If you have seen the news, there seems to be a lot of complaints about models. One was that a model that predicted that if you did nothing a lot of people would die. People did something. That number didn’t die. People complained to the expert about his model.
This isn’t an isolated problem. People can get fool by models all the time. How can we avoid that? And, how can we make better decisions when experts bring out their models?
- The map is not the territory
- Where experts can go wrong
- Models have pitfalls
- Missing information
- Incorrect assumptions
- Wrong information
- Bad implementation
- Prediction failures
The map is not the territory
There is a classic saying “The map is not the territory.” This is basically saying that any model is not a true reflection of reality nor can it be. A real simple example of this is Google Maps.
If you have ever used Google Maps, you have a good understanding of how useful it is. In most cases, it will help you get from point A to point B. Occasionally, Google Maps has a mistake and suggests a very odd detour or to go the opposite direction on a one way street. This happened to me in a rental car in Hiroshima, Japan.
We know not to trust the map 100%. There are going to differences between the map and real life. Google is extremely good a building and updating maps, but they are not perfect.
The same can go for the experts. Further most experts do not have the same level of resources that Google does. So, how do deal with this?
Where experts can go wrong
There is no way any of us are going to have the time and inclination to be smarter than any expert on their special subject. However, what we need to be careful of is:
- Experts focusing solely on their field ignoring other factors
- Experts commenting on fields outside their area of expertise
- Experts who use their authority to push their opinion and give no evidence
If you look at 1 and 2 you are in a particular pickle. A subject like what to do about lockdowns is a complex subject. An epidemiologist may say one thing and an economic expert may say another. They could be perfectly right when it comes to their respective fields. But if you have to make a policy decision, how do you know how much weight to give to either opinion? That can be a tough call.
Then there is the problem when a bunch of different experts saying contradictory things. They have contradictory models. What do you do? It is hard for any layperson to make sense of who is right. Sometimes it is just the last person who spoke who sounds the most convincing. Others just pick the one they want to believe in.
The problem continues when each expert trots out their model. We have seen all kinds of predictive models over the past few years. There have been models regarding the infection rate, crime rate, climate change, etc. Many of these are complex with filled with all kinds of assumptions. Which one can you believe?
Models have pitfalls
But let’s assume you don’t want to randomly pick one to believe in. You want to be able to cut the BS from the good. You want to make good decisions. Even so, it can be tough because even well-meaning people make mistakes. So, let’s look at what to look at what we should be careful about with models.
Models can have five problems:
- Missing information (due to not knowing or abstraction)
- Incorrect assumptions
- Wrong information
- Bad implementation
- Prediction failures
Any of these can lead to orders of magnitude of error. So, you need to be very clear as to what the model can do and what it cannot do. Not only that as I note in #3, you can have a good model, but if you have the wrong information you have a serious problem. “Garbage in is garbage out” as programmers say.
Any model will have missing information. That is the nature of the model. It is supposed to “model” the real world. If you included everything it would be the “real world.” That requires a huge amount of computing power and so complex that it is not useful at all.
If you wanted to determine how far a ball would go if you threw it. There is a simple mathematical formula for it.
Distance = v02 sin 2θ0/g
This doesn’t take into account the friction in the air or the fact that a tree may be in the way. Those are details that are not so important in most cases. For normal people, just getting around the above formula may be tough. But at the very least you can make good assumptions as to the speed ( v ) and the angle ( θ ). g is the constant for gravity.
Or you could put in every single detail about the ball, the person throwing it, the environment, etc. That would be a monstrous set of equations so large that there is no space to put it here. So I won`t.
Missing data by abstraction
Abstracting is about making things easier to understand and compute. The key here is to know what is abstracted and why. If you don’t know that you can get into big trouble. Circumstances can change. What was not a big deal can become a very big deal later.
Everything should be made as simple as possible, but not simpler.Not Albert Einstein
For example, we have a traffic map. The map doesn’t need to tell you about the traffic conditions. It is simple enough so you know how to get from one town to the next. It is not like you need to know where every pothole is or every dip in a country road. Knowing the basic shape and distances is enough to get the job done.
But there are cases, that where that abstraction is not enough. For example, what could look like a shortcut, could be a street clogged by construction and traffic jams. Most of the time there is no construction so you don’t need to worry about it. But for a specific case, you need this information in your model. Otherwise, you could be waiting in traffic for a very long, long time.
The other possibility is that the one road seems short but goes through the mountains, has lots of twists, steep slopes, etc. The other one is longer but has more straightaways and it is easier to travel at high speeds.
Abstractions are done to save time. But you still need to know what is included and what is not included to make intelligent decisions about them.
Missing information the size of Antarctica
If you look at any ancient map you would see lots of missing information, like no picture of North and South America as well as Antarctica. You know that because that was not on the map, it doesn’t mean they didn’t exist. It just means the information was missing.
Science in general is all about updating our models how of we understand the world. Since updates happen, we need to be careful of believing too strongly in any particular model. Science just uses a particular model because it is the best explanation at the time. This doesn’t mean that the model is the “truth.”
Because our models sometimes are missing really important pieces of information they can also go wrong. What we thought would work in most cases, sometimes doesn`t at all. This because we were missing a big piece of information all along.
Missing information in the case of government debt
For example, a lot is made about the debt situation for Japan and the US. In the case of Japan, it is 236% of the GDP of Japan. The US was about 105% when this article was written. Which for a normal person would seem to be an alarming amount. Except that the average American has about more than 7 times the debt compared to their average salary if you include mortgage payments. Most people tend to be OK with that. I don’t think anyone outside of Dave Ramsey is sounding that alarm.
If the debt was so horrible, you would expect that the currency would be in worse shape than the Argentinian peso. But that is not the case. In fact, if you look at the balance sheet of the country you will find that Japan`s assets and debt cancel each other out.
In addition, about 47% of the debt is owned by the Bank of Japan which is part of the Government of Japan. I don’t expect the Bank of Japan, nor private Japanese which own 36% of debt to be knocking on the door asking for their money back anytime soon.
So, any model of Japan declaring a default or the devaluing of its currency would be greatly effected by including or not including these factors. A Japanese citizen’s decisions on what to do about the government`s fiscal policy will also change greatly with this understanding.
Models are based on simplification. Not all simplifications produce accurate predictions. Sometimes simplification is based on a misunderstanding of how complex systems work.
When scientists bring out models of something like how fast a new infectious disease spreads, things take can a different turn. The reason for this is simple. Modeling biological events is hard. It is easy to make a bunch of assumptions, plug that into a formula, and get an answer. But, it is hard because how do you know what assumptions to make?
For the common person, the thinking is that “That is what experts are for. They are supposed to know what assumptions to make.” That is a perfectly fine way to think. But, it gets tricky when you dealing with a new phenomenon. Even experts make mistakes due to the “fog of war.” A new infectious disease isn’t going to advertise all the needed variables to you.
SIR model and wild assumptions
First, we have to know a couple of things about the virus before we can make any reasonable model. To understand that let’s look a the SIR model. The SIR is a mathematical classic model that looks at a fixed population for those who are suspected, infected, and recovered.
This model assumes:
- all individuals have an equal probability of contracting the disease
- rate of contact between two groups in a population is proportional to the size of each of the groups concerned
- rate of infection
- rate of recovery
- the rate of infection and recovery is much faster than births and deaths
Just to make the model easier it is assumed that everyone has equal risk of contracting the disease. But for genetic or other reasons that may not be true. For example, a weaker form of the infectious disease may have made its way through a part of the population or some parts may have gotten vaccinations for a similar disease.
Guessing is hard, accurately measuring is harder
The rate of infection is also very hard to measure correctly. This requires accurate reporting. It also requires reporting based on the same standard and the same method across the infected population. If the healthcare system nor the government is prepared don`t expect accurate and reliable information anytime soon.
Also, there are lots of differences in cultural norms, government policies, population structures, etc. that it can be very hard to use data from one country and compare it to another. Especially, if the country has an incentive to under report or doesn’t have the infrastructure to do good reporting in the first place.
If you hear any expert report with a good deal of certainty about their mathematical model, you should take it with a grain of salt. Make sure you know what assumptions they are making. Sometimes those assumptions are just guesses. There is a lot about different complex systems that we just don`t know. One wrong guess can make a magnitude of difference.
In complex systems, people have to make assumptions (or wild guesses) about certain variables. It can very hard to precisely measure these. Expect models for new phenomena can be wildly inaccurate.
Sometimes the information that we have is just wrong or not trustworthy. For example, there could be a problem with measuring. The PCR tests are currently only 70% right. It can make false positives and false negatives. Which would mean that if you test 100 people only 70 people would have a correct result. But which 70? That can be a tough question to answer if a large percentage is also asymptomatic.
In a different situation, I have an app that keeps track of my finances for me. I use that to keep taps of my spending. But sometimes it stops syncing with one of my bank accounts. This would also give me the wrong information about what I should do regarding my next purchase. I might think that I have plenty of money when actually the credit card company pulled a huge amount out. Having old outdated information is a bad thing too.
Then there is the issue where information just was not collected correctly. In most cases, you hope that people are trustworthy to do their jobs right without making mistakes like this, but sometimes you just don’t know. There have been times when someone made a mistake of putting 10 instead of 1,000 or the other way around. If people are doing the data entry, mistakes like that can creep in. Smart people have checks to prevent that. Occasionally, governments don’t.
On paper, a model can look fine. On paper, the math can also add up. But, sometimes the problem is in the implementation. What this means is that someone didn’t do a good job in the programming.
Complicated models require good programmers. Also, when dealing with new situations, it is important that the computer models are tested that they follow the math correctly.
There was one instance in the case of a UK model on how bad the coronavirus would get. What would be the best model is anyone’s guess. There are a lot of variables that people didn’t know initially. Some constants had to be made up. But that was not the worst part.
Was the code for the model reviewed?
A review of the code showed that no one probably tested it. If you put the same variables in you got different results each time. That is not a good thing. That is why computers need to be carefully checked to make sure the programming is as solid as the mathematics.
This goes for just about any software project. There will be software bugs because people make mistakes. But, when there is little time and there are few resources that risk becomes bigger. That is why that even if the model says one thing you should not believe it until you know that the model has been verified, the model is logically sound, and the assumptions are ok.
Another problem is the misinterpretation of the results of the model. In most mathematical models, you put data in and you get data out. What meaning you assign to that is all up to the person looking at it. Not understanding the assumptions of the model nor the context in which it was created can lead to people making assumptions that are well outside what the data or the model predicts.
Suppose that there is an infectious disease model that predicts that 400,000 people will die. This gets reported in the news with much alarm. The problem is that model makes that prediction based on a certain rate at which the disease would spread and its death rate. Both of these are just good guesses based on data from other countries. In addition, the model is based on people not making any changes.
So, what happens when assumptions and circumstances change?
Later, people and the government take various actions to control the spread. There is a lockdown and various other measures are put in place. The disease spreads, but nowhere near that many people die. The press then blames the scientist for getting it “wrong.” But, what was overlooked was the requirement that people did nothing.
There is no alternative universe where we could look to see where people didn’t take action and see the result. So, there is no way we could confirm if the model was really correct or not. But one thing we know for sure is that people behaved in a way that was outside the model’s original assumptions. Thus, the model is no longer valid. One should always check the model’s assumption before blaming or interpreting the results.
Prediction is a very hard business. There are so many things that could change that again you need to be very careful of the variables involved and the assumptions made. It is because of those two things that a former bank employee and business analyst turned cartoonist, Scott Adams, made an interesting remark.
He said that models were never meant to predict the future. Models are just used by experts to persuade non-experts. Throw out a couple of charts and graphs and you can hide the complicated mathematics and get politicians and CEOs to take some sort of action.
Models are just used by experts to persuade non-experts.Scott Adams, the Dilbert guy
I don’t completely agree that all prediction models are used for persuasion. After all, you need to make assumptions and test them. Prediction models are useful to test if your assumptions are right or not. But in most cases, models are most useful in better understanding known behavior.
“Sometimes models say what the experts want it to say…”
However, is a crisis people want certainty. And especially computer models can give that illusion. After all, it is just math, right? The problem is that experts can pick whatever variable they think is important and fit some kind of curve to the existing data. They can then make further assumptions as to how variables will change in the future.
In the case of a situation where there is a lot of unknowns, such as the future of sales in one business or the spread of a new disease, the key variables are anyone’s guess at the very beginning. In those situations, scientists can make the model say whatever they want. Sometimes even they don’t know their own biases.
But as more data come out, people become more and more aware of what the key variables are. It becomes easier to see what assumptions were right and what were wrong. Models can be adjusted and so can policy. Still, you need to be careful of any change in the situation.
Even though there are can be big problems with the accuracy of models, they can be useful in decision making. Most people try their best to make good models. But sometimes people make mistakes or make BS. When dealing with models you need to be very sure of assumptions made. Sometimes even key variables are left out for one reason or another.
It is better to consider multiple scenarios with different assumptions of how the future will change. Even then, if the situation is particularly new, have the understanding that the model could be off even by a magnitude.
In any case models are not the territory. They are simplifications that can help us understand it. They can be useful as a resource in making any decision, but they should not be the main reason for making it.
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