely self-aggrandizing, Carnegie Hall falls somewhere in between, being at once a significant contribution to our society and an obvious attempt to bring praise and adulation to himself. I would also include spending on Veblen goods that are mainly to show off your own wealth and status in this category. We can call this spending the philanthropic/status motive, or simply the other-directed motive.

There is some spending which combines both motives: A car is surely useful, but a Ferrari is mainly for show—but then, a Lexus or a BMW could be either to show off or really because you like the car better. Some form of housing is a basic human need, and bigger, fancier houses are often better, but the main reason one builds mansions in Beverly Hills is to demonstrate to the world that one is fabulously rich. This complicates the theory somewhat, but basically I think the best approach is to try to separate a sort of “spending proportion” on such goods, so that say $20,000 of the Lexus is for usefulness and $15,000 is for show. Empirically this might be hard to do, but theoretically it makes sense.

One of the central mysteries in cognitive economics right now is the fact that while self-reported happiness rises very little, if at all, as income increases, a finding which was recently replicated even in poor countries where we might not expect it to be true, nonetheless self-reported satisfaction continues to rise indefinitely. A number of theories have been proposed to explain this apparent paradox.

This model might just be able to account for that, if by “happiness” we’re really talking about the self-directed motive, and by “satisfaction” we’re talking about the other-directed motive. Self-reported happiness seems to obey a rule that $100 is worth as much to someone with $10,000 as $25 is to someone with $5,000, or $400 to someone with $20,000.

Self-reported satisfaction seems to obey a different rule, such that each unit of additional satisfaction requires a roughly equal proportional increase in income.

By having a utility function with two terms, we can account for both of these effects. Total utility will be u(x), happiness h(x), and satisfaction s(x).

u(x) = h(x) + s(x)

To obey the above rule, happiness must obey harmonic utility, like this, for some constants h0 and r:

h(x) = h0 – r/x

Proof of this is straightforward, though to keep it simple I’ve hand-waved why it’s a power law:

Given

h'(2x) = 1/4 h'(x)

Let

h'(x) = r x^n

h'(2x) = r (2x)^n

r (2x)^n = 1/4 r x^n

n = -2

h'(x) = r/x^2

h(x) = – r x^(-1) + C

h(x) = h0 – r/x

Miles Kimball also has some more discussion on his blog about how a utility function of this form works. (His statement about redistribution at the end is kind of baffling though; sure, dollar for dollar, redistributing wealth from the middle class to the poor would produce a higher gain in utility than redistributing wealth from the rich to the middle class. But neither is as good as redistributing from the rich to the poor, and the rich have a lot more dollars to redistribute.)

Satisfaction, however, must obey logarithmic utility, like this, for some constants s0 and k.

The x+1 means that it takes slightly less proportionally to have the same effect as your wealth increases, but it allows the function to be equal to s0 at x=0 instead of going to negative infinity:

s(x) = s0 + k ln(x)

Proof of this is very simple, almost trivial:

Given

s'(x) = k/x

s(x) = k ln(x) + s0

Both of these functions actually have a serious problem that as x approaches zero, they go to negative infinity. For self-directed utility this almost makes sense (if your real consumption goes to zero, you die), but it makes no sense at all for other-directed utility, and since there are causes most of us would willingly die for, the disutility of dying should be large, but not infinite.

Therefore I think it’s probably better to use x +1 in place of x:

h(x) = h0 – r/(x+1)

s(x) = s0 + k ln(x+1)

This makes s0 the baseline satisfaction of having no other-directed spending, though the baseline happiness of zero self-directed spending is actually h0 – r rather than just h0. If we want it to be h0, we could use this form instead:

h(x) = h0 + r x/(x+1)

This looks quite different, but actually only differs by a constant.

Therefore, my final answer for the utility of wealth (or possibly income, or spending? I’m not sure which interpretation is best just yet) is actually this:

u(x) = h(x) + s(x)

h(x) = h0 + r x/(x+1)

s(x) = s0 + k ln(x+1)

Marginal utility is then the derivatives of these:

h'(x) = r/(x+1)^2

s'(x) = k/(x+1)

Let’s assign some values to the constants so that we can actually graph these.

Let h0 = s0 = 0, so our baseline is just zero.

Furthermore, let r = k = 1, which would mean that the value of $1 is the same whether spent either on yourself or on others, if $1 is all you have. (This is probably wrong, actually, but it’s the simplest to start with. Shortly I’ll discuss what happens as you vary the ratio k/r.)

Here is the result graphed on a linear scale:

Utility_linear

And now, graphed with wealth on a logarithmic scale:

Utility_log

As you can see, self-directed marginal utility drops off much faster than other-directed marginal utility, so the amount you spend on others relative to yourself rapidly increases as your wealth increases. If that doesn’t sound right, remember that I’m including Veblen goods as “other-directed”; when you buy a Ferrari, it’s not really for yourself. While proportional rates of charitable donation do not increase as wealth increases (it’s actually a U-shaped pattern, largely driven by poor people giving to religious institutions), they probably should (people should really stop giving to religious institutions! Even the good ones aren’t cost-effective, and some are very, very bad.). Furthermore, if you include spending on relative power and status as the other-directed motive, that kind of spending clearly does proportionally increase as wealth increases—gotta keep up with those Joneses.

If r/k = 1, that basically means you value others exactly as much as yourself, which I think is implausible (maybe some extreme altruists do that, and Peter Singer seems to think this would be morally optimal). r/k < 1 would mean you should never spend anything on yourself, which not even Peter Singer believes. I think r/k = 10 is a more reasonable estimate.

For any given value of r/k, there is an optimal ratio of self-directed versus other-directed spending, which can vary based on your total wealth.

Actually deriving what the optimal proportion would be requires a whole lot of algebra in a post that probably already has too much algebra, but the point is, there is one, and it will depend strongly on the ratio r/k, that is, the overall relative importance of self-directed versus other-directed motivation.

Take a look at this graph, which uses r/k = 10.

Utility_marginal

If you only have 2 to spend, you should spend it entirely on yourself, because up to that point the marginal utility of self-directed spending is always higher. If you have 3 to spend, you should spend most of it on yourself, but a little bit on other people, because after you’ve spent about 2.2 on yourself there is more marginal utility for spending on others than on yourself.

If your available wealth is W, you would spend some amount x on yourself, and then W-x on others:

u(x) = h(x) + s(W-x)

u(x) = r x/(x+1) + k ln(W – x + 1)

Then you take the derivative and set it equal to zero to find the local maximum. I’ll spare you the algebra, but this is the result of that optimization:

x = – 1 – r/(2k) + sqrt(r/k) sqrt(2 + W + r/(4k))

As long as k <= r (which more or less means that you care at least as much about yourself as about others—I think this is true of basically everyone) then as long as W > 0 (as long as you have some money to spend) we also have x > 0 (you will spend at least something on yourself).

Below a certain threshold (depending on r/k), the optimal value of x is greater than W, which means that, if possible, you should be receiving donations from other people and spending them on yourself. (Otherwise, just spend everything on yourself). After that, x < W, which means that you should be donating to others. The proportion that you should be donating smoothly increases as W increases, as you can see on this graph (which uses r/k = 10, a figure I find fairly plausible):

Utility_donation

While I’m sure no one literally does this calculation, most people do seem to have an intuitive sense that you should donate an increasing proportion of your income to others as your income increases, and similarly that you should pay a higher proportion in taxes. This utility function would justify that—which is something that most proposed utility functions cannot do. In most models there is a hard cutoff where you should donate nothing up to the point where your marginal utility is equal to the marginal utility of donating, and then from that point forward you should donate absolutely everything. Maybe a case can be made for that ethically, but psychologically I think it’s a non-starter.

I’m still not sure exactly how to test this empirically. It’s already quite difficult to get people to answer questions about marginal utility in a way that is meaningful and coherent (people just don’t think about questions like “Which is worth more? $4 to me now or $10 if I had twice as much wealth?” on a regular basis). I’m thinking maybe they could play some sort of game where they have the opportunity to make money at the game, but must perform tasks or bear risks to do so, and can then keep the money or donate it to charity. The biggest problem I see with that is that the amounts would probably be too small to really cover a significant part of anyone’s total wealth, and therefore couldn’t cover much of their marginal utility of wealth function either. (This is actually a big problem with a lot of experiments that use risk aversion to try to tease out marginal utility of wealth.) But maybe with a variety of experimental participants, all of whom we get income figures on?

What can we do to make the world a better place?

JDN 2457475

There are an awful lot of big problems in the world: war, poverty, oppression, disease, terrorism, crime… I could go on for awhile, but I think you get the idea. Solving or even mitigating these huge global problems could improve or even save the lives of millions of people.

But precisely because these problems are so big, they can also make us feel powerless. What can one person, or even a hundred people, do against problems on this scale?

The answer is quite simple: Do your share.

No one person can solve any of these problems—not even someone like Bill Gates, though he for one at least can have a significant impact on poverty and disease because he is so spectacularly mind-bogglingly rich; the Gates Foundation has a huge impact because it has as much wealth as the annual budget of the NIH.

But all of us together can have an enormous impact. This post today is about helping you see just how cheap and easy it would be to end world hunger and cure poverty-related diseases, if we simply got enough people to contribute.

The Against Malaria Foundation releases annual reports for all their regular donors. I recently got a report that my donations personally account for 1/100,000 of their total assets. That’s terrible. The global population is 7 billion people; in the First World alone it’s over 1 billion. I am the 0.01%, at least when it comes to donations to the Against Malaria Foundation.

I’ve given them only $850. Their total assets are only $80 million. They shouldn’t have $80 million—they should have $80 billion. So, please, if you do nothing else as a result of this post, go make a donation to the Against Malaria Foundation. I am entirely serious; if you think you might forget or change your mind, do it right now. Even a dollar would be worth it. If everyone in the First World gave $1, they would get 12 times as much as they currently have.

GiveWell is an excellent source for other places you should donate; they rate charities around the world for their cost-effectiveness in the only way worth doing: Lives saved per dollar donated. They don’t just naively look at what percentage goes to administrative costs; they look at how everything is being spent and how many children have their diseases cured.

Until the end of April, UNICEF is offering an astonishing five times matching funds—meaning that if you donate $10, a full $50 goes to UNICEF projects. I have really mixed feelings about donors that offer matching funds (So what you’re saying is, you won’t give if we don’t?), but when they are being offered, use them.

All those charities are focused on immediate poverty reduction; if you’re looking for somewhere to give that fights Existential Risk, I highly recommend the Union of Concerned Scientists—one of the few Existential Risk organizations that uses evidence-based projections and recognizes that nuclear weapons and climate change are the threats we need to worry about.

And let’s not be too anthropocentrist; there are a lot of other sentient beings on this planet, and Animal Charity Evaluator can help you find which charities will best improve the lives of other animals.

I’ve just listed a whole bunch of ways you can give money—and that probably is the best thing for you to give; your time is probably most efficiently used working in your own profession whatever that may be—but there are other ways you can contribute as well.

One simple but important change you can make, if you haven’t already, is to become vegetarian. Even aside from the horrific treatment of animals in industrial farming, you don’t have to believe that animals deserve rights to understand that meat is murder. Meat production is a larger contributor to global greenhouse gas emissions than transportation, so everyone becoming vegetarian would have a larger impact against climate change than taking literally every car and truck in the world off the road. Since the world population is less than 10 billion, meat is 18% of greenhouse emissions and the IPCC projects that climate change will kill between 10 and 100 million people over the next century, every 500 to 5000 new vegetarians saves a life.

You can move your money from a bank to a credit union, as even the worst credit unions are generally better than the best for-profit banks, and the worst for-profit banks are very, very bad. The actual transition can be fairly inconvenient, but a good credit union will provide you with all the same services, and most credit unions link their networks and have online banking, so for example I can still deposit and withdraw from my University of Michigan Credit Union account while in California.

Another thing you can do is reduce your consumption of sweatshop products in favor of products manufactured under fair labor standards. This is harder than it sounds; it can be very difficult to tell what a company’s true labor conditions are like, as the worst companies work very hard to hide them (now, if they worked half as hard to improve them… it reminds me of how many students seem willing to do twice as much work to cheat as they would to simply learn the material in the first place).

You should not simply stop buying products that say “Made in China”; in fact, this could be counterproductive. We want products to be made in China; we need products to be made in China. What we have to do is improve labor standards in China, so that products made in China are like products made in Japan or Korea—skilled workers with high-paying jobs in high-tech factories. Presumably it doesn’t bother you when something says “Made in Switzerland” or “Made in the UK”, because you know their labor standards are at least as high as our own; that’s where I’d like to get with “Made in China”.

The simplest way to do this is of course to buy Fair Trade products, particularly coffee and chocolate. But most products are not available Fair Trade (there are no Fair Trade computers, and only loose analogues for clothing and shoes).

Moreover, we must not let the perfect be the enemy of the good; companies that have done terrible things in the past may still be the best companies to support, because there are no alternatives that are any better. In order to incentivize improvement, we must buy from the least of all evils for awhile until the new competitive pressure makes non-evil corporations viable. With this in mind, the Fair Labor Association may not be wrong to endorse companies like Adidas and Apple, even though they surely have substantial room to improve. Similarly, few companies on the Ethisphere list are spotless, but they probably are genuinely better than their competitors. (Well, those that have competitors; Hasbro is on there. Name a well-known board game, and odds are it’s made by a Hasbro subsidiary: they own Parker Brothers, Milton Bradley, and Wizards of the Coast. Wikipedia has their own category, Hasbro subsidiaries. Maybe they’ve been trying to tell us something with all those versions of Monopoly?)

I’m not very happy with the current state of labor standards reporting (much less labor standards enforcement), so I don’t want to recommend any of these sources too highly. But if you are considering buying from one of three companies and only one of them is endorsed by the Fair Labor Association, it couldn’t hurt to buy from that one instead of the others.

Buying from ethical companies will generally be more expensive—but rarely prohibitively so, and this is part of how we use price signals to incentivize better behavior. For about a year, BP gasoline was clearly cheaper than other gasoline, because nobody wanted to buy from BP and they were forced to sell at a discount after the Deepwater Horizon disaster. Their profits tanked as a result. That’s the kind of outcome we want—preferably for a longer period of time.

I suppose you could also save money by buying cheaper products and then donate the difference, and in the short run this would actually be most cost-effective for global utility; but (1) nobody really does that; people who buy Fair Trade also tend to donate more, maybe just because they are more generous in general, and (2) in the long run what we actually want is more ethical businesses, not a system where businesses exploit everyone and then we rely upon private charity to compensate us for our exploitation. For similar reasons, philanthropy is a stopgap—and a much-needed one—but not a solution.

Of course, you can vote. And don’t just vote in the big name elections like President of the United States. Your personal impact may actually be larger from voting in legislatures and even local elections and ballot proposals. Certainly your probability of being a deciding vote is far larger, though this is compensated by the smaller effect of the resulting policies. Most US states have a website where you can look up any upcoming ballots you’ll be eligible to vote on, so you can plan out your decisions well in advance.

You may even want to consider running for office at the local level, though I realize this is a very large commitment. But most local officials run uncontested, which means there is no real democracy at work there at all.

Finally, you can contribute in some small way to making the world a better place simply by spreading the word, as I hope I’m doing right now.

Scope neglect and the question of optimal altruism

JDN 2457090 EDT 16:15.

We’re now on Eastern Daylight Time because of this bizarre tradition of shifting our time zone forward for half of the year. It’s supposed to save energy, but a natural experiment in India suggests it actually increases energy demand. So why do we do it? Like every ridiculous tradition (have you ever tried to explain Groundhog Day to someone from another country?), we do it because we’ve always done it.
This week’s topic is scope neglect, one of the most pervasive—and pernicious—cognitive heuristics human beings face. Scope neglect raises a great many challenges not only practically but also theoretically—it raises what I call the question of optimal altruism.

The question is simple to ask yet remarkably challenging to answer: How much should we be willing to sacrifice in order to benefit others? If we think of this as a number, your solidarity coefficient (s), it is equal to the cost you are willing to pay divided by the benefit your action has for someone else: s B > C.

This is analogous to the biological concept relatedness (r), on which Hamilton’s Rule applies: r B > C. Solidarity is the psychological analogue; instead of valuing people based on their genetic similarity to you, you value them based on… well, that’s the problem.

I can easily place upper and lower bounds: The lower bound is zero: You should definitely be willing to sacrifice something to help other people—otherwise you are a psychopath. The upper bound is one: There’s no point in paying more cost than you produce in benefit, and in fact even paying the same cost to yourself as you yield in benefits for other people doesn’t make a lot of sense, because it means that your own self-interest is meaningless and the fact that you understand your own needs better than the needs of others is also irrelevant.

But beyond that, it gets a lot harder—and that may explain why we suffer scope neglect in the first place. Should it be 90%? 50%? 10%? 1%? How should it vary between friends versus family versus strangers? It’s really hard to say. And this inability to precisely decide how much other people should be worth to us may be part of why we suffer scope neglect.

Scope neglect is the fact that we are not willing to expend effort or money in direct proportion to the benefit it would have. When different groups were asked how much they would be willing to donate in order to save the lives of 2,000 birds, 20,000 birds, or 200,000 birds, the answers they gave were statistically indistinguishable—always about $80. But however much a bird’s life is worth to you, shouldn’t 200,000 birds be worth, well, 200,000 times as much? In fact, more than that, because the marginal utility of wealth is decreasing, but I see no reason to think that the marginal utility of birds decreases nearly as fast.

But therein lies the problem: Usually we can’t pay 200,000 times as much. I’d feel like a horrible person if I weren’t willing to expend at least $10 or an equivalent amount of effort in order to save a bird. To save 200,000 birds that means I’d owe $2 million—and I simply don’t have $2 million.

You can get similar results to the bird experiment if you use children—though, as one might hope, the absolute numbers are a bit bigger, usually more like $500 to $1000. (And this, it turns out, is actually about how much it actually costs to save a child’s life by a particularly efficient means, such as anti-malaria nets, de-worming, or direct cash transfer. So please, by all means, give $1000 to UNICEF or the Against Malaria Foundation. If you can’t give $1000, give $100; if you can’t give $100, give $10.) It doesn’t much matter whether you say that the project will save 500 children, 5,000 children, or 50,000 children—people still will give about $500 to $1000. But once again, if I’m willing to spend $1000 to save a child—and I definitely am—how much should I be willing to spend to end malaria, which kills 500,000 children a year? Apparently $500 million, which not only do I not have, I almost certainly will not make that much money cumulatively through my entire life. ($2 million, on the other hand, I almost certainly will make cumulatively—the median income of an economist is $90,000 per year, so if I work for at least 22 years with that as my average income I’ll have cumulatively made $2 million. My net wealth may never be that high—though if I get better positions, or I’m lucky enough or clever enough with the stock market it might—but my cumulative income almost certainly will. Indeed, the average gain in cumulative income from a college degree is about $1 million. Because it takes time—time is money—and loans carry interest, this gives it a net present value of about $300,000.)

But maybe scope neglect isn’t such a bad thing after all. There is a very serious problem with these sort of moral dilemmas: The question didn’t say I would single-handedly save 200,000 birds—and indeed, that notion seems quite ridiculous. If I knew that I could actually save 200,000 birds and I were the only one who could do it, dammit, I would try to come up with that $2 million. I might not succeed, but I really would try as hard as I could.

And if I could single-handedly end malaria, I hereby vow that I would do anything it took to achieve that. Short of mass murder, anything I could do couldn’t be a higher cost to the world than malaria itself. I have no idea how I’d come up with $500 million, but I’d certainly try. Bill Gates could easily come up with that $500 million—so he did. In fact he endowed the Gates Foundation with $28 billion, and they’ve spent $1.3 billion of that on fighting malaria, saving hundreds of thousands of lives.

With this in mind, what is scope neglect really about? I think it’s about coordination. It’s not that people don’t care more about 200,000 birds than they do about 2,000; and it’s certainly not that they don’t care more about 50,000 children than they do about 500. Rather, the problem is that people don’t know how many other people are likely to donate, or how expensive the total project is likely to be; and we don’t know how much we should be willing to pay to save the life of a bird or a child.

Hence, what we basically do is give up; since we can’t actually assess the marginal utility of our donation dollars, we fall back on our automatic emotional response. Our mind focuses itself on visualizing that single bird covered in oil, or that single child suffering from malaria. We then hope that the representative heuristic will guide us in how much to give. Or we follow social norms, and give as much as we think others would expect us to give.

While many in the effective altruism community take this to be a failing, they never actually say what we should do—they never give us a figure for how much money we should be willing to donate to save the life of a child. Instead they retreat to abstraction, saying that whatever it is we’re willing to give to save a child, we should be willing to give 50,000 times as much to save 50,000 children.

But it’s not that simple. A bigger project may attract more supporters; if the two occur in direct proportion, then constant donation is the optimal response. Since it’s probably not actually proportional, you likely should give somewhat more to causes that affect more people; but exactly how much more is an astonishingly difficult question. I really don’t blame people—or myself—for only giving a little bit more to causes with larger impact, because actually getting the right answer is so incredibly hard. This is why it’s so important that we have institutions like GiveWell and Charity Navigator which do the hard work to research the effectiveness of charities and tell us which ones we should give to.

Yet even if we can properly prioritize which charities to give to first, that still leaves the question of how much each of us should give. 1% of our income? 5%? 10%? 20%? 50%? Should we give so much that we throw ourselves into the same poverty we are trying to save others from?

In his earlier work Peter Singer seemed to think we should give so much that it throws us into poverty ourselves; he asked us to literally compare every single purchase and ask ourselves whether a year of lattes or a nicer car is worth a child’s life. Of course even he doesn’t live that way, and in his later books Singer seems to have realized this, and now recommends the far more modest standard that everyone give at least 1% of their income. (He himself gives about 33%, but he’s also very rich so he doesn’t feel it nearly as much.) I think he may have overcompensated; while if literally everyone gave at least 1% that would be more than enough to end world hunger and solve many other problems—world nominal GDP is over $70 trillion, so 1% of that is $700 billion a year—we know that this won’t happen. Some will give more, others less; most will give nothing at all. Hence I think those of us who give should give more than our share; hence I lean toward figures more like 5% or 10%.

But then, why not 50% or 90%? It is very difficult for me to argue on principle why we shouldn’t be expected to give that much. Because my income is such a small proportion of the total donations, the marginal utility of each dollar I give is basically constant—and quite high; if it takes about $1000 to save a child’s life on average, and each of these children will then live about 60 more years at about half the world average happiness, that’s about 30 QALY per $1000, or about 30 milliQALY per dollar. Even at my current level of income (incidentally about as much as I think the US basic income should be), I’m benefiting myself only about 150 microQALY per dollar—so my money is worth about 200 times as much to those children as it is to me.

So now we have to ask ourselves the really uncomfortable question: How much do I value those children, relative to myself? If I am at all honest, the value is not 1; I’m not prepared to die for someone I’ve never met 10,000 kilometers away in a nation I’ve never even visited, nor am I prepared to give away all my possessions and throw myself into the same starvation I am hoping to save them from. I value my closest friends and family approximately the same as myself, but I have to admit that I value random strangers considerably less.

Do I really value them at less than 1%, as these figures would seem to imply? I feel like a monster saying that, but maybe it really isn’t so terrible—after all, most economists seem to think that the optimal solidarity coefficient is in fact zero. Maybe we need to become more comfortable admitting that random strangers aren’t worth that much to us, simply so that we can coherently acknowledge that they aren’t worth nothing. Very few of us actually give away all our possessions, after all.

Then again, what do we mean by worth? I can say from direct experience that a single migraine causes me vastly more pain than learning about the death of 200,000 people in an earthquake in Southeast Asia. And while I gave about $100 to the relief efforts involved in that earthquake, I’ve spent considerably more on migraine treatments—thousands, once you include health insurance. But given the chance, would I be willing to suffer a migraine to prevent such an earthquake? Without hesitation. So the amount of pain we feel is not the same as the amount of money we pay, which is not the same as what we would be willing to sacrifice. I think the latter is more indicative of how much people’s lives are really worth to us—but then, what we pay is what has the most direct effect on the world.

It’s actually possible to justify not dying or selling all my possessions even if my solidarity coefficient is much higher—it just leads to some really questionable conclusions. Essentially the argument is this: I am an asset. I have what economists call “human capital”—my health, my intelligence, my education—that gives me the opportunity to affect the world in ways those children cannot. In my ideal imagined future (albeit improbable) in which I actually become President of the World Bank and have the authority to set global development policy, I myself could actually have a marginal impact of megaQALY—millions of person-years of better life. In the far more likely scenario in which I attain some mid-level research or advisory position, I could be one of thousands of people who together have that sort of impact—which still means my own marginal effect is on the order of kiloQALY. And clearly it’s true that if I died, or even if I sold all my possessions, these events would no longer be possible.

The problem with that reasoning is that it’s wildly implausible to say that everyone in the First World are in this same sort of position—Peter Singer can say that, and maybe I can say that, and indeed hundreds of development economists can say that—but at least 99.9% of the First World population are not development economists, nor are they physicists likely to invent cold fusion, nor biomedical engineers likely to cure HIV, nor aid workers who distribute anti-malaria nets and polio vaccines, nor politicians who set national policy, nor diplomats who influence international relations, nor authors whose bestselling books raise worldwide consciousness. Yet I am not comfortable saying that all the world’s teachers, secretaries, airline pilots and truck drivers should give away their possessions either. (Maybe all the world’s bankers and CEOs should—or at least most of them.)

Is it enough that our economy would collapse without teachers, secretaries, airline pilots and truck drivers? But this seems rather like the fact that if everyone in the world visited the same restaurant there wouldn’t be enough room. Surely we could do without any individual teacher, any individual truck driver? If everyone gave the same proportion of their income, 1% would be more than enough to end malaria and world hunger. But we know that everyone won’t give, and the job won’t get done if those of us who do give only 1%.

Moreover, it’s also clearly not the case that everything I spend money on makes me more likely to become a successful and influential development economist. Buying a suit and a car actually clearly does—it’s much easier to get good jobs that way. Even leisure can be justified to some extent, since human beings need leisure and there’s no sense burning myself out before I get anything done. But do I need both of my video game systems? Couldn’t I buy a bit less Coke Zero? What if I watched a 20-inch TV instead of a 40-inch one? I still have free time; could I get another job and donate that money? This is the sort of question Peter Singer tells us to ask ourselves, and it quickly leads to a painfully spartan existence in which most of our time is spent thinking about whether what we’re doing is advancing or damaging the cause of ending world hunger. But then the cost of that stress and cognitive effort must be included; but how do you optimize your own cognitive effort? You need to think about the cost of thinking about the cost of thinking… and on and on. This is why bounded rationality modeling is hard, even though it’s plainly essential to both cognitive science and computer science. (John Stuart Mill wrote an essay that resonates deeply with me about how the pressure to change the world drove him into depression, and how he learned to accept that he could still change the world even if he weren’t constantly pressuring himself to do so—and indeed he did. James Mill set out to create in his son, John Stuart Mill, the greatest philosopher in the history of the world—and I believe that he succeeded.)

Perhaps we should figure out what proportion of the world’s people are likely to give, and how much we need altogether, and then assign the amount we expect from each of them based on that? The more money you ask from each, the fewer people are likely to give. This creates an optimization problem akin to setting the price of a product under monopoly—monopolies maximize profits by carefully balancing the quantity sold with the price at which they sell, and perhaps a similar balance would allow us to maximize development aid. But wouldn’t it be better if we could simply increase the number of people who give, so that we don’t have to ask so much of those who are generous? That means tax-funded foreign aid is the way to go, because it ensures coordination. And indeed I do favor increasing foreign aid to about 1% of GDP—in the US it is currently about $50 billion, 0.3% of GDP, a little more than 1% of the Federal budget. (Most people who say we should “cut” foreign aid don’t realize how small it already is.) But foreign aid is coercive; wouldn’t it be better if people would give voluntarily?

I don’t have a simple answer. I don’t know how much other people’s lives ought to be worth to us, or what it means for our decisions once we assign that value. But I hope I’ve convinced you that this problem is an important one—and made you think a little more about scope neglect and why we have it.