A simple model of the dynamics of whhaaa?

March 25, 2011 3:58 PM

Physicists, or someone who is familiar with physics or mathematical models, please help me interpret "a mathematical model of social group competition with application to the growth of religious non-affiliation". I have never heard of Sociophysics before today.

It came up in one of my news feeds as"Religion may become extinct in nine nations, study says" from the BBC... I have been trying to read this article all day but it's too foreign to me. I just need a non-mathemical description of what these people think they are doing.

I can tell from the abstract & the brief bits of non-math in the paper that it is really not all that sophisticated from a social scientific perspective. I'm just curious about why these particular tools and models and being used. I have tried to understand it but I'm missing too much background. I'd like to have a little more understanding of this before I dismiss it.

I guess the distinction I'm looking for here is between bad science and pseudo-science. Is anything really being explained in a useful new way here? If so... can you translate it for me?

Thanks for taking the time.

posted by ServSci to science & nature (9 answers total)

I'm not familiar with diff-eqs, but it looks like what they think they're doing is this:

Someone's probability of converting either to religion or atheism depends on the how many other people are in each group and on a nebulous utility term.

Or, at an individual level, that you're more likely convert to a religion or lack thereof that lots of people belong to, or if there's something in it for you. Not really rocket science, as you note.

I'm just curious about why these particular tools and models and being used.

Because the authors are familiar with them.
posted by ROU_Xenophobe at 4:55 PM on March 25, 2011 [1 favorite]

Models work only to the extent that they capture the essential and omit the irrelevant. I have only skimmed the paper, but I once was a physicist and I recognize the signs of a theory extended far past its domain of applicability. The authors make a number of, as you say, not all that sophisticated assumptions, such as that my influence on you is the same as your influence on me, that my religious "environment" is the simple average of my neighbors' beliefs (mean field theory), that the probability I will convert to a religion is proportional to its number of adherents, that and that these relationships never change. Such a model has been quite successful in predicting the behavior of electrons in crystals, but in my experience people aren't like that.
posted by drdanger at 5:30 PM on March 25, 2011 [1 favorite]

I just need a non-mathemical description of what these people think they are doing.

They have numerical data and a curve-fitting hammer. That hammer makes sense with respect to certain abstract simplifications of how individuals might act. Wild extrapolations follow.

I guess the distinction I'm looking for here is between bad science and pseudo-science.

It's not nice to use names if you can't follow the paper.

Is anything really being explained in a useful new way here?

If you excise the math, the intuition is thus:
"We assume the attractiveness of a group increases with the
number of members, which is consistent with research
on social conformity[14–17]. We further assume that at-
tractiveness also increases with the perceived utility of
the group, a quantity encompassing many factors includ-
ing the social, economic, political and security benefits
derived from membership as well as spiritual or moral
consonance with a group ... We can generalize this model to include the effects of social networks: rather than an individual deriving
benefits from membership in the global majority group,
he or she will instead benefit from belonging to the local
majority among his or her social contacts[7, 19]
... We found that a particular case of the solution fits census
data on competition between religious and irreligious seg-
ments of modern secular societies in 85 regions around
the world. ... For decades, authors have commented on the surpris-
ingly rapid decline of organized religion in many regions
of the world. The work we have presented does not ex-
clude previous models, but provides a new framework for
the understanding of different models of human behavior
in majority/minority social systems in which groups com-
pete for members."

The piece that is interesting to the authors is that their simplistic curve-fitting hammer reproduces this behavior. You might think that you'd need something insanely complicated to, from theory, reproduce the rates at which people change affiliation to a "new" group.
posted by a robot made out of meat at 6:12 PM on March 25, 2011 [3 favorites]

Sorry for how long this is. Translating the math was fun, though. The assumptions that are built into equation one are:

(1) There are exactly 2 populations of people in the world: X (religious) and Y (non-religious). Little x and y are just the percent of the population in each group, so x=X / (number of people in the world).

This is very limiting, since in the real world "religious" and "non-religious" are actually very diverse populations. If you were to disagree with their results, this would be a point to attack.


(2) Every day, there is a certain probability that a religious person will decide that god doesn't exist, P_{xy}. This number is identical for _every_ religious person, but can change day to day. Likewise, there is a probability of an atheist to convert to religion, P_{yx} (which is not the same as P_{xy}).

This is somewhat limiting, but is the "mean field theory" that drdanger refers to. Essentially, the assumption is that we know that some people will convert more readily than others, but to simplify the math, we assume that all people are pretty much like the average. So, while a pretty significant approximation, it's also a sensible one. Still open to attack, though.


(3) The probability of a person converting, P_{yx}, depends on how many religious people there are. The more people believe in god, the more likely you are to convert. The fewer believers there are, the less likely you are to convert.

This sounds like a very pessimistic view of conversion, but it may not be that bad. Certainly to convert to "religion," you will have to have met a religious person. It is very unlikely to meet a religious person on any given day if only 1% of the population believes in god. So there _will_ be some dependence.


(4) There is some "utility" to being religious or non-religious. For example, religious people go to heaven and non-religious people get to have premarital sex. All of the advantages and disadvantages of religion can be quantified into a single number, u_y, between 0 and 1. Importantly, the utility of being non-religious is exactly equal to u_x=1-u_y.

This is their attempt to insert some sort of sociology in the problem. This is one of the weakest points in the assumptions, because most of us would agree that life is more complicated than that. However, it's also _really_ hard to figure out how to quantify an individual's perception of the quality of "religion" or "non-religion". This is certainly wide open to attack if you disagree with their results.


(5) The probability of giving up on god on any particular day is proportional to x^\alpha u_x (i.e. is proportional to atheism's utility, times the number of atheists raised to some power).

There is no apriori reason to believe this is correct. It is, however, the simplest thing you can guess. This is open to attack, but isn't really all that bad of an assumption.

//---------------------

On page 3, they define a network-based model. Essentially, they include the fact that you care about what your friend's beliefs are. So the probability that you convert depends on the fraction of your friends that believe, rather than the fraction of the population that believes. The "utility" argument is unchanged. That's equation 2 and 3.

The network model assumes that you are equally close to all of your friends (you don't have a best friend, you have people whose opinions who matter, and you don't care about anyone else). The later discussion on p. 3 tries to incorporate continuous values to how strongly you are connected to everyone. This is measured by the "coupling kernel" G in eq. 5. Their method basically assumes that everyone is located somewhere (lives in a town), and they care more about what nearby people think (regardless of whether they're friends).

All of this is nice, but they don't really know what any of these networks are. They show in the SI that the network approach is basically the same as the theory in eq. 1, as long as you're friends with _almost_ everyone in the world. And don't appear to do much else with it.

//-------------------------

So, that's basically all of the assumptions. All religious people are identical, and choose to abandon their beliefs based on how popular atheism is (globally or among your friends), and how they perceive the utility of atheism. There is a lot of room for attacking these premises, but it's worth noting that these are probably the simplest possible assumptions you can make to try to incorporate the details they want.

Take it with a grain of salt. But even if the results are wrong, this is definitely not pseudo-science. I personally wouldn't call it bad science either, but it may be bad sociology.
posted by bessel functions seem unnecessarily complicated at 8:00 PM on March 25, 2011 [3 favorites]

In my opinion as someone who has been around this kind of work a lot, this sort of modeling does a much better job of capturing, say, disease dynamics instead of opinion formation. Religion, in particular, has a lot of nuances that separate it from fads or technology uptake or the like. That being said, simple models like this (not necessarily this one) can have a lot of merit.

To my taste, having done work vaguely along these lines, I prefer to be explicit that the equations encode only a very particular subset of real behavior, and even then only a particular approximation to behavior. I'd rather work with an abstract model that is inspired by a real behavior (religious conversion, in this case) and note that the resulting trends could inform the real world. In this case, that it gives the same sort of exponential (-ish, at least) increase you see in real data. That being said, I suspect that this will be generically true of any model where the rate of conversion is proportional to number of adherents.

In sum, they are doing perfectly good analysis, though nothing that strikes me as incredibly novel, but probably overstating the applicability of their results to social dynamics. This is pretty much the norm for physics models of social behavior, but from a stochastic processes perspective they can often result in some cool behavior. A good review article is also on the arxiv.
posted by Schismatic at 8:18 PM on March 25, 2011 [3 favorites]

This is oddly reminiscent of the articles in the early sixties that predicted 100% black attendance in 100% of southern schools by the end of the sixties if the then current trends continued. The authors fail to acknowledge the likelihood of a saturation point for non-religious respondents.
posted by Blasdelb at 9:21 PM on March 25, 2011 [1 favorite]

I've read the article, and as an MA in religion: no, it ain't saying much new. Bessel functions (etc.) is completely correct in saying it might be bad sociology, because: it is. Bessel functions also gives a great literally summary of all the assumptions being made in the article, so yeah, Bessel rocks.

I am also going to bow to Schismatic's interpretation of the analysis as being solid and good, if not novel. I am solely interpreting the analysis from my religious studies background (MA student in a totally different subfield, but who has read a lot of the truly major literature on this debate).

It is a perfectly fine model if you do not actually try to apply it to a given person or group, do not try to apply it outside of the nine countries studies, and if you take its conclusions with a grain of salt. I just think it failing to deal with a lot of variables and a lot of problems with the census data. I also think it is coming to the wrong conclusion (e.g. the inevitable decline in religiosity).

OK, so basically, the argument that social networks lad to conversion is actually a fairly widespread one in the world of sociology of religion. I don't have problem with that.

But the number of aspects they simplify (X and Y being two mutually exclusive groups, all religions recruiting at the same rate in the 9 Western countries being studied, all conversion processes being equal and easy, all religions being X, no real information about the actual networks people are in other than by country) make this a bad study from the point of view of a religious studies student because they overstate the applicability of their model to actual studies of social behaviour.

They also do not give any information as to how they accounted for differences in the census terms (e.g. over time in one country, and differences in the "religion" questions across different countries).

The BBC interpretation of the study (which was originally "religion will die" with no qualifiers) was also problematic as in Soc of Rel studies, it is abundantly clear that in places like South America and Africa, certain forms of Christianity (esp. Pentecostalism and Catholicism) are flourishing and gaining a huge number of adherents.

That said: if you want to read more about this topic, the thing to read about is called "secularization thesis." The problem is that the term "secularization thesis" means three different things (to take this from Jose Casanova): one, the process of human beings becoming less religious (the most common use of the term today); two, the "emancipation" of things like science from the grip of religion; and three, the privatization of religious groups etc. You should try to focus on definition #1.

The problem being is that the idea that we are approaching and "end of religion" was very much in vogue during some parts of the 20th century, especially in the 60s and 70s, but is now a minority position. Why? In addition to the fact that studies about the "end of religion" tended to either discuss only the West (mainly Europe, as the US does not quite work well with secularization thesis), or assume every country would act like Western countries once they developed enough, it has come to light that there are a lot of religious practices that would not be covered by census data, which was the main source of the end-of-religion discussions. This includes being "spiritual, not religious" (which means being religious but without ascribing to a certain institutionalized form of religion, usually) and so-called mix-n-match types of religion, where someone could be a hella New Age lapsed Catholic who calls herself "other" or "non-religious" on the census form but is intensely religious (and admits to it), just not in an easy-to-identify institutional way.

I wish I could go into more detail, but this pretty well as far outside of my subfield as you can get while still staying in religious studies, but I know enough Soc of Rel to subject this article to a sniff test.

If you want suggested readings on secularization thesis, let me now and I'll post some.
posted by flibbertigibbet at 5:46 AM on March 26, 2011 [2 favorites]

Thank you for all the replies. These opinions are precisely the kind of help I needed.

Thanks flibbertigibbet, too, though I'm in religious studies myself and don't need the social science angle covered, so much. I just really couldn't read the math and every response was helpful, and bessel functions' response was really precisely what I needed.

Thanks everyone for even looking at it.
posted by ServSci at 11:23 AM on March 26, 2011

Damn, good to see another RelStudies person here! There are so few of us... 0.0021% of my university are RelStudies kids.
posted by flibbertigibbet at 9:27 PM on March 26, 2011