How Do You Fit an Elephant?



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My two previous blogs discussed the importance of argument in science and the first criticism advanced by Russell Thomas at our article. Today I want to discuss his second general charge, that our model is too simple.

More specifically, Thomas wrote in his PNAS critique:

…the core features are underspecified—too simple and too abstract—and therefore do not adequately model the labeled phenomena. ‘Ultrasocial traits’ could just as well be interpreted as any assets, resources, knowledge, or capabilities that endow a region with power or influence, and not just ultrasocial traits.

To which we replied:

…ultrasocial traits are not just any assets or resources that endow a region with power. In our model (and in real life) these cultural traits yield benefits at the collective level, but impose significant costs at lower levels of social organization. Why they spread, despite these costs, remains a central puzzle of social evolution.

And in his blog Thomas responds:

The authors misunderstand my objection.  I’m not objecting to the concept of “ultrasocial traits” nor am I conflating ultrasocial traits with “just any assets”.  … My objection is that their simulation does not model ultrasocial traits in a way that is distinct from the more general class of assets or resources that confer power.

It looks to me that it was Thomas who misunderstood our response. In our model ultrasocial traits are indeed quite distinct from the “general class of assets or resources that confer power.” To give an example, a climate suitable for reliably producing large amounts of food is certainly one of those factors that confer power, because if you can grow a lot of crops, you can feed a large population who will pay a lot of taxes and provide lots of recruits for you army. Such a climate is an undiluted blessing. If you got it, all you need to do is enjoy it. If you don’t have it, you are out of luck.*

*(Well, you can migrate to a better climate. On many occasions traveling in Sicily and Southern Italy, I could just imagine the reaction of the first Vikings who got there from the cold and gloomy Denmark. They must have said, “Oh my God!”, axed down a few hapless Italians, and settled in Sicily and Campania for good.)


If you could choose between living here (photograph source), or …


or here (photograph source), what would be your choice?

But ultrasocial norms and institutions are a completely different matter. Remember, they are the cultural traits that enable humans to cooperate in large-scale societies, encompassing many millions of people. An example I often use is social trust. I have written in a blog that just about the only explanation that makes sense for why the Danes live such good and happy lives (despite their miserable climate – last month we had only 17 hours of sunlight!) is that they have an abundance of social trust.

Social trust means that you don’t waste time guarding your assets. Instead of watching over your herd all night long, you get a good night sleep. You don’t have to hire guards. You don’t buy locks and armored doors, barbed wire, motion detectors, and anti-intruder computer systems.

Economic measures can miss this, because high social trust actually depresses the GDP. Paying armed guards or manufacturing barbed wire contributes to the GDP, but surely you are much better off if you live in a society where it is not necessary. So overall well-being and happiness increases (while GDP decreases).

There is a catch. You become very vulnerable to those groups that choose to take advantage of your trusting nature. In the technical language of game theory and the prisoner’s dilemma game, this is called ‘defection’, except now we are talking about agents that are not people, but whole groups of people.

When I started my visiting year in Denmark, I was warned to always lock my office door. A year ago a gang of ‘Eastern Europeans’ drove a truck to the building I am in and carried out all the computers in it. Just the other day I read in the newspaper how another group of ‘Eastern Europeans’ stole tractors worth 3 mln euros from French farmers.

The point is that ultrasocial institutions are very different from other assets or resources that confer social power. These cultural traits confer benefits at the level of the cooperating society, but impose costs on lower level units, of which the society consists. This creates a temptation for lower units (such as ethnic mafias) to profit from the cooperation but not to contribute to it. As a result, cooperation at the large scale is very fragile, and can easily collapse, if lower-level groups decide to behave selfishly.

This dilemma (Cooperator’s Dilemma) is very different from a fixed asset, such as favorable climate.

Admittedly, we model this multilevel nature of ultrasocial traits in a very simple way. But remember that our paper is just one brick in the cathedral. I am currently cooperating with Pete Richerson and Jenna Bednar in a working group that, I hope, will delve into the intricate mechanisms that underlie such cooperative dynamics.

So it’s not true that ultrasocial traits, as they are modeled, are just like any factor that confers power.

But at a more general level, Thomas is quite correct in that any modeling is what is known in the technical literature as a mapping of many to one. In other words, the specific formulation in any particular model has an infinite number of different interpretations in the real world.

This is, however, a generic feature of any modeling. No matter how complicated the model is, it always simplifies, which means that it can be accused to “not adequately model the labeled phenomena.” Thomas seems to agree that we don’t want to build overly complex models. But how do we decide what is the suitable complexity?

Different disciplines have different biases about how to answer this question. Our model with a dozen of parameters (of which only 4 are ‘tunable’, that is, were varied to achieve a better correspondence to data) seems overly simple to Thomas. Yet it seems horribly complicated to any of my physicist friends. To them a model with more than three parameters is suspect.

As John von Neumann reportedly said, “With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.”



Ideally, a model should have one parameter that would turn out to be a universe cosmic constant, such as c, the speed of light, or h, the Planck constant.

So are we stuck? Is the question of model complexity unresolvable in principle? Not so. We can use the famous Einstein dictum that the model should be as simple as possible, but no simpler than that.



So how can we objectively decide what is the optimal number of parameters – not too many, and not too few?

First you have to realize that there is no generic answer to this question. Different questions and different settings require models of different complexity. In our project we have a specific set of data, and that allows us to determine how adequate the model is.

So I challenge Thomas, or any other modeler, to improve on how well our model describes the data. Why don’t you model ultrasocial traits “in a way that is distinct from the more general class of assets or resources that confer power” and show that your more complex model explains data better, and I will be the first to take my hat off to you.

(This concludes my response to Thomas’s critiques)

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Gene Anderson

Reminds me of Jose Luis Borges’ story of the geographers who made a 1:1 map and wondered why it didn’t sell. A model HAS to be simpler than what it models, or it’s no use. How much simpler depends on the situation. When I was 7, I could make a fine model airplane with two box lathes. My son-in-law the Boeing engineer requires rather more complexity than that. But still not a whole plane.

Peter Turchin

Thanks, Gene – the story was in the back of my mind, but it’s great to bring it forward. For those not familiar with it, check it here:

From there: “we now use the country itself, as its own map, and I assure you it does nearly as well”.

Luigi Forlai

I guess you can try to reduce the model to 3 parameters and then check if the new model generate a reasonable description of the “story” or the new model loses the capability to “describe” the events. Then you can iterate with different parameters and different combination of them. A huge undertaking but probably a necessary one. My perception is that you are following the correct choices about the parameters. A possible test (not in the real world) could be to analyze “Games of Thrones” to see if the writer thinking is following your framework or is using another model for “Empire building”. The worldwide success of the Series is an indication that the “Series” framework resonate with the public. That is an indication the public perceive the Series as a “reasonable description” of Empire collapse and Empire building.

Peter Turchin

Remember that we reported in the paper what happens when you reduce the model complexity by turning off various component. This showed that the spread of military tech from the steppe and intensification of warfare were the key mechanisms in the model.

As to whether we should analyze the Game of Thrones, I’d rather analyze how players cooperate in massive online games! That would be an experimental approach to studying how cooperation evolved in large groups.


I’ve probably mentioned this before but this

“Economic measures can miss this, because high social trust actually depresses the GDP. Paying armed guards or manufacturing barbed wire contributes to the GDP, but surely you are much better off if you live in a society where it is not necessary. So overall well-being and happiness increases (while GDP decreases).”

isn’t really true although it’s a common misconception about GDP. I think it’s due to the fact that when non-economists think of GDP they think “demand for goods and services” while economists think, and define, GDP as “production of goods and services” (the way it’s actually measured means that it’s both)

If you think of it from the production side then if someone hires guards or buys barbed wire to protect their assets because of low social trust then the labor and capital involved in guarding and barbing is labor and capital which cannot be used for other purposes, to produce other stuff that goes into GDP (this is the essence of the famous “broken window fallacy”). In this basic, simple, view, social trust doesn’t decrease GDP it just reshuffles its composition (to barbed wire and guarding from other stuff).

In fact, a society with low social trust will probably have lower GDP simply because a greater proportion of people and resources are involved in trying to grab other people’s resources (rent seeking), which is usually illegal so they don’t show up in the statistics. Presumably that barbed wire and guards are guarding against someone. The basic ranking in GDP, from highest to lowest, would be something like: {High social trust, little barbed wire and guards} > {High social trust, lots of barbed wire and guards} > {Low social trust, lots of barbed wire and guards} > {Low social trust, no barbed wire and guards}

Now, in certain situations it is possible that lower social trust *could* increase GDP. If the economy is in a deep recession, there’s a bunch of unemployed workers standing around, and there’s a bunch of wire just laying around, and there’s an *exogenous* increase in the crime rate, and as a result people hire these unemployed workers, and utilize this idle capital to protect against thieves, then yes, GDP could increase.

The problem with that is that there is a fairly big literature on social trust in economics, going back to at least mid 1990’s, which has tried to estimate the effect of social trust via various measures on GDP and finds it to be positive. Even in recessions I think – basically in recessions other stuff matters much much more than purchases of guards and barbed wire.

The other important thing is that there’s a dynamic aspect to the effect. Generally, the effect of social trust works through investment. If there’s low social trust, I’m afraid that people will steal the return on my investment, so I invest less. And up to some point it is the investment rate which drives economic growth. So even if somehow higher social trust could decrease the *level* of GDP, it will raise the *growth rate* of GDP. Separating out the static from the dynamic effects can be tricky, but again, most studies find a positive correlation.

Denmark does have a very high (per capita) GDP after all.

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