A case of decision making under uncertainty
Abstract: I make an attempt to understand the options available to policy makers around the time lockdown was announced in India and what could have led to the decision to announce the lockdown. It makes an interesting case study on making decisions facing high uncertainties (which is almost always, though we may not know it). I end it with some ideas around how an individual should plan his personal lockdown now that we are well into Unlock 1.0, which means everyone is on his own.
Everyone has a view on how to tackle Covid-19. It is expected. For none are spared the agony and inconvenience induced by the disease, or by the measures implemented to tackle it.
Lockdown is bound to be controversial. It is like chemotherapy — not differentiating the healthy or diseased. When chemotherapy fails to eradicate the cancer, there would be questions: Is the doctor capable? Did he work in our best interest? Was there no other option left?
Analysing decisions is fun. Especially someone else’s decision, when the situation has played out. Hindsight is 20/20. Is it? But that’s a separate question. When a situation has played out, those whose theories emerge validated have the air of — “I told you so.” Others are likely to be sombre.
But is that the right way to evaluate a decision? Suppose I were to challenge Mike Tyson in his prime, for a bout to death. On the d-day, he falls ill and is unable to come — I win. Was it a good decision to challenge him? Most decisions are not so obviously skewed as the analogy. Yet every decision has elements it highlights.
The right way to judge a decision is based on what was known and knowable at the time of the decision. One needs to understand the options available, the possible futures these options unlocked with what probability, and the relative attractiveness — sometimes only unattractiveness — of these possible futures; then evaluate which option or options made sense.
There are aspects like reversibility, optionality etc that make a decision more robust, especially when facing many unknowns, but those make the analysis complex. We can keep them aside for now.
Let us travel back to around March 20th. Just before the first lockdown.
India officially had about 250 covid cases, doubling every 3 to 4 days. It is important to note the doubling is repeated every 3 to 4 days. Exponential curves are notoriously unintuitive, even to an investor like me who keeps chanting the mantra of compound interest.
At this doubling rate, we’d have about 1000 cases by the end of March. By April end, the cases will double 8 times… No! It will not be 8 times, but 256 times (2 x 2 x 2 … 8 times). That’s about 250,000 (2.5 lac) cases. Isn’t this about where we are today? Is that what we’ve saved — one month? Let us just run this growth for another month. At the same rate, we’d be 60 million (6 crore) by May end. Exponential curves are hard to intuit.
We were staring at a pretty bad outcome — we needed to get this right. How do we figure out what to do? Could we learn from the experience of other countries? Ones ahead in the curve, ahead here implying worse.
China, where it all started, executed a strict lockdown in Wuhan and lockdown of different intensities in other places. It brought the disease under control. In the 10 days to Mar 20th, China recorded about 700 new cases on a base of 80,000. Their numbers were suspect. Whether this was a temporary respite or not was suspect. But it was the only country at the time that seemed to have lived through a peak and turned it.
Japan, Singapore and South Korea were following the alternative strategy of no lockdown, aggressive contact tracing & quarantine with varying degrees of success. South Korea almost managed to completely arrest the curve, cases growing only by 1000 to about 9000 cases in 10 days to Mar 20th. These were nations with much greater per capita resources, where wearing masks is commonplace, are culturally more disciplined, and that had successfully combated SARS not too far back in the past.
The west seemed to be staring at doom. News of people dying waiting for hospital beds and overwhelmed medical systems filled the media, with no end in sight. Cases were doubling every 3 to 4 days in Italy, UK, US, France, and showing no signs of abating — doubling at these rates even with higher base counts. Projections seemed to get more dire; Respite seemed hard to come by. One after another, they were forced to announce lockdowns; lockdowns that were yet to start showing results — numbers still rising fast. Were they too late? Nobody knew. Things seemed hopeless.
There was panic in the air. Vaccine seemed distant, no cure was yet visible. It was hoped that in a few months, we might be able to better manage the disease, if not find a cure for it. But one couldn’t be sure.
The major point of concern was the severity of disease and fatality rate. Hospitalisation rate estimates varied from 10% to 20%, and fatality rate estimates from 1% to 3.5%. There were no control group experiments to test the hypotheses against. Nobody knew the real numbers because nobody could estimate the total number of people infected (we still don’t know) . Almost all countries were preserving resources — testing the symptomatics, or even fewer — symptomatics with an established contact.
There were theories floating around of the impact of heat, bcg vaccination, innate immunity, etc which were helping places like India. It could be true. Middle East, Africa, Indian sub-continent, all were showing a divergence from the experience of the West. But could we depend on this data? These nations might just be behind in the curve, testing much less, or maybe just hesitant to share real numbers. We still do not know for sure — though our own experience seems to suggest that with time, the numbers do seem to converge.
The plight of policy makers in India (and everywhere) is not hard to sympathise with. Take the least worst choice between
- Herd immunity
- Trace, test, quarantine
Herd immunity is kind of default — do nothing strategy.
It was what the UK seemed to be following around that time. The assumption was that the disease is disproportionately more dangerous amongst older people. Isolate them, and let the younger ones get infected to build immunity. Seemed like a reasonable strategy.
Maybe India could even be lucky and the projections will turn out too fearful — early estimates tend to err on the optimistic or pessimistic side depending on the mood prevalent. Or maybe they were not applicable to us. Early indicators seemed to point to this. Is this enough reason to take the bet?
What about the risks? It wasn’t known if immunity does get built up, and for how long. Neither could one be sure about severity in the younger population . The experience of the West was diverging from China where it seemed a larger number of younger people were getting severely ill and even dying.
Working out the numbers for India — Herd immunity required 60% or so of the population to be infected. Even if hospitalisation and fatality rates are just 2–3% and 0.2% in 30 to 60 year olds (which were the numbers floating around at that time), with about 500 million (50 cr) people in this age group in India, this would have led to 10 million (1cr) or so extra hospitalisations and 1 million (10 lac) or so extra deaths , deaths of people in prime productive years. That too if we are able to successfully isolate the older folks. If.
What would be the estimate of likelihood that we’d successfully shield the old and vulnerable? Pretty low. What happens then? In a median bad scenario which would be quite likely, the disease gets out of control. Within this year itself, about 700 million (70 cr) or so get infected, 70 million (7 cr) hospitalisations needed, and at about 1% to 1.5% dead — anywhere between 7 million to 10 million (70 lac to 1 cr).
The side effects of this kind of impact would probably count under unknowables, but expectation of an economy continuing to perform under this scenario would qualify as wishful thinking. That we’d even be able to maintain social contract under these circumstances would be questionable — India has about 2 million (20 lac) or so total hospital beds that fall short of requirements even without Covid . We could be staring at riots for beds. A country where people start beating the doctors if their patient dies; what are the possibilities if doctors had to decide to let one die to save another.
The above estimates were with the disease assumed at around the median range of severity. If hospitalisation and fatality rates were at the upper end of the range, outcomes could be catastrophic. Just a reminder, that we are talking with respect to what was known and knowable around 20th Mar.
Trace, test, quarantine — seems like Goldilocks approach.
Control the disease, retain economic growth, lives & livelihood both saved. It seemed to be working in the Far East. But the success of Japan, Korea, Singapore was not established. A small oversight and numbers start to explode, as was seen in case of Korea though they brought it back in control. Once numbers cross a certain threshold, it is simply hard to follow this model anymore . With 500,000 (5 lac) cases growing at 6% or 30,000 a day, and each with 20 oddd contacts means about 600,000 (6 lac) to be traced and tracked each day. Then ensure they self quarantine for 2 weeks — we are looking at tracking over 8 million (80 lac) people every day and hoping they follow the rules.
And yet, this seemed like the right approach with our numbers at 250. Why wouldn’t we use it?
We actually were. India was already following the process of test, trace and quarantine before the lockdown — yet cases were still doubling every 3 to 4 days. Maybe our testing wasn’t scaled enough, or trace/quarantine wasn’t aggressive enough — results were pointing to the fact that we were not able to replicate the success of Far East nations. We tried but we failed.
There was the option to double down on it given we were at less than a thousand cases by official numbers. We could have also augmented it with a containment zone approach that is being implemented now. Focused lockdowns.
It could have localised the spread, focused resources and maybe even turned the curve. It would have definitely bought us time. But there were some doubts. Were numbers the same as reported or much higher? How widespread was the disease? We needed to scale up testing quickly for this strategy to work. Did we have the capacity? The infrastructure? It required people to cooperate — remember who they met, inform authorities, then expect contacts to self quarantine. Could we expect people to do so at scale? Policy makers probably had access to more indicators and feedback from on-ground implementation, we don’t. The rapid rise in numbers even while implementing this strategy does suggest execution wasn’t reflecting the theory. The threat of run-away disease was increasing.
That brings us to lockdown.
Lockdown is like chemotherapy — ill the economy, kill the disease, save lives. Or like chemo, it may only postpone the inevitable. We couldn’t know for sure.
Logic for lockdown can be gleaned from global examples. We knew China successfully controlled the disease using strict lockdowns. We also had the example of western nations forced to implement lockdowns to control the disease once it got out of hand. It seemed like a reasonably high probability model to bring the disease under control. The experts seemed to concur.
If we were likely to be forced to do so later, why not do it earlier. With our hands forced and disease on rampage, we’d be tackling 2 big problems, impact of disease and impact of lockdown. Implementing it immediately would allow us to handle the impact of lockdown when we have the resources to handle it, before the disease drains us out — and hope it arrests the disease before it becomes a problem.
We were around the same numbers as China was when it announced lockdown in Wuhan. What if we implemented a stricter lockdown, throughout the nation. Could we replicate Chinese success and eradicate the disease completely. A shot at complete eradication, and the inevitability of lockdown as eventually necessary were factors pushing policy makers towards it.
That there would be economic costs was known. We could manage. People have savings to be used for hard times, countries have savings which can be used to support those with no savings. Businesses can replace revenues with debt that can be paid back as revenues clawed back.
Lockdown seemed to hurt the economic future; but the alternative could be economic ruin caused by the disease. Economic outcomes are hard to estimate, maybe hard to even estimate a range. Complex systems are just not easily predictable. We were exposed to big unknowns with any choice we made — side effects, effects of effects — not known at that time, not even knowable.
The likelihood and extent of lockdown success were hard to quantify too. China seemed like success, but that’s a different country, different system, different culture. West was still in the middle of lockdowns, more as a necessity than as a choice. And at neither place the outcomes were certain.
If lockdown failed to bring disease under complete control, it would still buy us time. Time was precious — allows us to augment capacity, know the disease better, and who knows, maybe we get a scientific breakthrough. If nothing else, we’d have more data to make nuanced choices. Then there was the possibility of complete eradication!
With limited data, we cannot speculate beyond a point. The oscillations between why it made sense and why it didn’t only point to the difficulty in making the choice. That’s the burden of the decision maker — damned if you do, damned if you don’t.
The choice was made. Here we are now, after Lockdown 1, 2, 3, 4 and in the middle of Unlock 1.0.
Did it work?
Since absolute numbers are less reliable, it is better to look at growth rates, assumption being that we have been consistent in our shortcomings in measuring the numbers. Let us look at the movement in daily new cases, cumulatives and actives at the points of various lockdowns:
Like most other decisions, it worked and it didn’t work.
It brought down the growth rate, gave us time to prepare, probably enough to keep the disease under controlled growth. It failed to flatten the curve (actives keep increasing), created significant hardship for people, and maybe just postponed the pain while inflicting an additional economic pain.
What about the experience of other countries that did not go for a lockdown? Can we trust their data? Can we trust our own data? Or maybe it is just the heat — with rise in temperature, the spread decreased. That might require some statistical expertise, but isn’t what I am interested in right now.
A wise man said, “It is hard to make predictions, especially about the future.” One could add — “It is hard to evaluate a decision, especially when looking at results.” Results add the dimension of “I told you so,” to the evaluation.
Whether lockdown seems like a success or not will depend as much on the ideology one subscribes to, and personal tastes as it would on the real outcomes. The idea of this essay isn’t to call out how good or bad the decision turns out to be, but whether it made sense given the knowns at the point of the decision. Was it a good decision when it was made? It turns out, that too is not easy to decipher. It never is.
Ending lockdown — Was this the right decision?
To some extent the Govt hands are forced. One cannot lock down the economy indefinitely. And lockdowns are not perfect . The leakages were enough to keep the disease brewing, in fact growing. It had to be at some point replaced with a different strategy.
Numbers seem to also suggest that the Gov was reacting to the situation as it developed — opening up the lockdown as the growth rate declined, but failed to keep declining. There might have been an initial hope to arrest the rise completely. The costs, both economic and political, as well as the realities on ground likely shattered those hopes. Could this have been known earlier? Would that have changed the decision?
We have more resources today to tackle the disease, more skill to handle the ill, and more information too. There is also probably increased insight into the severity of disease, and its impact on different age groups. That too changes persepctives and relative attraction of different options.
The goal has shifted to focus on keeping disease in check, not on eradication. That won’t happen.
What about the future? Where do we go from here?
The important parameter is active cases — that determines current spread, stress on medical infra, and even your odds of catching the disease.
New cases are still growing, so the number of Active cases will keep increasing, hopefully at a slow rate, but still compounding. Unless the number of daily new cases stabilizes or degrow, the number of active cases won’t decline since this requires daily recoveries, that follow new additions with a lag, to catch up.
At current rates of daily growth, given enough time, we are eventually likely to run out of our increased resources, even if we keep augmenting them. New cases increasing at 4.5% means doubling every 15 days or so, so 4 times in a month. By the end of Jun, we’ll be seeing 32000 new cases daily, by the end of July, close to 130,000 daily. But this is maths — it may not play out as such.
Other factors come into play. As current hotspots get saturated, new ones may take time to take their place — remember at a base of 10, even a 100% a day growth rate will increase numbers by 10. The high growth of cities may not be replicated in the smaller places due to lower population density. Maybe we are already at a much higher number (sampling tests done everywhere seem to suggest a large number of asymptomatic / not tested populations). So it may not come to be as maths may suggest, but it is highly likely to get worse. We know it from experience of other nations who have gone through the peak.
Whatever be the case, the current growth rates need to decline — I don’t think we can handle 100,000 new cases everyday. Otherwise we are betting all on the quick availability of a vaccine or of a cure.
What are the Govt actions signalling?
It seems we’ve now taken a turn towards herd immunity — a controlled one, using containment zones augmented with some level of trace-test-quarantine. A mix of the other 2 alternatives. Maybe after the harsh lockdown, it is easier to get people to do what’s required to make these work. Or there isn’t really an alternative.
If the current strategy succeeds in arresting the growth in numbers, one can expect the response to sustain, a slow easing process with maybe some retractions off and on. All bets are off if the numbers sustain or begin to rise rapidly.
Herd immunity also means the choice is left to an individual. What are his options?
At one extreme, one can throw caution to the wind and get on with life. Live with increased chances of catching the infection, run low but unquantified risks — a severe illness, potential long term impacts or even death — risks that increase with age or comorbidities. If getting on with life is imperative or very important for you, and other factors are favorable, one can potentially take the risk.
Or at the other extreme you can lock yourself out. Avoid catching it as long as possible — increase the chance of never getting it. The cost you pay is lifestyle and livelihood. This isn’t even an option for a majority of people. Maybe worth a try if you can afford it, and definitely advised for the vulnerables.
There exist innumerable middle paths. Do only the necessary activities, avoid high exposure probability situations. Always weigh benefits against exposure odds. Take preventive measures — wear a mask, distancing etc.
How should we think about the odds?
I am neither a statistician, nor an epidemiologist, so these are just quick and dirty ways to think about my chances of getting infected. They may be way off in terms of real odds, but I use them to help guide my general sense of direction, the same as I do in investing. They are in no way dependable estimates. So with disclaimer out of the way, here we go.
Assuming herd immunity kicks in at 66%, the default odds of getting the infection eventually are 2 in 3. It does not mean if 66% of people get the disease, you will never get it, but odds keep reducing as we approach this number and become very low beyond it. There is an implicit assumption that immunity lasts for a significant time, which is unknown at this time.
There are 2 factors that affect odds of catching the infection. Number of infected people you meet, and the odds of transmission per such meeting. Reducing odds of either / or both leads to reduction of odds of infection.
The basic hygiene measures like wearing a mask, social distancing, avoiding crowds etc help reduce both odds of meeting and odds of transmission — thus helping one reduce the chance of being part of the 66%. If these measures reduce infection odds by even 50% over those without, and if half the population does not adopt these, the chance of getting infected goes down to 4 in 10. For those who don’t adopt these, chance of infection goes up to almost 9 in 10. So there’s a good reason to follow these simple measures — you don’t want to be in the second group.
By locking in, one may be able to significantly reduce the odds — by reducing the chance of meeting a carrier. If the exposure goes down by a fifth over a normal person (it can actually go down much more), one is looking at close to 1 in 10 chance of getting infected. This strategy though is impractical for most — doesn’t mean we can’t borrow elements of it.
Time also shifts the odds. Keep an eye on active cases — in your local area. National numbers don’t matter. As I stated earlier, the infection chance depend on odds of encountering a current active. People who venture out more when active case numbers are close to peak are more likely to bump into one, and hence be amongst the ones getting infected. So as active cases increase in your area, increase caution — activities need to clear a higher bar of value to be done if they require interaction with others. In a simplistic way, if total population in your area is 10,000 and there are 500 active cases, you can expect 1 in 20 encounters to be with an active case. Of course quarantine of cases etc lowers the odds significantly, but we are interested in relative scaling to adjust our activity levels, not in the true odds.
At some point the number of active cases will peak and start declining as more people get infected and fewer are left to be. Herd immunity isn’t reached at a moment — it will be a slow regress. As active cases start to decrease, one can relax the bars and become slightly more adventurous, tracking the level of relaxation along with the decline in number of active cases.
Delaying infection has another benefit. The odds of finding a vaccine or a cure that significantly changes the impact of exposure increase with time. People who are not infected by that time will get a big drop in odds of getting the infection if a vaccine becomes available. If it is a cure that’s found, you may be spared the risk of a severe disease / death. There’s also a possibility of the virus becoming less severe and fatal over time as it mutates.
There is no fool proof method — even low probabilities are not zero probabilities, vaccines and cures have their own probabilities and side effects. A chance of 1 in 10 mean that out of 10 such cases, 1 will still get it, at least on an average. And the odds aren’t static — One has to continually weigh the benefits of activities against the costs as disease progresses or new information emerges.
Decision making isn’t easy. It isn’t a one time event, but a continuous process. One has to be on watch for signs that confirm or disconfirm initial hypotheses, shift available options & odds, or shift relative attractiveness of different options. Then adjust actions accordingly. In this case, you have to do it repeatedly till either you get infected, or get a vaccine, or the disease peters out.
Covid-19 has affected us all. We have all seen the impact on our lives of decisions made for us by the Govt. It serves as an interesting case to appreciate the difficulties involved in making decisions under high uncertainty and how to revise your decisions as future states play out.
Since each individual is now left to make his own choices, thinking thus might even help us improve our own decisions about how to maximise our safety and wellbeing — medical or economic.