Those of you who have ever attended a ‘Fête Nos’, a typical Brêton festival-type of gathering with music and people dancing, may immediately understand what I’m going to write about. All the others who have attended another gathering of a large number of people will also be completely familiar with my revived curiosity in a specific subject: The collectivity of human behavior and its occurrence in large masses of people.

Every time the music starts at a crowded ‘Fête Nos’, something peculiar happens: within seconds the mass of people all talking to each other and walking seemingly random suddenly are dancing all together in familiar patterns. This pattern is way too complex to be laid upon all those people: it must, somehow, emerge from the individual moves these people make. Interesting and intriguing, don’t you think?

Even before I started studying sociology I had read `Critical Mass’ (2004) by Philip Ball. I loved this overview of popular science and still do, but somehow it had moved to the back of my memory. I remembered the actor- or boid-based simulations, but I did not really understand how this could be related to the theory-driven sociology that I was studying. I recognized the possibilities offered by the described simulation techniques, but saw them as theories, rather than empirical tests: we can easily make assumptions about behavior and simulate the consequences of that, but then we still don’t know if these assumed behaviors indeed exist and happen in reality.

This all changed when I read `Dissecting the Social’ (2005) by Peter Hedström last year. In this seminal work, he combines a variant of rational action theory with agent based simulation models. Subsequently, he argues that these models can and should be empirically calibrated, using the outcomes of (regression) analyses and survey data. In this manner, the simulation model do no longer function as a (very explicit) form of theory, but as an actual test. This test is mainly focused on the question whether the found individual level relationships and behavior indeed can bring about the emergent social effects that are the focus of many sociological studies.

Re-invigorated regarding the use of simulation models, I recently bought `Micromotives and Macrobehavior’ by the 2005 Nobel Price laureate Thomas Schelling. I had played around with a segregation-simulation of my own, so I was interested in his famous work on this. His well-known opening passage made clear to me how easy it is to connect simulations to empirical observations. Schelling describes how he was to give a lecture to a large audience. To his amazement, he finds the first 12 rows to be empty, but the back 24 rows to be completely filled. He questions whether this has happened purposely (which it hadn’t), or whether this emerged from individual choices. On the first page of his book he is already theorizing and doing empirical ‘tests’ by asking the organizer of the lecture questions on the behavior of the people in the audience while they entered the auditorium. So, in his 1978 book, Thomas Schelling was already combining agent-based models with empirical observations.

It came all full circle when I realized what an important article Schelling wrote on his segregational models. When we understand that these agent-based models can easily be tested empirically, the fact that this isn’t done on every occasion is no longer valid criticism on the technique in general. Observing severe ethnic residential segregation, Thomas Schelling developed a theoretical model on how this might be brought about a subsequent individual choices. By simulating this model, he showed that only very slight preferences are needed to allow the emergence of severe segregation. The hypothetical statement a distinction needs to be made between large outcomes with minor causes, is quite an achievement for one article. To top that: it is easily testable by doing the right observations!

The scientific community wouldn’t be itself if it hadn’t brought forward such an empirical test. And indeed, amongst others, Ruofff and Schneider (2006) performed such an empirical test on segregation in the classroom. Deriving explicit and easily testable hypotheses from theory, these authors use a combination of seating observations and data from questionnaires to confirm the general premise of segregation theory: students of a kind sit together.

So, what does this come down to? Basically, I found it interesting to learn how I revalued a book on social theory and analysis that I read some years ago based on work I read more recently. The combination of these works does also show that the general critique on the artificiality of simulation models does not hold, for when described clearly, it is easy to write out testable hypotheses. Most intriguing to is to find that this has all been there for all that time, from the first page in Schellings book.

Schelling, T. (1971). Dynamic Models of Segregation. Journal of Mathematical Sociology
Ruoff, G. (2006). Segregation in the Classroom: An Empirical Test of the Schelling Model. Rationality and Society, 18(1), 95-117. DOI: 10.1177/1043463106060154

Recently, I discussed the M.A.R.S simulation models developed by Iannaccone and Makowsky. Based on what I read, I decided to try to work out a similar simulation myself. I did so using R-Project and it resulted in the simulation shown below. For more details on the syntax I used, visit the `my functions’ part of my site, which has a page on the syntax for this specific simulation. Please read further for some interpretation of this animation.

In this lattice, we see white, red, and blue squares. White squares represent empty positions, the red and blue squares represent people with different characteristics. Their positions on the lattice are determined randomly. A typical Schelling simulation is performed in rounds. In this case: every round a random person is selected to move to another location, which is randomly selected as well. When this is performed randomly indeed, no patterns will emerge. However, I gave the persons in this simulation slight preferences: people living adjacent to people of the other color have a larger chance to move. When selected to move, people have a slight preference to move to a position which is not adjacent to many squares of another color than the own. When we run this simulation for 100 rounds, we see the emergence of enormous segregation.

When we focus on the histogram on the right, which shows the number of blue squares surrounding each red square, we see that especially the number of blue squares not surrounded by any of the red squares increases rapidly at one point, but does so in a non-linear manner.

Unique characteristics

Schelling-like simulations have at least two unique characteristics: They have become famous by showing that minor differences can lead to enormous aggregate outcomes. Also, even in this very basic simulation, it is possible that the aggregate outcomes vary over time and do so in a non-linear manner, even when the individual level processes are linear. In other words: from constant individual preferences, varying rates of segregation can emerge.

Additionally, the use of these types of simulations is attractive because several authors claim that they can bridge the methodological divide from micro- to macro-, thereby being applicable to this research proposal, since religious regionalism is an aggregate phenomenon. Finally, although in this research project I will address several shortcomings of a specific form of simulation models, I argue that the models can become (at least) as realistic as regression analyses. This can be a point for discussion.

Sometimes, you just know that the authors of an article you are reading, have had a lot of fun while writing it. The amount of fun just radiates from the pages (or your screen, in the digital age), and somehow, these articles are often the really interesting ones as well. Perhaps this has something to do with the authors feeling certain about their work and their grasp on it.

It must have been pleasant days in the `laboratories’ of Iannaccone and Makowsky when they wrote their article in `Agent-Based Explanations’ of religious dynamics. They start their article with a thought-experiment concerning a magic trick, have named the model they propose MARS (multi-agent religion simulation), and titled their paragraphs with variations as `Life on MARS’ and `Exploring MARS’. 

Despite all the fun, the authors have addressed an important problem in the study of regional segregation of religious (and non-religious) people. Regarding this religious regionalism in America they describe an apparent paradox of persistent mobility and persistent regionalism. The standard-approach to tackle such a problem (variants of regression analysis) fails, for it does not provide a “coherent model linking individual behavior to aggregate outcomes and vice versa”, thereby “ignoring social structure”. I gave an example of this problem of aggregation earlier (in Dutch), which illustrated how one can easily be led to the wrong conclusions, when the social restrictions people act within are not taken into account. 

In order to overcome such problems in the study of religion, Iannaccone and Makowsky have taken the famous Schelling-model and altered it to their needs. The basic version of the Schelling simulation model investigates locations people choose to live and the (segregational) consequences of these choices. The model is famous for showing how very small preferences for living amongst similar people will lead to large degrees of segregation.

Iannaccone and Makowsky have “turned the Schelling-model around”, meaning that people do not adjusttheir location to live based on their preferences, but adjust their preferences based on the location they live in and the neighbors they have. More specifically, the authors simulate whether or not people change their religious preferences (church membership, strength of conviction) based on the preferences of the people directly surrounding them. Moreover,  the MARS simulation model allows the researchers to `solve’ the paradox of persistent religious regionalism by showing that this pattern emerges from their simulations when individuals have both moderate levels of social conformity (being influenced by other people’s beliefs) and personal identity (adhering to own religious beliefs). 

In subsequent examples the authors show the flexibility of the MARS models (which can be seen and played interactively with on www.marsmodels.com). It is illustrated that the model is able to take into account Schelling-like preferences; that is the preferences people have when they select a new place to live, for instance amongst people of a similar religious conviction. It also is capable of simulating the impact of a ‘religious superstar’, that is a strong and influential person, and finally it allows immigration, that is an increase in the number of people present in a specific area. The model is also capable of not only investigating whether or not people are a member of church, but also takes into account which church one is member of, the strength of the religious conviction, changing religiousness without moving, and most of all: the preferences of individuals can be somewhat randomized so that not a single individual has exactly identical preferences (just like real life). 

All in all, I would say that the authors have succeeded in building a very interesting and flexible simulation model, the full power of which is only illustrated in the article. More than a solution to the single problem of the “paradox of persistent religious regionalism”, they have offered a perspective which will probably solve many problems in the (near) future.

There are however two characteristics to the (present) model that I do have some problems with. I’m sure they can be solved rather easily, but to my opinion that would bring enormous improvements to the model. The problems are basically: in real life people aren’t forced to move, and more in general: `where’s reality?’.  

To start with the first problem: since the authors turned the Schelling-model around, people in the simulation are randomly forced to move to another location. This is only valid under the assumption that moving has nothing to do with religious preferences. The authors cite additional research showing that indeed religious preferences hardly influence the choice to move. However, these are motivations of moving people, and thereby does not take into account the people that do not move at all. That might still be religiously motivated. Additionally, the assumption the authors make is only valid under the condition that nothing related to religious preferences (i.e. educational level, social economic status, gender, spouse) is related to the motivations of moving as well, for otherwise there is the alternative explanation for the outcome of segregation based on self-selection. I do not believe that this strong assumption can hold, and therefore the motivation for moving (or not moving) should be taken into account in the model. That would lead to a truly dynamic perspective.

The other issue, `where’s reality’, probably entails the need for a more elaborate extension of the model. Indeed, the model allows the authors to show that the combination of moderate values of both social conformity and personal identity allows for the explanation of the paradox of persistent religious regionalism. But is it a real explanation, or just a possible one. For starters, I would argue that it should be shown as well that these moderate values indeed prevail, for instance by using survey data. But, then again, we are almost back at the beginning, for the survey data does not allow for the aggregation that was achieved using the simulation model (MARS). A thought-provoking solution to this problem is suggested by Peter Hedström, who in his book `Dissecting the Social’ suggests that the actors of any simulation model should be `calibrated’ using observations, such as surveys. Basically, this would mean that the MARS simulation model should be able to replicate the persistent religious regionalism, when all actors are individually modeled after representative survey data. Technically, this would require the model to incorporate for each actor a vector of background-characteristics similar to many of the variables often used in other types of research on this subject, so that each actor represents a respondent from certain surveys. Additionally, from this it follows that the number of actors should preferably be close or identical to the number of (large scale) surveys. Only then we could consider the possible explanations offered by the MARS model (or any other simulation model, for that matter) as real explanations. 

All in all, I think that Iannaccone and Makowsky have developed a very interesting perspective and a powerful explanatory framework, drawing from mechanism-based explanations. There is some work to be done, but despite that the model already shows its potential. I’ll be looking forward to new publications based on this work, but for now, I’m off to play some more with the interactive MARS-models on www.marsmodels.com.

IANNACCONE, L.R., MAKOWSKY, M.D. (2007). Accidental Atheists? Agent-Based Explanations for the Persistence of Religious Regionalism. Journal for the Scientific Study of Religion, 46(1), 1-16. DOI: 10.1111/j.1468-5906.2007.00337.x

Schelling, T.C. (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1(2), 143-186.