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Generally speaking, if you are going to offer criticism, try and offer a solution or ask a question that would address that criticism.

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?

> if you are going to offer criticism, try and offer a solution or ask a question that would address that criticism.

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.

Honestly, this looks to me like a word salad -- I can't pull anything out of this other than "models are useless, so don't bother", which is a non-answer.

No, models are useful.

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.

Sometimes it's fun to do things that are pointless.

> 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.

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.

I think their point is something like what's discussed here:

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

https://en.wikipedia.org/wiki/Well-posed_problem

Wow, thank you so much.

> game of assigning quantitative value to lives is almost never going to help you make better decisions

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?

Not really. National healthcare systems are maybe the one reason why I said "almost never" and not "never". When your problem is literally and directly, not indirectly, about assigning finite resources where lives are on the line, that's the cases where a model that relates the two is most likely to be useful. And even then most healthcare systems don't even try.

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.

It doesn't change mine! This came into vogue in the early 70s when they wanted to cut funding as much as possible to make the operation more efficient while still providing a high level of care, according to these "metrics" like QLAY, which are fundamentally broken (as are and have been all attempts to reduce to metrics). It managed to operate without them with a great deal of satisfaction from both the providers and the patients until this came in, and then things got really shitty while improving along the metrics so it was nobody's fault because it was just "science".

> But it's going to be some complex function.

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...

I'm not sure it's useful even as an order of magnitude check, because there's so much uncertainty about how many lives different policies cost. People who believe a response is too loose inevitably also think it kills more people than their opponents; those who believe a response is too strict inevitably think it saves fewer.

Not the OP, just wanted to add that not all problems have solutions, especially the hard problems. Believing otherwise is very "technicist" (for lack of a better word), is believing that the "world" is a closed-system that "moves"/behaves in a predictable and computable manner. It doesn't.

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.

All problems do however have outcomes, and doing nothing still results in an outcome.

But at least we're honest with ourselves that we don't know what we're doing (or what we're about not to do, in this case).

Sure, so give me a number. Eventually somebody[1] has to make a high-level decision on which strategy to pursue. And they have to give directives that can be followed by people who don't know your entire thought processes. That's what it means to be a bureaucracy. So which is it, will you choose an imperfect quantitative model where some numbers are pulled out of your ass? Or will you just let every low-level functionary pull entire decisions out of their individual asses and hope something resembling a coherent strategy will emerge?[2]

[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.

> Sure, so give me a number

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 $n$.

Hanson explicitly disagrees, to quote:

>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.

>> 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.

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".

If the counterexamples are so trivial and obvious, the author must be a complete idiot, right?

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.

> If the counterexamples are so trivial and obvious, the author must be a complete idiot, right?

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.

A "counterexample" like infinite negative value breaks the system so easily that you ought to consider whether it's out of bounds, instead of being so certain that it's a counterexample.

But Deontology is an entire school of ethics that basically does exactly that. Calling all of it "out-of-bounds" seems like not the most reasonable assumption for a reader to make.

Does exactly what?

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.

-infinity is clearly out of bounds as the whole discussion is about the policy to take to save the most lives, therefore assuming lives have values (or else you wouldn't want to save them). Even the quote itself implies it with "more money, more lives saved", clearly implying you want to save lives.

Putting in nonsensical extreme values is mot how you evaluate a claim like this. I dont think negative value is in the domain of that optimization function for any rational argumentation. Let's say it costs something to save a life, then the domain would be ]0, infinity[.

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.

In order to make trade-offs - balancing benefits vs opportunity costs - in a health system, you need a common unit. You can't do a case by case analysis everywhere, and you can't consider categories of cases separately or you'll get deviance in evaluation and global inconsistency, which directly implies less efficiency and worse outcomes for some categories.

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.)

Agreed, I think people get too caught off on deontology when assigning monetary value to life.

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 of the uncertainty around COVID-19 means that we'll build whatever complex models we want, but then just stare blankly and wonder how the hell to choose values for various coefficients.

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.

"COVID-19's behavior has been quite simple so far."

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.

Overall behavior - how it spreads and effects people in aggregate. It spreads by air primarily (aerosol isn't "the latest news", it's what's been said from the start with any other transmission method speculative). Yes, a zillion uncertain details.

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.

> All of the uncertainty around COVID-19

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...

With respect to specific modelling efforts policy makers sometimes act as antagonists because, without joint modelling of all the concerns they are trying to balance, they are forced to rely on their intuition. This leaves society particularly exposed to the character traits of our leaders, because it is they who end up modelling the interaction effects (in their heads).

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.

To add to the above, the distribution of population-level COVID outcomes has fat tails (the system evolution is non-ergodic), so computing point estimates with ensemble average “expected values” is junk modeling. And computing the (correct) time averages requires owning up to the uncertainty and fatness of tails (which is a very hard thing to model), so people have the lamppost bias of doing the easy (but useless) calculation.

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).