Tithing makes quite a lot of sense

Dec 22 JDN 2458840

Christmas is coming soon, and it is a season of giving: Not only gifts to those we love, but also to charities that help people around the world. It’s a theme of some of our most classic Christmas stories, like A Christmas Carol. (I do have to admit: Scrooge really isn’t wrong for not wanting to give to some random charity without any chance to evaluate it. But I also get the impression he wasn’t giving a lot to evaluated charities either.) And people do really give more around this time of year: Charitable donation rates peak in November and December (though that may also have something to do with tax deductions).

Where should we give? This is not an easy question, but it’s one that we now have tools to answer: There are various independent charity evaluation agencies, like GiveWell and Charity Navigator, which can at least provide some idea of which charities are most cost-effective.

How much should we give? This question is a good deal harder.

Perhaps a perfect being would determine their own precise marginal utility of wealth, and the marginal utility of spending on every possible charity, and give of your wealth to the best possible charity up until those two marginal utilities are equal. Since $1 to UNICEF or the Against Malaria Foundation saves about 0.02 QALY, and (unless you’re a billionaire) you don’t have enough money to meaningfully affect the budget of UNICEF, you’d probably need to give until you are yourself at the UN poverty level of $1.90 per day.

I don’t know of anyone who does this. Even Peter Singer, who writes books that essentially tell us to do this, doesn’t do this. I’m not sure it’s humanly possible to do this. Indeed, I’m not even so sure that a perfect being would do it, since it would require destroying their own life and their own future potential.

How about we all give 10%? In other words, how about we tithe? Yes, it sounds arbitrary—because it is. It could just as well have been 8% or 11%. Perhaps one-tenth feels natural to a base-10 culture made of 10-fingered beings, and if we used a base-12 numeral system we’d think in terms of giving one-twelfth instead. But 10% feels reasonable to a lot of people, it has a lot of cultural support behind it already, and it has become a Schelling point for coordination on this otherwise intractable problem. We need to draw the line somewhere, and it might as well be there.

As Slate Star Codex put it:

It’s ten percent because that’s the standard decreed by Giving What We Can and the effective altruist community. Why should we believe their standard? I think we should believe it because if we reject it in favor of “No, you are a bad person unless you give all of it,” then everyone will just sit around feeling very guilty and doing nothing. But if we very clearly say “You have discharged your moral duty if you give ten percent or more,” then many people will give ten percent or more. The most important thing is having a Schelling point, and ten percent is nice, round, divinely ordained, and – crucially – the Schelling point upon which we have already settled. It is an active Schelling point. If you give ten percent, you can have your name on a nice list and get access to a secret forum on the Giving What We Can site which is actually pretty boring.

It’s ten percent because definitions were made for Man, not Man for definitions, and if we define “good person” in a way such that everyone is sitting around miserable because they can’t reach an unobtainable standard, we are stupid definition-makers. If we are smart definition-makers, we will define it in whichever way which makes it the most effective tool to convince people to give at least that much.

I think it would be also reasonable to adjust this proportion according to your household income. If you are extremely poor, give a token amount: Perhaps 1% or 2%. (As it stands, most poor people already give more than this, and most rich people give less.) If you are somewhat below the median household income, give a bit less: Perhaps 6% or 8%. (I currently give 8%; I plan to increase to 10% once I get a higher-paying job after graduation.) If you are somewhat above, give a bit more: Perhaps 12% or 15%. If you are spectacularly rich, maybe you should give as much as 25%.

Is 10% enough? Well, actually, if everyone gave, even 1% would probably be enough. The total GDP of the First World is about $40 trillion; 1% of that is $400 billion per year, which is more than enough to end world hunger. But since we know that not everyone will give, we need to adjust our standard upward so that those who do give will give enough. (There’s actually an optimization problem here which is basically equivalent to finding a monopoly’s profit-maximizing price.) And just ending world hunger probably isn’t enough; there is plenty of disease to cure, education to improve, research to do, and ecology to protect. If say a third of First World people give 10%, that would be about $1.3 trillion, which would be enough money to at least make a huge difference in all those areas.

You can decide for yourself where you think you should draw the line. But 10% is a pretty good benchmark, and above all—please, give something. If you give anything, you are probably already above average. A large proportion of people give nothing at all. (Only 24% of US tax returns include a charitable deduction—though, to be fair, a lot of us donate but don’t itemize deductions. Even once you account for that, only about 60% of US households give to charity in any given year.)

What if the charitable deduction were larger?

Nov 3 JDN 2458791

Right now, the charitable tax deduction is really not all that significant. It makes donating to charity cheaper, but you still always end up with less money after donating than you had before. It might cause you to donate more than you otherwise would have, but you’ll still only give to a charity you already care about.

This is because the tax deduction applies to your income, rather than your taxes directly. So if you make $100,000 and donate $10,000, you pay taxes as if your income were $90,000. Say your tax rate is 25%; then you go from paying $25,000 and keeping $75,000 to paying $22,500 and keeping $67,500. The more you donate, the less money you will have to keep.

Many people don’t seem to understand this; they seem to think that rich people can actually get richer by donating to charity. That can’t be done in our current tax system, or at least not legally. (There are fraudulent ways to do so; but there are fraudulent ways to do lots of things.) Part of the confusion may be related to the fact that people don’t seem to understand how tax brackets work; they worry about being “pushed into a higher tax bracket” as though this could somehow reduce their after-tax income, but that doesn’t happen. That isn’t how tax brackets work.

Some welfare programs work that way—for instance, seeing your income rise high enough to lose Medicaid eligibility can be bad enough that you would prefer to have less income—but taxes themselves do not.

The graph below shows the actual average tax rate (red) and marginal tax rate (purple) of the current US federal income tax:

Average_tax_rate
From that graph alone, you might think that going to a higher tax bracket could result in lower after-tax income. But the next graph, of before-tax (blue) and after-tax (green) income shows otherwise:

After_tax_income

All that tax deductions can do is shift you left on the green line. Without the tax deduction, you would instead shift left on the blue line, and then read off your position on the green line. Thus the tax deduction benefits you if you were already donating, but never leaves you richer than you would have been without donating at all.

For example, if you have an income of $700,000, you would pay $223,000 in taxes and keep $477,000 in after-tax income. If you instead donate $100,000, your adjusted gross income will be reduced to $600,000, you will only pay $186,000 in taxes, and you will keep $414,000 in after-tax income. If there were no tax deduction, you would still have to pay $223,000 in taxes, and your after-tax income would be only $377,000. So you do benefit from the tax deduction; but there is no amount of donation which will actually increase your after-tax income to above $477,000.

But we wouldn’t have to do it this way. We could instead apply the deduction as a tax credit, which would make the effect of the deduction far larger.

Several years back, Miles Kimball (an economist who formerly worked at Michigan, now at UC Boulder) proposed a quite clever change to the tax system:

My proposal is to raise marginal tax rates above about $75,000 per person–or $150,000 per couple–by 10% (a dime on every extra dollar), but offer a 100% tax credit for public contributions up to the entire amount of the tax surcharge.

Kimball’s argument for the policy is mainly that this would make a tax increase more palatable, by giving people more control over where their money goes. This is surely true, and a worthwhile endeavor.

But the even larger benefit might come from the increased charitable donations. If we limited the tax credit to particularly high-impact charities, we would increase the donations to those charities. Whereas in the current system you get the same deduction regardless of where you give your money, even though we know that some charities are literally hundreds of times as cost-effective as others.

In fact, we might not even want to limit the tax credit to that 10% surcharge. If people want to donate more than 10% of their income to high-impact charities, perhaps we should let them. This would mean that the federal deficit could actually increase under this policy, but if so, there would have to be so much money donated that we’d most likely end world hunger. That’s a tradeoff I’m quite willing to make.

In principle, we could even introduce a tax credit that is greater than 100%—say for instance you get a 120% donation for the top-rated charities. This is not mathematically inconsistent, though it is surely a very bad idea. In that case, it absolutely would be possible to end up with more money than you started with, and the richer you are, the more you could get. There would effectively be a positive return on charitable donations, with the money paid for from the government budget. Bill Gates for instance could pay $10 billion a year to charity and the government would not only pay for it, but also have to give him an extra $2 billion. So even for the best charities—which probably are actually a good deal more cost-effective than the US government—we should cap the tax credit at 100%.

Obvious choices for high-impact charities include UNICEF, the Red Cross, GiveDirectly, and the Malaria Consortium. We would need some sort of criteria to decide which charities should get the benefits; I’m thinking we could have some sort of panel of experts who rate charities based on their cost-effectiveness.

It wouldn’t have to be all-or-nothing, either; charities with good but not top ratings could get an increased deduction but not a 100% deduction. The expert panel could rate charities on a scale from 0 to 10, and then anything above 5 gets an (X-5)*10% tax credit.

In effect, the current policy says, “If you give to charity, you don’t have to pay taxes on the money you gave; but all of your other taxes still apply.” The new policy would say, “You can give to a top-impact charity instead of paying taxes.”

Americans hate taxes and already give a lot to charity, but most of those donations are to relatively ineffective charities. This policy could incentivize people to give more or at least give to better places, probably without hurting the government budget—and if it does hurt the government budget, the benefits will be well worth the cost.

How much should we give?

Nov 4 JDN 2458427

How much should we give of ourselves to others?

I’ve previously struggled with this basic question when it comes to donating money; I have written multiple posts on it now, some philosophical, some empirical, and some purely mathematical.

But the question is broader than this: We don’t simply give money. We also give effort. We also give emotion. Above all, we also give time. How much should we be volunteering? How many protest marches should we join? How many Senators should we call?

It’s easy to convince yourself that you aren’t doing enough. You can always point to some hour when you weren’t doing anything particularly important, and think about all the millions of lives that hang in the balance on issues like poverty and climate change, and then feel a wave of guilt for spending that hour watching Netflix or playing video games instead of doing one more march. This, however, is clearly unhealthy: You won’t actually make yourself into a more effective activist, you’ll just destroy yourself psychologically and become no use to anybody.

I previously argued for a sort of Kantian notion that we should commit to giving our fair share, defined as the amount we would have to give if everyone gave that amount. This is quite appealing, and if I can indeed get anyone to donate 1% of their income as a result, I will be quite glad. (If I can get 100 people to do so, that’s better than I could ever have done myself—a good example of highly cost-effective slacktivism.)

Lately I have come to believe that this is probably inadequate. We know that not everyone will take this advice, which means that by construction it won’t be good enough to actually solve global problems.

This means I must make a slightly greater demand: Define your fair share as the amount you would have to give if everyone among people who are likely to give gave that amount.

Unfortunately, this question is considerably harder. It may not even have a unique answer. The number of people willing to give an amount n is obviously dependent upon the amount x itself, and we are nowhere close to knowing what that function n(x) looks like.

So let me instead put some mathematical constraints on it, by choosing an elasticity. Instead of an elasticity of demand or elasticity of supply, we could call this an elasticity of contribution.

Presumably the elasticity is negative: The more you ask of people, the fewer people you’ll get to contribute.

Suppose that the elasticity is something like -0.5, where contribution is relatively inelastic. This means that if you increase the amount you ask for by 2%, you’ll only decrease the number of contributors by 1%. In that case, you should be like Peter Singer and ask for everything. At that point, you’re basically counting on Bill Gates to save us, because nobody else is giving anything. The total amount contributed n(x) * x is increasing in x.

On the other hand, suppose that elasticity is something like 2, where contribution is relatively elastic. This means that if you increase the amount you ask for by 2%, you will decrease the number of contributors by 4%. In that case, you should ask for very little. You’re asking everyone in the world to give 1% of their income, as I did earlier. The total amount contributed n(x) * x is now decreasing in x.

But there is also a third option: What if the elasticity is exactly -1, unit elastic? Then if you increase the amount you ask for by 2%, you’ll decrease the number of contributors by 2%. Then it doesn’t matter how much you ask for: The total amount contributed n(x) * x is constant.

Of course, there’s no guarantee that the elasticity is constant over all possible choices of x—indeed, it would be quite surprising if it were. A quite likely scenario is that contribution is inelastic for small amounts, then passes through a regime where it is nearly unit elastic, and finally it becomes elastic as you start asking for really large amounts of money.

The simplest way to model that is to just assume that n(x) is linear in x, something like n = N – k x.

There is a parameter N that sets the maximum number of people who will ever donate, and a parameter k that sets how rapidly the number of contributors drops off as the amount asked for increases.

The first-order condition for maximizing n(x) * x is then quite simple: x = N/(2k)

This actually turns out to be the precisely the point at which the elasticity of contribution is -1.

The total amount you can get under that condition is N2/(4k)

Of course, I have no idea what N and k are in real life, so this isn’t terribly helpful. But what I really want to know is whether we should be asking for more money from each person, or asking for less money and trying to get more people on board.

In real life we can sometimes do both: Ask each person to give more than they are presently giving, whatever they are presently giving. (Just be sure to run your slogans by a diverse committee, so you don’t end up with “I’ve upped my standards. Now, up yours!”) But since we’re trying to find a benchmark level to demand of ourselves, let’s ignore that for now.

About 25% of American adults volunteer some of their time, averaging 140 hours of volunteer work per year. This is about 1.6% of all the hours in a year, or 2.4% of all waking hours. Total monetary contributions in the US reached $400 billion for the first time this year; this is about 2.0% of GDP. So the balance between volunteer hours and donations is actually pretty even. It would probably be better to tilt it a bit more toward donations, but it’s really not bad. About 60% of US households made some sort of charitable contribution, though only half of these received the charitable tax deduction.

This suggests to me that the quantity of people who give is probably about as high as it’s going to get—and therefore we need to start talking more about the amount of money. We may be in the inelastic regime, where the way to increase total contributions is to demand more from each individual.

Our goal is to increase the total contribution to poverty eradication by about 1% of GDP in both the US and Europe. So if 60% of people give, and currently total contributions are about 2.0% of GDP, this means that the average contribution is about 3.3% of the contributor’s gross income. Therefore I should tell them to donate 4.3%, right? Not quite; some of them might drop out entirely, and the rest will have to give more to compensate.
Without knowing the exact form of the function n(x), I can’t say precisely what the optimal value is. But it is most likely somewhat larger than 4.3%; 5% would be a nice round number in the right general range. This would raise contributions in the US to 2.6% of GDP, or about $500 billion. That’s a 20% increase over the current level, which is large, but feasible.

Accomplishing a similar increase in Europe would then give us a total of $200 billion per year in additional funds to fight global poverty; this might not quite be enough to end world hunger (depending on which estimate you use), but it would definitely have a large impact.

I asked you before to give 1%. I am afraid I must now ask for more. Set a target of 5%. You don’t have to reach it this year; you can gradually increase your donations each year for several years (I call this “Save More Lives Tomorrow”, after Thaler’s highly successful program “Save More Tomorrow”). This is in some sense more than your fair share; I’m relying on the assumption that half the population won’t actually give anything. But ultimately this isn’t about what’s fair to us. It’s about solving global problems.

What we could, what we should, and what we must

May 27 JDN 2458266

In one of the most famous essays in all of ethical philosophy, Peter Singer famously argued that we are morally obligated to give so much to charity that we would effectively reduce ourselves to poverty only slightly better than what our donations sought to prevent. His argument is a surprisingly convincing one, especially for such a radical proposition. Indeed, one of the core activities of the Effective Altruism movement has basically been finding ways to moderate Singer’s argument without giving up on its core principles, because it’s so obvious both that we ought to do much more to help people around the world and that there’s no way we’re ever going to do what that argument actually asks of us.

The most cost-effective charities in the world can save a human life for an average cost of under $4,000. The maneuver that Singer basically makes is quite simple: If you know that you could save someone’s life for $4,000, you have $4,000 to spend, and instead you spend that $4,000 on something else, aren’t you saying that whatever you did spend it on was more important than saving that person’s life? And is that really something you believe?

But if you think a little more carefully, it becomes clear that things are not quite so simple. You aren’t being paid $4,000 to kill someone, first of all. If you were willing to accept $4,000 as sufficient payment to commit a murder, you would be, quite simply, a monster. Implicitly the “infinite identical psychopath” of neoclassical rational agent models would be willing to do such a thing, but very few actual human beings—even actual psychopaths—are that callous.

Obviously, we must refrain from murdering people, even for amounts far in excess of $4,000. If you were offered the chance to murder someone for $4 billion dollars, I can understand why you would be tempted to do such a thing. Think of what you could do with all that money! Not only would you and everyone in your immediate family be independently wealthy for life, you could donate billions of dollars to charity and save as much as a million lives. What’s one life for a million? Even then, I have a strong intuition that you shouldn’t commit this murder—but I have never been able to find a compelling moral argument for why. The best I’ve been able to come up with a sort of Kantian notion: What if everyone did this?

Since the most plausible scenario is that the $4 billion comes from existing wealth, all those murders would simply be transferring wealth around, from unknown sources. If you stipulate where the wealth comes from, the dilemma can change quite a bit.

Suppose for example the $4 billion is confiscated from Bashar Al-Assad. That would be in itself a good thing, lessening the power of a genocidal tyrant. So we need to add that to the positive side of the ledger. It is probably worth killing one innocent person just to undermine Al-Assad’s power; indeed, the US Air Force certainly seems to think so, as they average more than one civilian fatality every day in airstrikes.

Now suppose the wealth was extracted by clever financial machinations that took just a few dollars out of every bank account in America. This would be in itself a bad thing, but perhaps not a terrible thing, especially since we’re planning on giving most of it to UNICEF. Those people should have given it anyway, right? This sounds like a pretty good movie, actually; a cyberpunk Robin Hood basically.

Next, suppose it was obtained by stealing the life savings of a million poor people in Africa. Now the method of obtaining the money is so terrible that it’s not clear that funneling it through UNICEF would compensate, even if you didn’t have to murder someone to get it.

Finally, suppose that the wealth is actually created anew—not printed money from the Federal Reserve, but some new technology that will increase the world’s wealth by billions of dollars yet requires the death of an innocent person to create. In this scenario, the murder has become something more like the inherent risk in human subjects biomedical research, and actually seems justifiable. And indeed, that fits with the Kantian answer, for if we all had the chance to kill one person in order to create something that would increase the wealth of the world by $4 billion, we could turn this planet into a post-scarcity utopia within a generation for fewer deaths than are currently caused by diabetes.

Anyway, my point here is that the detailed context of a decision actually matters a great deal. We can’t simply abstract away from everything else in the world and ask whether the money is worth the life.

When we consider this broader context with regard to the world’s most cost-effective charities, it becomes apparent that a small proportion of very dedicated people giving huge proportions of their income to charity is not the kind of world we want to see.

If I actually gave so much that I equalized my marginal utility of wealth to that of a child dying of malaria in Ghana, I would have to donate over 95% of my income—and well before that point, I would be homeless and impoverished. This actually seems penny-wise and pound-foolish even from the perspective of total altruism: If I stop paying rent, it gets a lot harder for me to finish my doctorate and become a development economist. And even if I never donated another dollar, the world would be much better off with one more good development economist than with even another $23,000 to the Against Malaria Foundation. Once you factor in the higher income I’ll have (and proportionately higher donations I’ll make), it’s obviously the wrong decision for me to give 95% of $25,000 today rather than 10% of $70,000 every year for the next 20 years after I graduate.

But the optimal amount for me to donate from that perspective is whatever the maximum would be that I could give without jeopardizing my education and career prospects. This is almost certainly more than I am presently giving. Exactly how much more is actually not all that apparent: It’s not enough to say that I need to be able to pay rent, eat three meals a day, and own a laptop that’s good enough for programming and statistical analysis. There’s also a certain amount that I need for leisure, to keep myself at optimal cognitive functioning for the next several years. Do I need that specific video game, that specific movie? Surely not—but if I go the next ten years without ever watching another movie or playing another video game, I’m probably going to be in trouble psychologically. But what exactly is the minimum amount to keep me functioning well? And how much should I be willing to spend attending conferences? Those can be important career-building activities, but they can also be expensive wastes of time.

Singer acts as though jeopardizing your career prospects is no big deal, but this is clearly wrong: The harm isn’t just to your own well-being, but also to your productivity and earning power that could have allowed you to donate more later. You are a human capital asset, and you are right to invest in yourself. Exactly how much you should invest in yourself is a much harder question.
Such calculations are extremely difficult to do. There are all sorts of variables I simply don’t know, and don’t have any clear way of finding out. It’s not a good sign for an ethical theory when even someone with years of education and expertise on specifically that topic still can’t figure out the answer. Ethics is supposed to be something we can apply to everyone.

So I think it’s most helpful to think in those terms: What could we apply to everyone? What standard of donation would be high enough if we could get everyone on board?

World poverty is rapidly declining. The direct poverty gap at the UN poverty line of $1.90 per day is now only $80 billion. Realistically, we couldn’t simply close that gap precisely (there would also be all sorts of perverse incentives if we tried to do it that way). But the standard estimate that it would take about $300 billion per year in well-targeted spending to eliminate world hunger is looking very good.

How much would each person, just those in the middle class or above within the US or the EU, have to give in order to raise this much?
89% of US income is received by the top 60% of households (who I would said are unambiguously “middle class or above”). Income inequality is not as extreme within the EU, so the proportion of income received by the top 60% seems to be more like 75%.

89% of US GDP plus 75% of EU GDP is all together about $29 trillion per year. This means that in order to raise $300 billion, each person in the middle class or above would need to donate just over one percent of their income.

Not 95%. Not 25%. Not even 10%. Just 1%. That would be enough.

Of course, more is generally better—at least until you start jeopardizing your career prospects. So by all means, give 2% or 5% or even 10%. But I really don’t think it’s helpful to make people feel guilty about not giving 95% when all we really needed was for everyone to give 1%.

There is an important difference between what we could do, what we should do, and what we must do.

What we must do are moral obligations so strong they are essentially inviolable: We must not murder people. There may be extreme circumstances where exceptions can be made (such as collateral damage in war), and we can always come up with hypothetical scenarios that would justify almost anything, but for the vast majority of people the vast majority of time, these ethical rules are absolutely binding.

What we should do are moral obligations that are strong enough to be marks against your character if you break them, but not so absolutely binding that you have to be a monster not to follow them. This is where I put donating at least 1% of your income. (This is also where I put being vegetarian, but perhaps that is a topic for another time.) You really ought to do it, and you are doing something wrongful if you don’t—but most people don’t, and you are not a terrible person if you don’t.

This latter category is in part socially constructed, based on the norms people actually follow. Today, slavery is obviously a grave crime, and to be a human trafficker who participates in it you must be a psychopath. But two hundred years ago, things were somewhat different: Slavery was still wrong, yes, but it was quite possible to be an ordinary person who was generally an upstanding citizen in most respects and yet still own slaves. I would still condemn people who owned slaves back then, but not nearly as forcefully as I would condemn someone who owned slaves today. Two hundred years from now, perhaps vegetarianism will move up a category: The norm will be that everyone eats only plants, and someone who went out of their way to kill and eat a pig would have to be a psychopath. Eating meat is already wrong today—but it will be more wrong in the future. I’d say the same about donating 1% of your income, but actually I’m hoping that by two hundred years from now there will be no more poverty left to eradicate, and donation will no longer be necessary.

Finally, there is what we could do—supererogatory, even heroic actions of self-sacrifice that would make the world a better place, but cannot be reasonably expected of us. This is where donating 95% or even 25% of your income would fall. Yes, absolutely, that would help more people than donating 1%; but you don’t owe the world that much. It’s not wrong for you to contribute less than this. You don’t need to feel guilty for not giving this much.

But I do want to make you feel guilty if you don’t give at least 1%. Don’t tell me you can’t. You can. If your income is $30,000 per year, that’s $300 per year. If you needed that much for a car repair, or dental work, or fixing your roof, you’d find a way to come up with it. No one in the First World middle class is that liquidity-constrained. It is true that half of Americans say they couldn’t come up with $400 in an emergency, but I frankly don’t believe it. (I believe it for the bottom 25% or so, who are actually poor; but not half of Americans.) If you have even one credit card that’s not maxed out, you can do this—and frankly even if a card is maxed out, you can probably call them and get them to raise your limit. There is something you could cut out of your spending that would allow you to get back 1% of your annual income. I don’t know what it is, necessarily: Restaurants? Entertainment? Clothes? But I’m not asking you to give a third of your income—I’m asking you to give one penny out of every dollar.

I give considerably more than that; my current donation target is 8% and I’m planning on raising it to 10% or more once I get a high-paying job. I live on a grad student salary which is less than the median personal income in the US. So I know it can be done. But I am very intentionally not asking you to give this much; that would be above and beyond the call of duty. I’m only asking you to give 1%.

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.