What do you find to be the strongest reason to use VSLY's to value lives saved at different income levels? My intuitive approach would have been to use the value of utility from one year of consumption directly, not divided by people's marginal utility of consumption (i.e., $u\left(c\right)$ instead of $\frac{u\left(c\right)}{u^{\prime }\left(c\right)}$). We would then value extra life-years only based on the utility received during that year. In the constant utility case, for example, we'd place the same value on an additional life-year regardless of income level.

"Value" is a slippery term here. You're referring to utility value, but when we calculate cost-effectiveness, we have to place a monetary value on the outcome, because

1. Utility functions are not normalized to scale – we could multiply utility functions by 1000 and nothing would change, even though the utility numbers would increase by 1000x. So already "utility" is not a meaningful concept to put into cost-effectiveness calculations.
2. We anyways have to compare health interventions and income interventions, which requires having some willingness-to-pay for the utility purchased by a health intervention. "We are willing to pay $X to extend life by one year" – that X has to come from some framework. Whether you call it a VSLY, or a moral weight, or a willingness-to-pay, it comes from somewhere.

The choice of VSLY as a source of moral weight comes from the premise that when comparing interventions that increase health or increase income among poor people, we should make the tradeoff in the same way that they would, rather than imposing our own preferences of how to make that tradeoff. The reason why VSLYs satisfy that is because they are either estimated from revealed-preference decisions of the relevant populations, or from the stated preferences of the relevant populations. (If they were just dictated from on high, they would not be good moral grounding!) Specifically, in a neoclassical framework where people can pay for health improvements, their willingness to pay is exactly the marginal utility of a health improvement, divided by the marginal utility of income $u^{\prime }\left(c\right)$. That's why we divide by $u^{\prime }\left(c\right)$.

Of course, that leads to indeterminacy when comparing interventions between two populations with different $c$ and thus different VSLYs. So when organizations have a single consistent moral weight on health vs income, they are implicitly treating the VSLY as common between all populations. That basically implements what you're saying (have a common valuation for years of life across countries). But it doesn't resolve our earlier discussion, since if you grounded your moral weight on lives saved in a VSLY, and you adopted a new $\eta$, you would get a new moral weight on lives saved, which would be the first-order determinant of how $\eta$ affects grantmaking.

You're pointing out that the value of life shouldn't depend on consumption $u\left(c\right)$. But even if you assumed there was a fixed utility from saving lives, the VSLY would still be different across populations, and all of the conclusions I talked about would still hold. The reason is because of the monetization of utility. The VSLY is grounded in how an individual would trade off health vs income, and that tradeoff depends on their marginal utility of income $u^{\prime }\left(c\right)$.

Assume there was a fixed utility from someone being alive for a year, $\overline{u}$. Then their willingness to pay for an extra year of life is $\overline{u}/u^{\prime }\left(c\right)$. This varies less with income than if the value of life was $u\left(c\right)$, but it still varies with income. Poor people are willing to spend less (in absolute terms) on health than rich people are, because their competing needs are higher than rich people's competing needs.

If this is the case, then all of our discussion of $\eta$ still goes through. For an isoelastic utility function, the VSLY is $\overline{u}\cdot c^{\eta }$, which increases in income, and increases exponentially in $\eta$. The replacement of $u\left(c\right)$ with $\overline{u}$ changes nothing qualitatively; higher $\eta$ still leads to higher VSLYs even when everyone enjoys a year of life equally. That then causes health interventions for the rich to dominate health interventions for the poor.

The reason why this matters is because it renders the following statement problematic:

Take again the purely utilitarian view that we should value utility increases the same irrespective of the beneficiary. Then, note that there is some fixed number $x$ of income doublings such that people are indifferent between them and an extra year of life, regardless of income level (assuming the VSL-income elasticity is 1).

Assuming the VSL-income elasticity is 1 is equivalent to assuming $\eta =1$, since you have to assume that income doublings are worth the same to people regardless of their income levels. So I don't really understand how that assumption helps you draw conclusions about what would happen if $\eta >1$. If $\eta >1$, then even if the value of life was common to everyone, the VSL-income elasticity would be greater than 1. Basically, the marginal utility of income doublings declines, but the marginal value of life does not, so the VSL has to grow faster than income.

Now, the key assumption is that we monetize VSLs using individual willingness-to-pay. Maybe you think social willingness-to-pay should be determined by the marginal utility of money to the social planner, which is common across people, rather than by the WTP of individuals who vary in their income levels. This is a defensible normative position. I would just note that the marginal utility of money from a donor's perspective is the value you could otherwise get by spending that money. For us, that benchmark use of money is GiveDirectly cash transfers. If you think that way, you will end up with a marginal utility of money that is close to a poor person's marginal utility of money, so the original framework is still representative of how valuable health interventions are among poor people.

Both VSLY utility models don’t seem to align with people’s reported VSL preferences with regards to the mortality risk vs income gain tradeoff.

I think it fits fine? Under the log utility model with no set point, WTP for an extra year of life is $c\ln \left(c\right)$. Normalize this by income levels $c$ to get the VSLY-income ratio as $\ln \left(c\right)$. Eyeballing the graph from OP's collection of VSL estimates, they look vaguely consistent with a logarithmic relationship between the VSLY-income ratio and income. Or take the general isoelastic utility model, where WTP for an extra year of life is $\frac{c^{\eta}-c}{\eta-1}, so the VSLY-income ratio is $\frac{1}{\eta -1}\cdot c^{\eta -1}-\frac{1}{\eta -1}$. This is a general sub-linear function of $c$ for $\eta >1$, and you could probably fit a value of $\eta$ to match the estimates best. Robinson et al (2019) take this elasticity approach and find a roughly log-linear relationship between VSLY-income ratio and income.

Now, these studies can't statistically reject a flat VSLY-income ratio across countries, so you would be on fair ground to assume a constant VSLY-income ratio. But it's definitely not right to say that the isoelastic utility model doesn't fit the data on VSLs across countries.

I have nothing to say about the philosophical arguments. But I think it's important to adopt mental frameworks that are compatible with you having a fulfilling life. To me, that is the highest moral principle, but that's why I'm not a moral philosopher. To you, who cares more about moral truth seeking, I appeal to the life jacket heuristic; you should always put the life jacket on yourself first, and then others, because you're no good to other people if you don't take care of yourself first. A mental framework that leaves you incapacitated by moral anxiety is detrimental to your ability to help all sentient creatures.

Concretely, I encourage you not to think yourself into nightmares. If your views push you to internalize a moral conclusion, you can take that conclusion without internalizing the moral panic that prompted that conclusion. You can decide that AI sentience and invertebrate welfare are the top moral priorities without waking up in a cold sweat about them. You can think about possibilities like alien welfare as questions to be answered rather than sources of anxiety.

And if you fail to live up to your moral standards, be disappointed, strive to be better, but don't doom spiral. Ultimately, we are human and fragile. Don't break yourself with the weight of being something more.

Thanks for clarifying!

That is because, in practice, there are situations where the inconsistency will lead us to that conclusion. Take, for example, deworming in Madagascar (~$500 GDP/capita) vs cash transfers in Kenya (~$2k GDP/capita). For simplicity, assume deworming generates income benefits in year 1 and 2 while cash transfers only generate them in year 1. In our CEAs, we assign the same value for income doublings in year 1 of an intervention. Because we set the comparison point there, we value doubling the income of the $500 and $2k earners the same, but value the income doubling of the $502 earner in Madagascar in year 2 less than for the $2000 earner in Kenya.

I don't think it makes sense to frame this as valuing rich people over poor people. What's happening in this example is favoring benefits in year 1 over benefits in year 2, regardless of a person's income. This is definitely a nitpick, but I think many people's intuitions about time discounting precede intuitions about rich vs poor people's income doublings, so it's more clarifying to frame it that way.

Put another way, if we consistently apply the income doublings framework (log-utility), the CEA implies a 2.6% annual discount rate of pure time preference.

An equivalent way to frame this would be "we use a log utility framework because of <benefits>, but we recognize that it overestimates the value of income growth at higher levels of income, so we will fix that by discounting future income in a way that would be consistent with $\eta >1$."

In other words, the inconsistency is just a practical way to reconcile two frameworks with different pros and cons, rather than an endorsement of the ethical position of pure time preference. Now, ad hoc approaches like that could rub you the wrong way, but I would put that in the general category of "this is bad because it's arbitrary", and not "this is bad because it implies a rate of pure time preference, which has repugnant ethical conclusions".

I'm not sure this is necessarily true? It seems like higher values of $\eta$ would primarily increase the slope of the marginal rate of substitution between health benefits and income doublings, as a function of absolute income levels. (We prefer health benefits more strongly at higher vs lower levels of income). Whether this shifts our portfolio more towards health- or income-generating interventions depends on our choice of income level at which we believe income doublings and health benefits should trade off as they currently do.

Yeah, I thought this through more and I skipped a few steps + stated some incorrect things.

The first step is to note that higher values of $\eta$ decrease the value of saving poor people's lives compared to rich people's lives. In the basic isoelastic utility framework, the value of saving a year of life is^[1] $$VSLY=\frac{u\left(c\right)}{u^{\prime }\left(c\right)}=\frac{c^{\eta }-c}{\eta -1}$$ which means it is higher for rich people than for poor people. Now, this is also true for log utility, but notice that the gap between rich and poor VSLYs is increasing in $\eta$, meaning that higher values of $\eta$ make it even less attractive to save a poor person's life than a rich person's life. This is a conclusion that nobody likes.

The second step is to note that the only way I know of to modify the isoelastic utility model to avoid that conclusion, is to add a set point to utility, so that $$u\left(c\right)=k+\frac{c^{1-\eta }-1}{1-\eta }$$ Then for a high enough set point, the VSLY will vary much more slowly with income, and rich and poor lives will be closer together in value. However, this is where the health vs income tradeoff comes in. If you have a high enough set point, income-creating interventions become unattractive compared to health-creating interventions, because most of a person's utility comes from their set point, not from being rich or poor, so there's little value to increasing their income a lot. So I was wrong to say that high $\eta$ would make income-generating interventions more attractive. [Edit: also worth noting that high set points would be incompatible with low VSL estimates in poor countries]

But the basic point is, the standard isoelastic utility model doesn't create much implication for health vs income, but it creates a repugnant conclusion about valuing rich vs poor lives. A modified isoelastic utility model that fixes that problem will have sharp implications for trading off health vs income.

Inconsistency doesn't lead to favouring income doublings for the rich; it just leads to inconsistency

The post gives the impression that inconsistent choices of $\eta$ systematically favor income doublings for rich people compared to poor people. This isn't true.

Consider three people, A, B, and C, with respective incomes of 5, 10, and 10 USD. Suppose we compare doubling the income of A twice (from 5 -> 10 and 10 -> 20) to doubling the incomes of both B and C (10 -> 20 each). The income doubling from 5 -> 10 for A has the same value as doubling the income from 10 -> 20 for B because we use log-utility across people. Doubling A's income from 10 -> 20 is less valuable than doubling it from 5 -> 10 because we use $\eta$ > 1 for each individual. Since the other three income doublings are all worth the same (A: 5 -> 10, B and C: 10 -> 20), we prefer doubling the incomes of both B and C compared to doubling A’s income twice. Now, since the income doubling for A from 10 -> 20 has the same value as that for B from 10 -> 20, it must be that we prefer doubling C’s income from 10 -> 20 over doubling A’s income from 5 -> 10. But that means we prefer doubling the richer person’s income.

Imagine that instead of doubling A's income twice, we considered doubling C's income twice.

U(2x C's income from 10 to 20) = U(2x B's income) = U(2x A's income) with $\eta =1$. And U(2x C's income from 10 to 20) > U(2x C's income from 20 to 40) with $\eta >1$. So U(2x C's income from 10 to 20) + U(2x C's income from 20 to 40) < U(2x B's income) + U(2x A's income). Since income doublings are worth the same across people, we get U(2x C's income from 20 to 40) < U(2x A's income).

So with the exact same example, we have concluded both that doubling A's income is worth more than doubling C's income, and that doubling C's income is worth more than doubling A's income. This is a pure logical inconsistency. It is not the case that the richer person's income doubling is generically valued higher than the poorer person's income doubling.

Likewise with the second example:

Say that, for example, doubling the income of the average earner in a country is worth the same across countries. Now, doubling the mean income in the US (~$50k) is worth the same as doubling the income of the average earner in Madagascar (~$500). However, within Madagascar, doubling the income of a richer person is worth less than doubling the income of a poorer person, so doubling the income of a person making $1000 is worth less than doubling the income of a person making $500. Since doubling the income of a person making $500 in Madagascar was worth the same as doubling the income of a person making $50k in the US, we have that doubling the income of a person making $1000 (in Madagascar) is worth less than doubling the income of a person making $50k (in the US). So we are again preferring doubling the income of a richer person relative to a poorer person.

Within the US, doubling the income of a $50k earner is worth more than doubling the income of a $100k earner. Across the US and Madagascar, doubling the income of a $500 earner in Madagascar is worth the same as doubling the income of a $50k earner in the US. Putting these two together, doubling the income of the $500 earner in Madagascar is worth more than doubling the income of the $100k earner in the US. So in this example, the inconsistency also favors doubling the income of the poorer person.

Now, this doesn't contradict the title of the post. I agree that pure logical inconsistencies in the way that we compare interventions are undesirable. But I don't want people to come away from this post with the conclusion that this inconsistency systematically favors interventions for rich people over interventions for poor people.

This inconsistency is not analogous to a rate of pure time preference

I'm puzzled at the argument for why inconsistent $\eta$ implies a rate of pure time preference.

The CEA roughly assumes that each treated person experiences the same persistent % consumption increases each year over the course of their life. These income benefits are discounted by our default rate, so that an income doubling today is worth 3x as much as the same income doubling in 48 years solely because recipients will be about 4 times as rich. At the same time, current-year income doublings in Madagascar ($500 GDP/capita) and Côte d’Ivoire ($2.5k GDP/capita) are valued the same[7]. This leads to the following weird conclusion:

In Madagascar, we value the income doubling of someone who makes $500 about 3x as much as the income doubling of someone who makes $2.5k. However, if the person who makes $2.5k lives instead in Côte d’Ivoire, we value their income doubling the same as doubling the income of the $500 earner in Madagascar.

Put another way, the CEA implies a 2.6% annual discount rate for pure time preference: even if the income % increases are as certain to occur in 48 years as they are now, we value an income doubling 3x more today.

I don't think I follow this argument. There's no time dimension in the Madagascar-Cote d'Ivoire example, so I don't understand how it tells us anything about the rate of pure time preference. Moreover, in the general CEA, the discount rate contains three factors: pure time preference, uncertainty, and diminishing marginal utility of consumption. Your example eliminates uncertainty, shows that there's still a large discount rate, and then concludes that that must reflect pure time preference. But it actually reflects the diminishing marginal utility of consumption, which you also note at the start. So then how does this imply a discount rate for pure time preference?

Choices of eta are probably back-filled from moral weights on health vs income

In practice, grantmaking by GiveWell/FP/AIM is quite heavily loaded onto health-generating interventions rather than income-generating interventions. But the moral weights on health vs income depend in large part on the marginal utility of consumption. Higher values of $\eta$, combined with low income levels for recipients, would make income-generating interventions much more attractive than health-generating interventions, and shift your portfolio substantially towards income-generating interventions.

This is an econpilled view that I'm quite comfortable with. But for most people, intuitions about the moral value of health vs income precede intuitions about the right value of $\eta$, so $\eta$ values are back-filled to be consistent with those intuitions. I think this is the true reason for the inconsistency you point out. $\eta =1$ is the value that people are most comfortable back-filling to match their moral intuitions about health vs income, and is very convenient for not having to measure income levels. $\eta >1$ is more realistic, but is admissible with these moral intuitions only when comparing income gains to income gains (within a program).

Now, that's not to say that $\eta >1$ is necessarily better. I think it's more likely to be true but was convinced by Alexander Berger's counter-argument that it provides worse prescriptions than $\eta =1$.

But regardless, it would be a mistake to think about $\eta$ choices primarily through the lens of how they affect comparisons of livelihood interventions, because any shift from $\eta =1$ would substantially affect income vs health moral weights, and most of its effect on your portfolio would go through that channel.

(Caveats: I am working at GiveWell, but views are my own and don't represent any larger position)

"these people have been the most effective altruists in history" is about them being effective and altruistic, not members of a community called Effective Altruism.

Good to know, what's the source of this info?

Self identification seems like an obvious condition. If you were sharing news that Mr Beast was calling himself an EA, none of these comments would apply.

Ahh, that makes sense.

Makes sense!