The UK government (and various other governments around the world) have decided, at least in effect, that the expected utility of having a lockdown is greater than the expected utility of not having a lockdown (or that the expected disutility of having a lockdown is less than the expected disutility of not having a lockdown).
[For a very basic primer on expected utility, decision theory/risk-benefit analysis, see this recent blog post from me.]
Let’s start with what’s called a ‘toy model’, a very simplified version of the situation. (This isn’t going to get that technical, so don’t worry.) I’ll start by assuming that the probabilities involved are 50/50.
Several problems should be obvious at this point. One is, how do I get these utility and disutility scores? This is a good point, but that doesn’t really matter at the moment as I’m just going to be illustrating some general principles. And anyway the serious modellers will be trying to use objective monetary values instead (although I do think that these will be inadequate to the task, especially when it comes to expressing the damage done to society).
Another issue is that the model should have a ton more possible outcomes, corresponding to how bad a killer Covid-19 may or may not be. And a lot more actions, because we can consider various combinations of things we could do, and other things. These points are true, but I can still make my general points using the toy model.
Another thing you might say along these lines is that we really need to be looking at varying lengths of lockdown, as obviously longer lockdowns have much greater damage than short ones. This last point is relevant, and I’ll say more about it below.
First thing to look at is 50/50 probability assignment. You may have already wondered what justifies the use of those particular probabilities. And this brings us to the heart of one of the big problems with the lockdown. If we vary the probability then our expected utilities will change a lot. My view is that while there’s some possibility that Covid-19 is a mass killer, the probability of this is on the low side. If we run the table again but with my probabilities, then we get a different outcome. (I’ll assume 0.2 here, but in actuality I’d go lower.)
You can see that this change in the probabilities gives us a different result. This time, not locking down is the more rational course of action. And we also see the general, and under-appreciated point, that the less likely the mass killer outcome is, the lower the expected utility of the lockdown. You can’t just look at the utility of the lockdown outcomes, even assuming that Covid-19 is a mass killer. You have to weight it by the probability of that. And even if you think that is more probable than I do, that probability is never going to be 100%.
Now, it may be that with the government’s figures (assuming they’re even doing this sort of thing) the lockdown would still be justified even with a low probability assigned to the mass deaths scenario. You could easily rig up the sort of table I have used to show this, where you can just plug in whatever utility scores suit you. And maybe the real modellers advising the government (assuming their are any) have actually assigned a low probability to this, but their results, based on better and more objective monetary-based utility scores, still support the lockdown. My suspicion, though, is that they haven’t assigned a low probability.
But anyway, we can say this. It looks like the expected utilities of both courses of action are currently (in the UK, and probably the US too) in the same ballpark. Lockdown is comfortably higher at the moment, but not massively so. But as we have just seen, a change in probability can have a big effect on the expected utilities (and the same is true on a change in utility values). So a change in the probabilities can easily reverse the situation, so that lockdown becomes the irrational action.
Are any of the probabilities changing? What does seem to me to be clearly changing, as time goes on, is the probability of the mass deaths scenario. I don’t mean because of the lockdown. I mean that the claim that Covid-19 is a mass killer is becoming more unlikely as time goes on and we don’t see any mass deaths, even in Sweden which has no lockdown. We are certainly seeing evidence that Covid-19 is a killer, possibly even worse than influenza, and also evidence that Covid-19 causes serious illness in a lot of people. But the once-in-a-century mass killer claim isn’t getting much support from the real data, the sort that I’ve been looking at, even in Italy. The mass deaths are still only occurring in the computer models.
Even the most recent media reports, once we take into account how misleading they are (for example, daily deaths currently being reported in the UK press aren’t totals that take place on just the previous day, they’re totals that are spread out over a number of previous days), aren’t going to bump figures up to mass death levels. This doesn’t mean that the mass deaths scenario cannot be right, and cannot happen further down the line, but it means that the probability of it being right is receding. And that means that the expected utility of the lockdown must also dwindle. Conversely, the expected utility of no lockdown will rise, as that is increased by the increasing probability of Covid-19 not being a mass killer.
(An alternative version of this argument, which perhaps is closer to my view, is that the probability of Covid-19 being a mass killer has always been low, and remains low, and the UK and others governments have simply made a mistake when they increased their probability estimates of it a few weeks ago, and this is becoming more obvious as time goes on, and it’s time to reverse this mistake.)
You might, of course, take the opposite view to me, and say that you are strongly persuaded that there is a high probability of Covid-19 being a mass killer. This response, I would say, is not credible. The data we have for Covid-19 is fairly flimsy at the moment, as we don’t have much in the way of hard data on transmission rates and fatality rates. In addition, the studies that claim mass deaths will happen are based on computer models (such as Neil Ferguson’s) that we should have serious doubts over, due to (a) the poor track record of such models, particularly Ferguson’s, (b) the black box nature of these models (Ferguson, for example, still hasn’t released his code), and (c) rival studies from serious scientists which come to different conclusions. The onus is strongly on anyone who holds that there is a high probability of Covid-19 being a mass killer to back it up with hard evidence.
Bear in mind that assigning a high probability to x means that we are very sure of x. How, though, can anyone say that we can be very sure, or even pretty sure, that Covid-19 is a mass killer when so many experts are saying it isn’t? And when it has only killed a tiny fraction of the world’s population (0.00125% at last count, and that’s probably an overcount)? Even most of the alarmists seem to be operating on the basis of better safe than sorry, which is what you say about low probability outcomes, not high probability ones. So this view is not a serious one. But, as I have said, if the likelihood of Covid-19 being a mass killer is becoming more and more unlikely then the expected utility of the lockdown plunges as we revise this probability downwards.
The probability of economic damage, on the other hand, is very high. It’s a virtual certainty that there will be extensive economic damage, the only question is how much, so the horribly negative expected utility will remain horrible. It would be incredible, I think, if the expected utility of a long lockdown outweighs the expected utility of no lockdown (or no lockdown but with some other measure like protecting the vulnerable).
Update: Speaking of the economic damage, there is another important matter to take into account here. The longer the lockdown goes on, the more economic and societal damage is done. (In reality we should be modelling a range of lockdowns of different lengths. You can see why these models start to spiral out of control once the situation gets complex.)
That means that the expected utility score of the lockdown will also rapidly diminish the longer it goes on, as the economic damage score goes up. A lockdown of two weeks, that does some damage but not a huge amount, and you could see how it may have a high enough expected utility score to make it rational to do it. But a three-month lockdown, which will involve vastly more economic damage, will have a vastly lower expected utility score. Six months is economic armageddon.
Is the expected utility score of a long lockdown really going to outweigh the expected utility of doing nothing (or having more moderate measures that fall short of a lockdown)? Of course we cannot say for sure without seeing some actual utility and disutility scores grounded in reality, but it seems unlikely. It’s going to take an incredible amount of deaths to justify contracting the world’s economy by 25% or more, especially when we consider that such a contraction would itself cause a lot of deaths and misery and poverty and ruined careers and ordinary desires unfulfilled.
Update 2: The only public intellectual who has tried to do any real calculations of this sort is Toby Young (see here and here), although he assumed for the sake of argument that Ferguson was right and the mass deaths he predicted would occur. I agree with Toby’s conclusion that the lockdown is not worth it even if Ferguson was completely right, but of course in reality I think that the chances of Ferguson being right are low, which makes the lockdown vastly more irrational.
Update 3: Just to make clear, I’m not generally an advocate of the government making decisions on the basis of this sort of population-level utilitarian economics. But this is basically what the government is doing, even if they’re not explicit about it. I’m just pointing out that if we use this sort of analysis it seems more likely that no lockdown wil still win out over lockdown, once we take into account the low probability of Covid-19 being a mass killer.
34 thoughts on “Covid-19 and decision theory: some general morals to draw”
Aha, so you’re pretty much looking at the government’s past decision. In that case it’s worth pointing that their decision was based on the data they had then, not the data they have now. Which means it’s also worth pointing out that you were almost immediately examining the publicly available data concurrent with the start of the lockdown, and immediately questioning the policy.
It seemed clear enough three weeks ago that there was no evidence that COVID-19 was a mass killer.
I get the feeling there was no careful cost-benefit consideration; that the politicians were presented with a politically nightmare prediction and panicked. I hope they are also being presented with the much clearer economic armageddon nightmare.
Apart from the utilitarian issues, it is necessary to calm down a panicked public. I doubt that simple utterance of Mr. Jones’ catchphrase would do the job.
To that end the government needed to be seen to do something, and preferably something that involved the regular joe. Which it has.
Despite certain wilfully blind people the only available way of ending the outbreak is the acquisition of herd immunity, and unless a vaccine is in production soon that will mean a lot of people being infected. That is not a choice it is just be nature of infectious diseases. As you point out it is unclear how unpleasant the results will actually be, but the public has been led to expect the worst.
Measures have been taken to quell the panic and ensure that those needing treatment actually receive it.
The ticklish part is getting a people who have panicked to the point of fearing each other’s proximity to actually go back to normal or at least towards normal. Especially as there will be plenty of Medics and Journos eager to prolong the “emergency “.
> the politicians … panicked
Yes. The sensible approach discussed in this post probably isn’t going to play much part in the government’s decisions unfortunately.
The saddest part of this whole disaster (of hysteria, not a virus) is that the public has lapped it up. There’s no sign of popular skepticism of coronapanic. Lockdown obedience, so far as I can see, is near complete, helped by Boris’s strangely brief and comfortable visit to an ICU. So they’re not under much pressure to take the strain off the little people. The little people want firm measures and they’re getting them good and hard.
The lockdown will have to come off before we are completely wiped out economically. Figs suggest that the USA already has MILLIONS more people unemployed than at the height of the 1930s Depression. I would be willing to defy the lockdown NOW and I think a lot would already agree but the shops and the sheep would still be on the states side. Once they realise they have been ruined over a mirage and their own hysteria –and another few weeks without the “exponential” mass deaths will surely do the job–then they will be very mad against everyone but themselves of course.
> Measures have been taken to quell the panic
Are you in a parallel universe? The one I’m in has had systematic full volume Coronapanic for the past three weeks, and it isn’t slacking.
I agree that the ‘public has lapped it up’ but greatly assisted by a bug eyed, screeching MSM where there has been very limited (if any) time for any alternative viewpoints. The worse case of this was a couple of nights ago when Ch 4 (I think) showed videos sent of people literally drawing their last breath in hospital. These were sent in by their relatives because ‘they want to show the public how terrible this virus is’. This is an utter disgrace. Then you have people clapping for the NHS under the misguided view that all hospitals everywhere are ‘like a war zone’ To top it off I also read that the websites of scientists in Germany opposed to the measures being taken have been closed down. I wonder why?!
How did the relatives have these videos? I thought this virus was so dangerous no relatives were allowed to visit.
> Once they realise they have been ruined … they will be very mad
I hope you’re right but I’m not optimistic. My fear is the our rulers are pleasantly surprised at how easy it was to get the populace to step off an economic cliff. It must be tempting to see what else can be extracted from them.
How about requiring some sort of certificate or test result to declare that you’re healthy enough to travel? Millions would need to apply, for a suitable fee of course, and there’s a £Billion or two for starters.
I’m sure the creative minds in government and their corporate partners can come up with more ideas. If the public show that they’re credulous fools who are ripe for fleecing, wouldn’t it be a waste not to oblige them?
“Millions would need to apply, for a suitable fee of course, and there’s a £Billion or two for starters.”
This doesn’t make any sense to me. Why would a government hell-bent on “seeing what can be extracted from the public” spend hundreds of billions in benefits & employment support in the hope of somehow charging enough for a certificate to make a couple of billion quid.
I can buy the argument that they’ve made a bad decision simply because the political consequences of being accused of “putting the economy before lives” are intolerable to them, but the idea that it’s some kind of state money-spinner feels absurd.
Well Dave I tend to agree, but when they look how much is the petty cash tin, they might be tempted. New taxes will have to be levied.
I have always thought that the lock down was purely a political decision (i.e. Boris bottled it) rather than being informed by any science.
This comment by BecJT on Disqus on a recent Spectator article
https://disqus.com/by/disqus_2FurlhXsuK/
supports my prejudices about politicians so I prefer to believe it:
BecJT 2 days ago
I have a neighbour who is a Tory Chairman, his candidates won a lot of seats in last election from Labour, is very well connected. Just got off the phone to him. You won’t be surprised to learn that they KNOW this is shaping up to be Foot and Mouth 2.0, that they aren’t really saving lives, and are killing many more due to lock down, he also said they are calling it, and I quote, ‘economic armageddon’. They know the austerity that’s coming will kill many more. I said so why are we doing it then? And he said, ‘no prime minister wants to go down in history as the granny killer, it’s the right POLITICAL decision’. I said, but you are killing so many more and he said ‘we know’. He basically said that they know that the public are in such a tizzy, they won’t countenance common sense right now. So there you go, we are going to tell in a handcart on the back of middle class hysteria. And when Leveson 2.0 rolls around, I hope our absolute shower of journalists who brought this down upon us go to jail.
As Prof. Drummond says: “Another issue is that the model should have a ton more possible outcomes, …. And a lot more actions …”
It seems we would not need particularly sophisticated modeling to suggest some less damaging alternatives to total lockdown. For example, lockdown only of the At Risk population of those who are elderly & medically compromised.
Academics and politicians seem to love the expression “herd immunity” — probably because they already think of us peons as their herd. Still, the point about “herd immunity” is that lots & lots of people have to get infected — preferably the young & healthy who (we now know) will probably not even notice they have been infected.
Back in the Bad Old Days before vaccination for chickenpox, if one kid in a neighborhood got the illness, concerned parents would send their own children to stay in that house for a sleepover, to try to get their own children infected while they were young enough to get over it with no long-lasting problems. Maybe a thinking government could have a campaign urging healthy working age people to do their civic duty by going to soccer matches and rock concerts and crowded bars — and get infected with C-19!
Stupid as that may sound, is it any less stupid than police helicopters patrolling the bonny, bonny banks of Loch Lomond, to make sure no citizen gets out to enjoy being alone in the virus-killing sunshine?
Any thoughts on why The Economist are so keen to hype the virus? I pasted a link of their promoted Tweet claiming that official figures underestimate the death toll but it was blocked by your firewall.
https://en.wikipedia.org/wiki/The_Economist#Organisation
Given Holland & Barrett the health food store have seen their own staff petition that they should not be counted as an essential business and allowed stay open, voting to lose their jobs, we are well into mob hysteria.
I’ve heard from people in education that the school closure was more about staff refusing to come to work than anything else
“I get the feeling there was no careful cost-benefit consideration; that the politicians were presented with a politically nightmare prediction and panicked.”
That is my feeling as well. In NZ Ardern has stated she decided on the lockdown policy when a friend of her’s in the UK said he had it and said it was ‘really bad’.
I’m not kidding.
I’m reminded of the cartoon’s where everyone runs from the huge, scary shadow and as it comes into focus it’s an ant walking on a lamp.
Full time tracking via your phone would be the first thing they will want. It will be handy for them in so many ways.
Schools are the main channel for herd immunity. Shutting them is an act of madness.
It’s an epidemic of massive pussies. Totally agree on the teachers putting pressure on closing the schools, fear is in control.
*although I do think that these will be inadequate to the task, especially when it comes to expressing the damage done to society*
Occam’s razor: simplest explanation most likely to be correct: it’s *intended* to damage society. Supposing it to be true, that’s the meaning of Conquest’s Third Law of Politics.
One can’t underestimate corrupting influence of political power. Martin Amis claimed that he became “intolerable” when he was given a secretary as a young political editor ‘high on the power’.
Boris Johnson is a communist. If Jeremy Corbyn announced an amnesty for people here illegally he’d be denounced as communist by the same people cheering for Boris. ‘Communist’ being another way of saying pursuing political power for its own sake, because that’s all communism really means.
GK Chesterton was on the money a century ago prefiguring Conquest’s Third Law:
“Bolshevism and Big Business are very much alike; they are both built on the truth that everything is easy and simple if once you eliminate liberty. And the real irreconcilable enemy of both is what may be called Small Business “
Re the schools and others closing due to staff feeling anxious.
How many would be quite so keen to avoid work if they had to bear the economic consequences directly, i.e. pension fund dropped 50 % and no money coming in.
The biggest problem for the lock down is it’s advocates and enforcers do not suffer any loss of income or pension themselves.
That is my take exactly on this utter nonsense.
And, I feel the real worry is yet to materialise: What happens when, next Winter, someone coughs in China?
> Why would a government … spend hundreds of billions in benefits & employment support
That comes from taxes, borrowing and money printing. Business as usual.
> in the hope of somehow charging enough for a certificate to make a couple of billion quid.
The profits go to well-connected contractors who reward their political benefactors with speaking engagements, directorships, consultancies etc. The “revolving door”.
I think you need to catch up a bit on how Democracy works.
> Any thoughts on why The Economist are so keen to hype the virus?
What, do you mean you found some mainstream outlets that are *not* hyping the virus?
I think it’s pretty clear there is a massive and systematic effort to heighten fear, probably on government instructions. For example, the Department of Health is clear in its reports that the death counts are *with* (or even just suspected with) not *from* the virus. Every news outlet I’ve seen reports them as “coronavirus death toll”, ignoring the distinction.
> claiming that official figures underestimate the death toll
They’ve noticed that the virus isn’t much good at killing anyone who isn’t already near death. They are getting their alibi in early.
It’ll work. A few grumblers like us will see some little-reported studies within the next year saying the fatality rate was much lower than thought. The big public won’t notice and will be thankful that although they’re poorer they survived the great plague.
For many people— especially public sector, nice comfortable office job doing nothing very much, salary paid every month, house with garden— this has yet to bite, it is not that much different to the extended shutdown that has become the habit over New Year. But now it starts to bite: maybe spending so much time with the wife and kids isn’t such fun, all those little jobs around the house can’t be completed with shops closed. The doctors appointments for things that were not yet urgent, now maybe more worrying. Gradually the inconveniences of daily life add up until they are more urgent than the hobgoblin.
Agree.
They were taken on mobile phones, but yes I thought there was a no visiting policy
“The biggest problem for the lock down is it’s advocates and enforcers do not suffer any loss of income or pension themselves.”
Wonderful point. Most people I see as being strongly in favour of a lockdown do seem to all be well insulated from the consequences. Media, government officials, IT guys, NHS workers, teachers, police. None are getting pay cuts or made redundant. If anything, they have the potential to be elevated in relative terms. There is a benefit to them.
I wonder if the police would behave differently if they had a 50% pay cut for the duration of the lockdown?
Incentives matter…
Suspect he was admitted to the ICU because of who he is and the questions that would have been asked if something had suddenly happened to him somewhere else in the hospital where immediately resuscitative actions would have been below optimum.
The headline was clear that he had not suffered with pneumonia.
@M
Reports are that Boris walked into hospital ICU. Playing better safe than sorry as he’s PM?
@Bored Lockdownee
+1 Gov and MSM have been in hysteria and encouraging/ordering public to panic
@Stewie
BecJT confirms what I’ve been saying: lockdown is to protect politicians careers, not to protect or be in UK’s best interests
The ‘saving one life’ mantra annoys too, for CV19 it’s mostly delaying death by a few weeks/months. Saving a life would mean patient will live for ever
@Gavin Longmuir
At least one F1 team – Red Bull iirc – have urged drivers and rest to become infected during this long pause in races
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