Social Complexity

Month: September 2021

Definitions can completely change dynamic behaviour (and your model too!)

You analyze a dataset and figure out that political polarization has been steadily rising in UK for the last 10 years.
You tell this to your colleague who looks surprised: apparently, in her analysis, polarization has been decreasing for the last 10 years! And she used exactly the same dataset as you.
What is going on?

What we know about measurements

i.e. recap of the last post on measurements

In our last post we discussed that, in the social sciences, quantities are defined in a general way. This is different in fields like physics where they employ “operative definitions” which tell you exactly how to measure a specific quantity.

Of course, we have many more interesting details in that post, but the short story is: different people will end up measuring different things (and these measurements are usually non-comparable).

We used the example of counting potato chips and noticed that everyone will count a “full chip” as one. However, everyone will have a different approach when counting broken chips. For example, one may count each fragment as a separate chip, while someone else may not consider them as “chips”.

End of the recap!

What about the dynamic behavior?

The big question now is: we know these measurements are non-comparable, but should they all produce the same dynamic behaviour?

For example, if I add a chip to the bag, all the measurements will increase by one. And if I remove 10 chips from the bag, all measurements will decrease by 10, right?

Yes, indeed, in some cases all the measurements will behave nicely and produce the same behaviour. However, what happens if we start crushing some chips in the bag?

Now, the measurement which counts only the full chips will tell you the number of chips is going down (we are losing a lot of full chips) but the measurement counting each fragment separately will register an increase! We are observing two opposite dynamic behaviours even if we are still measuring the same “macro-concept” (i.e. the number of chips)

Why we have this, again?

As discussed last time, we should be careful with the difference between “macro-concept” and the measurement itself (i.e. “operative definition”). Indeed, while the macro-concept may sound clear and intuitive (“we are just counting how many chips we have in the bag”) it is actually hiding the fact that we can perform this operation in many different ways. And, unfortunately, every way consists of measuring something different.

But maybe you are still not seeing exactly what is causing this problem, nor how this can impact the social sciences. Well, in the next paragraphs we will address this using political polarization and a few elephants.

What is an elephant?

There is a nice story about some blind men trying to figure out what an elephant actually is. One grabs its trunk (i.e. the nose) and thinks that elephants are like snakes; while another one grabs one leg and thinks that elephants are like trees, etc. Maybe this story may teach you something important about life, but we are not interested in life, but in science, measurements and definitions!

So, let us replace the blind men with 3 researchers wanting to write an article on Nature Elephants. They also ask independently their assistants to put a sensor on the elephant to track its movements. One assistant puts the sensor on the tip of the nose, one on the leg and the last one on the chest. However, the researchers are unaware of these differences; they only know that their sensors are on the elephant (and nothing more).

When the elephant is moving, all three measure roughly the same behaviour (i.e. horizontal motion). But when it stops walking, they start observing completely different dynamics.

One, measuring the chest, start observing a rhythmic movement. The one on the leg measure almost complete stillness, while the sensor on the nose shows big irregular movements in different directions.

The three eventually start arguing and debating. Should they use more precise sensors? Or maybe run an experiment with 1,000 elephants? Should they use some statistical technique for removing big or small movements?

This may sound very silly, but unfortunately, it is not too different from the way we discuss when we face more abstract concepts, such as political polarization…

Is polarization increasing?

Some times ago, I gave a talk in which I showed how, with a method we are currently developing, we could explore different aspects of political polarization. At the end of my talk, a person asked me: “so, practically, is polarization increasing or not in the US?

If are not familiar with the term, polarization represents how “split in two” a certain society is. As you may guess, this is a quite general concept, which incorporates almost endless measurements. Let us see a couple of examples. Polarization can be thought as:

  1. How many people are at the “extremes” (e.g. most people hold neutral attitudes VS most peple hold more extreme attitudes)
  2. How extremists are the ideas (e.g. in society 1 extremists think we should not accept immigrants; in society 2 extremists think violence against immigrants is acceptable).
  3. How “flat” the society is (e.g. a society in which if you are a left-winger you also have specific food, music, and other habits which you share with he other left-wingers)

Take also into account that you can also combine the previous definitions. For example, you can produce a measurement that is mostly sensitive to effect (1) and only a little to effect (2). This means that we have pretty much infinite possible measurements!

Ok, but this was not the initial question. The question was: “is polarization increasing?” And it is clear that the person who asked wants a pretty simple answer, such as “yes” or “no.”

But, before answering it, let us warm up testing it on the elephant.

The elephant game

Let us play the following game: I will give you a situation and a question. You can answer only “yes” or “no.” Ready?

SITUATION: The elephant is running.
QUESTION: Is the elephant moving?
Wow, you are pretty good at this game!

SITUATION: The elephant is standing while eating.
QUESTION: Is the elephant moving?
Ok…

SITUATION: The elephant is sleeping.
QUESTION: Is the elephant moving?
Interesting…

We could go on, but you probably got the point: a simple “yes” or “no” does not fully represent what is going on. Actually, it does not represent it at all.

And this is the reason why I totally disappoint the person asking me the question initial question, by answering her: “Polarization is increasing or decreasing depending on what you mean by polarization.”

What about the models?

As you know, I am very interested in the dynamic modelling of social phenomena. Specifically, in agent-based models. So, how does this knowledge related to modelling?

1. Making the model

The first important thing to consider is how you will build the model. Some people build a model directly from data and experiments, other from more general theories and frameworks. Whatever you do, you will also select a specific definition of the phenomenon you want to model (even if you are not aware of this choice).

So, make sure you know which choice you are making, and that you keep being coherent with that choice. For example, you may mix two theories, or experiments, but make sure they refer to the same specific phenomenon.

2. Using the data

It is probable that one day you will use data with your model. Maybe it will be for calibrating it, or for validation, or whatever. The thing that you have to keep in mind is that there will be many types of data all under the same name.

To stick with the elephant example, you will find data on the nose’s movement, on the ear’s movement, etc. But, probably, they will all be labelled as “elephant’s movement.”

So, when using data with your model, you will have to make sure that both model and data refer to the exact same phenomenon.

3. What can go wrong?

The short answer is: everything. Here, just as an example, enjoy the following:

  • The case in which your model makes totally different predictions depending on the measurement used for collecting the data [link].
  • The case in which you can actually transform one model into another just by changing the measurement scale [link].

This does not fully explain it!

As you may see, one solution is the simple “just stick to one measurement.” However, this is a little limiting. Indeed, whenever we stick to one single concept of “polarization” we are also neglecting all the others. Similarly, if we track only the elephant’s nose, we lose all the information about its ears, eyes, tail, etc. What to do?

A common thing that people say is something along the lines of “this problem is just too complex because humans are infinitely complex. We should not even attempt to solve this problem. Enjoy life while it lasts.”

While I agree (especially with enjoying life), I think there are a series of things we can do to make things better while doing our research:

  1. Being as clear as possible about definitions, models and measuring process
  2. Study the phenomenon using different definitions and measurement (but being clear about these differences!)
  3. Trying to summarize the results and look for similarities and differences between different measurements and models

Will this solve all the problems? Definitely not, but I am pretty sure it will allow us to make some pretty amazing discoveries.

What’s next?

In these posts we analyzed this problem on a very general level (i.e. broad definitions vs operative definitions).

But it is time to start facing a little more in detail how measurements are made in the social world.

Coming up next, ordinal scales and measurement distortions!

When (and why) you can actually compare measurements from the social sciences

Can I compare my measurement of happiness with the one in another study? Is it just like comparing meters to miles?
Why my measurement shows that polarization is increasing but another study shows the opposite?

Today we will clarify one crucial aspect of the social sciences: measurements. Especially, we will see that (1) these measurements are quite different from measurements in physics, (2) what we can do with them and (3) when we have to be careful.

What is this all about?

Let me start by telling you that this is not about the difference between interval and ordinal scales. They are important too, and they can mess everything up as well; that is why we will have an entire series just dedicated to them. But not today.

Today we speak about something even more basic: how quantities are defined. Let us start by looking at the world of physics.

Concepts in physics

I am pretty sure you are familiar with the concepts of length and distance. And you can discuss these with anyone without worrying that the other person may interpret distance in a completely different way. Besides relying on common knowledge, we can also check how the units of distance are defined, reading for example that:

The metre is currently defined as the length of the path travelled by light in vacuum in 1/299 792 458 of a second.

(from wikipedia)

Something you may be wondering now is: why does this sounds so ugly and boring at the same time? Why do we have a damn fraction in the definition?

The short answer is: because physics heavily relies on operative definitions. These definitions are not aimed at explaining a general concept, but more at telling you how to practically measure something.

Have you ever heard of the fact that science is “reproducible?”

Well, these definitions are aimed exactly at that. They make sure that everyone would measure exactly the same things. They make sure that we all know exactly what 100 meters are, with no room for interpretation.

Concepts in the social sciences

As you may expect, the social sciences do not rely much on operative definitions. This is not because social sciences are bad, or worse, or anything else along these lines; but mostly because they focus on general concepts.

Indeed, if you get the definition of happiness from the APA Dictionary of Psychology you read:

an emotion of joy, gladness, satisfaction, and well-being.

As you can tell, this does not contain any information about the measuring process. But is this a problem?

As we will see in the next lines, this will definitely be a problem if we do not understand this process.

Let’s explore it better

Ok, let’s suppose we want to measure how many potato chips are in a bag of chips. Sounds like an easy task, right? Well, actually it is quite a complex one. Indeed, while we have no problem with “full chips,” we do not really know what to do with a broken potato chip.

Take as an example the image on the left. Should we count this as 1 chip? It someway makes sense as you could recompose it to be a “full” chip. But it also makes sense to consider it 0 as, it is clearly not a full chip.

Someone else may also claim that we count each fragment separately, as every piece in the mouth is indistinguishable from a small chip. Therefore we should count this as 6.

Notice that this debate could go on forever getting progressively more and more complex, with questions such as:

  • How big should be a fragent to be still considered in the count?
  • When a “full chip” becomes a fragment? (consider a chip with a very small missing piece)
  • etc.

The main problem is that we do not have an operative definition of potato chips. Nor do we have a unit of measurement for chips.

This means that every person will measure a different number of chips.

Can we convert them?

Let us suppose that the measurement that takes into account both full chips and fragments tell us that we have 100 chips. How many full chips do we have? That is: how do we convert this number into another measurement?

As you may expect you cannot precisely do this, as the first measurement simply merged everything together (i.e. full and fragments of chips). So the only thing you know is that the number you are looking for is between 0 and 100; which is not very precise…

Similarly, if you know that in another bag you have 50 full chips, you still have no idea of how many fragments+full chips you may have. Maybe it is 50, maybe it is 10,000; who knows?

And this is quite a big range of uncertainty!

This is not a statistical problem

Many people here may feel like this is the same old problem of sampling: you may get a bag with 20 chips or a bag with 30 chips; so what’s new here?

The fact is that this is not a sampling problem but a measurement one. Indeed, the bag is always the same. We did not resample or replaced it with anything else. What we changed is how we are measuring, but the object is still the same.

Is this an artifact?

An argument that I hear often is that “this is an artefact.” This can also be rephrased as “one of these measurements is the correct one and the other is simply wrong“. And, someway, this argument is correct; but it is also quite wrong. Let’s see why.

Let us suppose we want to predict the number of times a certain child (le’ts call her “child X”) will put her hand in the bag of chips for eating. We know that this child picks fragments and full chips one by one, as long as they are above a certain size S.

In this case, we want to count as 1 each peace above size S and ignore smaller pieces. Every other measurement would generate artefacts… in this context.

Suppose, instead, we are dealing with child Y. This child eats full chips one by one, while she does not eat fragments. So, in this case, the correct measurement would be counting as 1 full chips and every fragment should be counted as 0.

This means that the right measurement is determined by what we want to measure. And all the other measurements will introduce some artifacts.

Therefore, we cannot have a measurement which is good in every situation.

Just use differnt names

Another interesting argument that I hear sometimes is that we need better classification. For example, instead of using the general concept of “chips” we may distinguish them into “full chips” and “fragments.”

While this approach is helpful, as it limits the possibilities we have, it still does not completely solve the problem. Indeed, as we discussed before, when does a full chip become a fragment?

You can observe something similar in this article where they notice that the concept of “polarization” is too vague and the authors come up with 4 main sub-types of polarization. However, the same article then highlights how the same sub-type can be still measured in different ways.

Indeed, at the end of the day, what specifies exactly how to measure something is the measurement process itself (i.e. the operative definition). This is why better (non-operative) definitions ay help but not solve the problem.

Can correlation save us?

An important ally of every scientist in the social sciences is our friend correlation. Indeed, as we will see, it can strongly help us in solving some of these problems. Even if we should not blindly trust it as we may still end up with some bad surprise.

When to trust it

Consider a chips brand whose bags contain usually 90% full chips and 10% fragments. In this case, you can easily convert one measurement into the other. For example, if you measure 100 in the measurement which counts also fragments, you should have a number very close to 90 in the full-chips measurement.

If this relationship (i.e. 90-10) is not given to you as initial data, you can still explore it using tools such as linear modelling or simple correlation. You just need the process to be reliable. In this case, you will be able to know:

  • How to transform one measurement in the other
  • How precise your estimate of the second measurement will be
    (i.e. how uncertain your prediction is going to be)

If it is so simple, why even bother with the first part of this post? The problem is that things are not always so simple…

When you should not trust it

You figured out that for brand X, the percent full/fragment is 90/10. So now you can use both the full-chips measurement and the full+fragment since you can convert one into the other; very well!

What happens now if you apply this relationship (90/10) to another brand? Or if the same brand changes something in their production chain altering this ratio?

The problem here is that you can convert the two measurements as long as they have a stable relationship. But this relationship may change in time or not be universal at all (i.e. it works only for a specific brand).

For example, two measurements of polarization may be perfectly equivalent in France but not in Germany. If you know this phenomenon, you will not be surprised to see the two methods diverging. However, many scientists are unaware of this and they may get totally puzzled by these results.

Summing up…

Some people may reach this point and ask: if we are always measuring the same thing, why do we end up having different results?

And the answer is: because we are actually measuring different things!

Yes, we started from the same macro-definition (chips, polarization, happiness, …). But then, we ended up using different operative definitions. This means that practically we measured different things (e.g. full chips vs fragments). This generates the following situations/problems:

  1. We cannot directly compare results.
  2. We can estimate one measurement from the other by using correlation/linear modelling and making sure that we are not changing anything important between the two measurements (finger crossed­čĄ×).
  3. The measurement which is the best for us may actually be bad for other people/studies.
  4. Different measurements may actually produce different dynamic behaviors (e.g. one measurement shows increasing polarization and the other shows decreasing)

While we explored points 1 to 3, we did not really discuss point number 4. This is because it deserves a lot of attention and we will have a post just on that (coming up in 1 or 2 weeks).

If you are interested in measurements and how this may affect modelling (especially I am interested in agent-based modelling), check out this blog or my social media, as I will keep exploring this topic.

See you soon!

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