The Value of Life
overcomingbias.com
overcomingbias.com
You can drive the suggested analysis here as far as you want, but ultimately, you will lift your head and realize it's all useless for actual policy making wrt COVID-19.
The ultimate answer is that there is no ultimate answer. Abstract mathematical modeling for these sorts of questions is therefore mostly useless. Useful answers come from going in and dealing with lots of messy particularities in a very messy reality.
I like to think that this problem with quantitative rationality, where you build a model about one thing and get a very precise answer, but then realize your answer is really just another question, is exactly what's being alluded to in "42".
(e: moved this sentence to the bottom of my comment because it seems to be causing some distracting hostility: "This sort of thought process is exactly how you go about convincing a wise person to just give up on the whole hard core rationality project. It's an unintentional strawman.")
[1] Well, ideally. The US response to covid was pretty much [2]. If it wasn't clear, [2] was a rhetorical question and you should not do that.
42? I'm genuinely not sure what number you're asking for.
> Eventually somebody[1] has to make a high-level decision on which strategy to pursue.
Yes, of course, but that decision making doesn't require a quantitative model assigning value to life (or not). You can make a lot of very well-informed decisions without ever thinking about that particular aspect of optimization theory with any particularly high level of detail. "Aggressively avoid protracted exponential growth" doesn't require knowing anything about the value of life relative to other things.
Mathematical modeling can be useful for responding to covid-19. However, mathematical modeling for this question is not useful, because your answer gets plugged into yet another model where there's too much uncertainty for your answer to the have any quantitatively justifiable impact on decision making.
To give a toy example, spending a bunch of time figuring out the value of $c$ in $f(x) = x^n + c$ is a waste of time if you don't know much about the value of $n$.
>Yet it is easy to show that we can both have more money and save more lives if we are more consistent about the price we pay for lives in the many different death-risk-versus-cost choices that we make.
He's not even saying you need an accurate value, he's saying you need a consistent value.
TBH I'm not even quite sure what is meant by that assertion, but the article certainly doesn't contain a compelling justification and the claim is almost prime facie false.
There are such completely trivial counter-examples for the plain meaning that I'm not even sure what the author's intended meaning was. E.g., "lives are worth negative infinity" is consistent, and you'll always end up with more money and save fewer lives. Ditto for "1 life = GDP of the world".
But of course they're not a complete idiot, so maybe there's another explanation, that you could have arrived at with a dash of charitable thinking.
No. Smart people make simple mistakes all the time. Being wrong doesn't make one an idiot. Fortunately for me :)
Also, the realization that "lives vs. other-resource" is unnecessary to model because it's either dominated by other uncertainty or else results in deontology is not at all an obvious conclusion. It took me a decade to arrive there.
What I was pointing out in the above comment is how choosing extreme values for one resource or the other effectively gives you a deontological ethics that strictly prioritizes one thing over the other. You can solve the optimization problem if you want, but the solution is obvious. deontological ethics is the subset of utilitarian ethics where you don't have to do some calculations because you just max out the value of certain objectives.
> But of course they're not a complete idiot, so maybe there's another explanation, that you could have arrived at with a dash of charitable thinking.
Maybe. Can you explain why I'm confused, then? The plain meaning of the author's quote, even taken in context, seems like it has some trivial counter-examples. What am I misunderstanding?
BTW, I'm not being coy. I am being charitable. When I say "I'm not even quite sure what is meant by that assertion", I mean it. The thing I think the author means has trivial counter-examples, so the author must mean something aside from what I assume. Or else hasn't thought about the extreme values. Which would also be possible.
Given that the discussion is of a utility function for human life, the first assumption a reader should make is that deontology isn't part of the picture: it's incompatible with utility functions from the get go.
He's saying that valuing 2 lives that are the same to 2 different values will not be optimal, because if one is valued more than the other, then another identical life could have been saved for the price of the lower valued one, therefore saving 2 lives for less than the inconsistently priced option.
EDIT: to prove that negative values are non-sensical, assume you gain money by saving a life, then the only possible optimization is to save every life.
Do you disagree with this? How do you deal with the existence proof of systems which do use quantitative models?
(In the absence of models, there's still people who allocate resources, and resources are quantified. There is still a quantitative judgement made in the form of allocation. I'm finding it hard to understand your position in any rational sense.)
It's just a common unit, if you can save one life by investing 20$ more in healthcare, then losing one life to make 20$ is rationally neutral (considering the lives are equal based on some metric, e.g. expected years left to live).
All I see here is "The value of human life is incalculable, so just give up."
Am I wrong? What am I missing?
We don't have infinite resources or infinite capacity to distribute them. That means we need to make hard decisions about things like medical care. That is reality. If I get some kind of crazy-aggressive brain cancer that costs a billion dollars to treat, I fully expect to die.
The best way to make those decisions is to have some kind of model that can (a) be readily understood; and (b) helps us make those decisions fairly and with as little unintentional bias as possible.
There will always be bias -- it's part of the human condition -- but if we can be transparent about our biases and willing to discuss them, we open the door to improving our decision-making systems later on.
With that in mind, what would you suggest as a model for determining, say, how we budget for healthcare?
My solution is that the solution probably isn't useful so don't bother. Seriously. The game of assigning quantitative value to lives is almost never going to help you make better decisions.
> All I see here is "The value of human life is incalculable, so just give up."
Nope. It's exactly not that! I don't think it's incalculable. You can definitely choose a way to calculate it. Precisely, even. But it's going to be some complex function. And you're going to plug that function into another model. And when you do that, one of two things will happen:
1. you'll ground out in a deontology because you choose extreme values, or
2. the uncertainty in the other parts of the model will dominate.
In COVID-19, #2 is what happens.
> With that in mind, what would you suggest as a model for determining, say, how we budget for healthcare?
I suggest that any reasonable model would look more like an entire industry of mathematicians thinking about edge cases than what we would recognize as a single mathematical model. And even then the answer would probably suck. And definitely nowhere would you find it useful to have a quantitative assignment of lives vs. money, because anywhere you try to use that is going to have a ton of uncertainty that dominates the useful range of possible values. Which pretty much comports with my original comment that "there is no universal answer". I'm not an actuary or policy analyst, though.
However, models of "value of life vs. other-thing" are almost always useless.
Why? Because you don't care about that question. You care about other questions.
And, crucially, the models you use to answer those other questions tend to have so much uncertainty that your model of "value of life vs. other-thing" turns out to not really contribute anything useful to the analysis.
If I ask for a policy that maximizes the value of some function $f(x) = \theta_1 * x^n + \theta_2 * c$, for example, then will you focus your effort on modeling $n$ or $c$? What if I tell you that the best you can do is get $n$ down to an interval $[-100, 100]$? Will you then go on to think a bunch about what to do with $c$, especially if you know that whatever $c$ is it's probably between -1 and 1?
My suggestion is that, in most cases, "value of life vs. other-thing" is the $c$ in this example.
In the case of COVID, you want all your smart modelers thinking about how to minimize the chance of protected exponential growth within any region. If you do that, you have the right answer. The exact trade-off between lives and other things doesn't matter because, with covid, __preventing localized protected exponential growth is always the right answer__. The "lives vs other-thing" question is a complete distraction in the decision space.
> I can't pull anything out of this other than "models are useless, so don't bother", which is a non-answer.
Is it? Models are always modeling something! Modeling the effect of reddit meme spread on covid-19 spread is probably useless. That doesn't mean cluster SIR models are useless.
Don't model things that don't help you make decisions.
The “value of a statistical life” (or to use a better term, “value of a prevented fatality”), is weighed against other things in a large number of public policy choices. For example: environmental pollution, biodiversity, quality of landscapes, noise pollution, economic activity. It’s also important to aim for reasonable levels of prevention of different risk categories: food safety, road safety, air transport safety, medical safety in hospitals, industrial safety, etc. If public policy (via regulatory obligations for instance) uses very different implicit values for a prevented fatality, it means that more statistical lives could have been saved by allocating prevention effort in a different way.
https://news.ycombinator.com/item?id=22915837
I'd distill it as:
1. Every model should be presented alongside a discussion of whether the fitting process is well-posed[1]
2. If the fitting process is ill-posed, the model cannot be used to guide policy
3. If the fitting process is well-posed, but only via Bayesian regularization of some kind, before being used to guide policy it should be checked for sensitivity to choice of regularization, and the regularization scrutinized in exhaustive detail
4. Compositions of models must be checked for well-posedness
Quality adjusted life years is part of the analytical basis of funding of interventions in the UK's national health system (NHS).
Does this change your position?
When the effects of sacrificing lives are more disconnected, the model becomes less useful. In particular, I don't think these sorts of models are useful for making decisions about how to respond to COVID, which is what this article is about.
Or you can pick a number from Wikipedia [0]. Somewhere between $50 thousand and $10 million.
I agree with what I suspect is your central point; which is when it comes to COVID-19 there are other more important uncertainties than the value cost of a life. But it is useful for an order-of-magnitude check to see if the response is overblown.
[0] https://en.wikipedia.org/wiki/Value_of_life#Estimates_of_the...
It's easier for us as a species to say what a star billions of light-years away has been "doing" since its "inception" and the most probable way in which it will "die" than to say what the 5-year old kid next doors is going to do in a year or two, heck, what he's going to do tomorrow.
There is far less uncertainty around COVID-19 now than there was at the beginning of the year. It is possible to see which countries are successfully tracking and tracing to eliminate, which are entering second waves and need to mitigate, and which haven't even finished their first.
https://www.lemonde.fr/les-decodeurs/article/2020/03/27/coro...
References? COVID-19's behavior has been quite simple so far. Exponential growth with variations. It's more predictable than the weather next week, overall.
The American curve and European curve are somewhat different, yes but the differences can be explained by the total fucked-up the American virus control efforts have been.
Oh, and the American failures were accompanied by complaints about uncertainty and how much virus control efforts would cost. Now, we will find out how much a lack of control is going to cost.
What do you mean with behavior? People are still discussing how it spreads.
The latest news is it travels as aerosol and that in badly ventilated rooms keeping 1.5m distance is not going to help much. And also that the amount of virus particles you inhale determines how sick you get.
So it is only predictable when we know how it is growing exponential.
The still ongoing discussion about how it spreads creates uncertainty.
Covid is a simple as any of the things we meet in daily, in aggregate, as simple as rain or dirty. The behavior in detail of any of these things is incredibly complex, of course. The forms rain takes are distinctly complex but is nearly falls roughly downwards and gets things wet (exceptions to everything, of course).
People have more incentive to look at the details of Covid 'cause it's much deadly than rain or dirt. But even more, lots of people use Covid's uncertainty to argue against any mitigating measures they find inconvenient - and that part is kind of despicable.
For example they might claim in the early stages of an epidemic that we actually just have linear case growth. It is then up to the modeller to try to justify why that isn't the case, which in limited-information regimes can be near impossible in any rigorous sense, for the reasons you describe.
However, assumptions are important, and showing decision makers what might happen given certain assumptions (and providing a justification for those assumptions), which is part of what a model does, can cause them to reassess their current thinking, and it is for this reason that these kinds of models can remain useful, even if it is not possible to reasonably distinguish between some set of models given available data.
Returning to the epidemic example, justifying why exponential rather than linear growth is likely in the early stages of spread is something that can be done on an intuitive level, and explaining this to policy makers, and showing them the range of possible outcomes that are consistent with current (at the time limited) knowledge, can be extremely powerful.
An alternative way to explain the meaning of “large uncertainties” is that you can fudge input numbers slightly to get whatever output decision you want, so whoever is making the policy decision is likely to keep fudging numbers till the outcome “feels right”. At that point, the modeling is just dangerously misleading pseudo-science.
An intuitive approximation of the decision based on time averages is to “play it safe” in the presence of fat negative tails. “How safe tho?” is a very hard question to answer because of the uncertainties involved (as parent post explained).
If lawmakers are deciding the price, then we're already wrong.
Each person perceives the subjective value of their own life differently. There shouldn't be a unified "value of life". Each person should do their own cost-benefit analysis and decide how much they're willing to risk their own safety. The incentives should be placed in such a way that each person's decision doesn't directly impact other people's lives though.
And maybe those that "want lower estimates" don't really want lower estimates, but they don't want any specific estimate to be shoven down their throats. In the same vein that those that want less safety regulations don't really "want more accidents", they want more agency and freedom of choice so that each person can make their own decision depending on their priorities.
The "ship pollution to poor countries" is a great example of this -- hey, we have this metric, and according to this metric, it's a net win. This is one path to doing monstrous things in the name of minimizing a metric, rather than actually making progress.
To convince yourself that the task of "value of human life" is futile, the following thought experiment suffices -- there are different penalties for deliberately causing the death of another (and distinction based on the quality and recency of those motives) vs. negligently causing a death vs. recklessly causing a death, in all justice systems invented by humans.
The article says that attempts to do this have "shown puzzlingly great variation across individuals and contexts", but then attempts to reduce it to new and interesting metrics instead. Uncertainty is the fact of life; this pursuit is meaningless except as a post-mortem examination of the impact of an action taken in ignorance of the metric. If the metric is involved in the decision making in any form it immediately becomes useless and counterproductive.
How does that prove the futility of the exercise? It only proves that there must be more than one way to do it, and that the right method depends on context. There are metrics for use in criminal cases, civil cases, insurance, etc. It's not like we can fail to make these determinations -- failing to put a value on human life in each relevant context is akin to saying there is no value to human life at all.
This is the crux of the problem with metric-based examination of nearly everything except physics.
It is not nearly akin to that. If anything, saying that you can have a metric that measures the value of human life is much more akin to saying there is no value to human life at all -- all of life is "haggling over the price" as it were.
Saying that it cannot be measured is just making an epistemological declaration of lack of knowledge. Not of the general form of "well, we just have to find the right variable and plug them in to the right formula" but of the form of "this is not well-suited to being reduced to a metric, as any such reduction will mask aspects of its value that are obvious but not easily measured".
To be clear on the dangers (as if the McKinsey-fication of "dump the pollution in pooristan" wasn't enough) the problem is that given an imperfect approximation to some theoretical perfect metric, we have absolutely no way of determining how imperfect it is. There's nothing to measure it against except other potential metrics. There's absolutely no concept of ground truth -- the universe will not correct you (as it will if you measure mass incorrectly when doing physics).
First, I don't think there is a universal model that we can apply to every possible case. Budgeting medical care, for example, will depend pretty heavily on funding cycles, and a surplus at the end of the quarter raises the question of "could this have been better allocated to serve patients' medical needs during the quarter?"
Off the top of my head... I'm thinking that something like a lifetime maximum with some sort of payback mechanism may be the answer. E.g., you get $2M of medical care over the course of your life, but when the medical system has a surplus, those numbers are adjusted.
Liability, on the other hand, is a whole 'nother ball game.
A manufacturer that deliberately chooses not to implement a safety feature because "the lawsuits will be cheaper" is making both a moral and an economic choice, and that's something that needs to be addressed via both torts and corporate law. Broadly speaking, I think that putting the customer -- rather than the shareholder -- back in the economic drivers' seat would do a lot to remedy this.
It discusses various ways that the value of a life have been calculated and how it has been used to determine whether product labels are worth changing to save lives. They suppose that the shutdown could have saved $10 trillion worth of lives.
I suppose it could have cost $10 trillion worth of lives. Not sure what the calculus of suppose is exactly, once I have figured that out I can take this to the bank.
> Infinite – Pay any price for any chance to save any human life.
> [...]
Say you take this position, that the value of a human life is infinite. Then you come to a situation where you have to make a trade-off: some must die in order for others to live. Something of a Sophie's Choice, though perhaps less dramatic. Now what?
This does happen! When it happens it's not necessarily obvious, but it happens. TFA gives an example.
Putting an infinite value on human life isn't practical. Putting a finite value on human life seems crass, but is practical. We just have to be a bit crass then -- what else can we do?
It's like the trolley problem -- the reality of that problem is somewhere between "how the fuck should I know what this lever does, I'm not a trolley engineer" and "what if the people move".
If one person, Bob, seems likely to you, a police officer, to murder another person, Alice, then you don't say "well, Bob has greater expectations of higher lifetime earnings and Alice is too risk-averse". The idea that you can look at this outside of the direct context by examining a metric is ridiculous on the face of it.
I mean, in a wrongful death case, nobody is going to die for anyone to live.
The healthcare thing is more nuanced, and is part of the problem with any sort of centralized decision-making around it. On an individual level it's not usually any sort of tradeoff -- your choices don't make anyone else live or die except in imaginary fantasies. For governments they do have to make the choice AND THAT IS EXACTLY THE PROBLEM. Governments have been dominated by the pursuit of efficiency against metrics and avoiding any responsibility for outcomes because it's a "science".
If more people are dying than should be dying, then you just spend more in accordance with your principles; this is the way that the NHS (for example) was designed to run, until the 1970s, when this obsession with deference to "experts" and pursuit of metric-driven efficiency (not just in England but in most other countries too) drove it to become a managerial culture and alienated the entire workforce associated with the program.
Really? What about your choices regarding people you have power of attorney over, or, say, minors whose guardian you are?
Should a family bankrupt itself to pay for treatment for a child whose life expectancy with treatment is only a few years anyways? Should a family bankrupt itself to pay for an elderly member's care who has no assets left and little life expectancy? These are difficult decisions to make if you should ever have to, and god forbid you ever have to. But they do come up in real life, and implicitly or otherwise, people do put a value on life.
I don't know how much they deny it; what fascinates me is that different departments of the US government assign different dollar values to a life (e.g. when it is too expensive to mandate a change to the road building code).
Driving 10km/h slower to save lives? People could accumulate hundreds of man-years essentially not lived while driving very quickly.
Speed limits have an implicit value comparison. If you want to minimize dwaths you could ban all modes of transportations or set a 1 mph speed limit, but we value our economy and time more than the amount of deaths caused by higher speed limits.
You aren't evil for saying human life is not infinitely more valuable than all other life. There's a point where the scale tips.
I enjoyed reading a book by the late Finnish conservationist Pentti Linkola, who said that to achieve healthy levels of biodiversity that the value of a species should become less valuable as it becomes overpopulated. (e.g. house cats are not as important as tigers right now, given tiger endangerment). It applies to humans.
(Slate Star Codex going down is related to news item https://news.ycombinator.com/item?id=23610416 ; https://slatestarcodex.com/2020/06/22/nyt-is-threatening-my-... )
We live in a world of great abundance of every measurable sort, and insistence on putting economic expansion ahead of protection of our friends, families, and neighbors would be better analyzed using the lens of ethics rather than that of finance.
We could, say, ban driving except by professional trained drivers, and get rid of tens of thousands of deaths per year, at the cost of "only" a hit to the economy. Should we do that?
Would this analogy hold up if we instead considered the cost of defending against an invading army? Would it really be reasonable to ask if we had enough money to build the machinery to hold them at bay?
In past times we and other successes societies have worked in concert to defeat threats to our collective and worried about fixing any economic consequences later.
Value of life is relevant when comparing different possible actions that cost different amounts of resources. If it's clear that the benefit is more than the cost, you might not actually have to do the analysis. But if the cost is measured in trillions of dollars, then it becomes very relevant to see exactly what the expected benefits are. If the invading army is going to kill a hundred thousand people, and defending against them requires using up resources equivalent to letting five hundred thousand people die, then it's very much a question that should be asked.
Black people are dying at a rate more than 1.5 times higher than their population share [0].
I'm also not sure what you mean about my estimation of abundance. We have all of the resources we need to focus our efforts on minimizing the spread of this disease and building the infrastructure to find a cure. What resource do you think we lack?
It is one thing when talking about fungible goods, just things of which any two can be compared and evaluated. A box of crackers, maybe a brand of crackers. A donut versus a cookie or some other snack; compared to a healthy food or complex meal of some degree.
Money is supposed to be good at valuing things that are willing to be traded.
This is why placing money on quality of life, and on medical care, and the basics needed to live is unethical. Ability to pay does not assess value. As far as I know, in more morally aligned countries, waiting lists for 'spare' organs (from the recently no longer in need of them) are based mostly on who is within reach of viable transfer completion, first in 'line' first received. If our medical technology were better even that wouldn't be necessary. Those lines would see output from growth fabs and be fulfilled in that order.
Emergencies are one thing; triage is used by doctors to take a logical, predetermined, approach to making decisions no one should ever have to make. They're going to suck anyway.
The current global pandemic is a different kind of emergency. It's like some comic book villain has a death ray that turns n% of the population into sub-critical masses of radioactive material. Get enough together and there will be 'clicks' (on a Geiger Counter), maybe cancer. Get even more together and there will be an actual explosion (hospitals overflowing).
It's a __preventable__ emergency, where if people take the correct steps the risks are reduced or eliminated.
* Every normal person wearing a mask that disrupts outward airflow and reduces the spread of exhaled particles, REDUCES the exposure risk of everyone else to that person. That's why __EVERYONE__ needs to wear a mask, not just some people.
* The same is true for properly and fully washing hands, to reduce contact transmission.
* An even more effective strategy is to limit, or even eliminate if possible, exposure between people. That's what everyone avoiding unnecessary in person meetings is about and why working from home (when possible) is the best strategy.
The issue with that last step, however, is that our entire economy is absolutely not oriented to supporting that behavior. Major systemic changes are necessary to support it. Even things like the design of air-circulation which should be optimized to drive expelled particles down to the floors (much like in cleanrooms). At least in public spaces and work settings (including warehouses). Though it might be cheaper to have tele-operated robots controlled by workers in a videogame like way for the warehouses.
If 'we' as a society respond to the global pandemic correctly, maybe we can even start to automate a lot of the jobs that can be done by robots and focus less on everyone working as much as they currently do.
This whole article is based on a false premise. We can spend x dollars to stop this virus from getting to poor old grandma. We cannot stop this virus. Any vaccine will not help significantly either as it has mutated many times and will continue to do so. The shutdown and stay at home were only measures to slow infection rates, buying time to prepare hospital beds, tests, masks ETC.
This virus will continue to spread until 80% of the population has had it (herd immunity). The financial cost has been paid, we are re-opening and will not close again unless we overwhelm the measures that we have put in place. The second wave of the 1969 pandemic virus is still with us folks (it's one of the seasonal flu varieties). This one isn't going away save a miracle.
Pandemics are nothing new. We get through them and move on (sounds harsh but is the reality). We are a communal people. It isn't possible to "burn out" this particular virus. This article seems to think we somehow can buy our way out of it.
> This virus will continue to spread until 80% of the population has had it (herd immunity).
If the virus mutated as rapidly as you assume (I haven't seen any sources for this) there wouldn't be any natural herd immunity either.