Dear Scatterplotters: Would you say there are any “controversial issues” about or within mathematical sociology? This would be either debates inside the terrain of mathematical sociology OR debates between mathematical sociologists (or subsets of mathematical sociologists) and “others”? If you can point me to sources, that would be cool.

Why am I asking? I’ve assigned honors students a paper that is supposed to include some sort of controversial issue with advocates on both sides. One student is really interested in mathematical sociology and I’d like to nurture that if at all possible. As a onetime quasi-mathematical sociologist, I’ve certainly felt that some sociologists thought the entire enterprise was illegitimate, and have received reviews along the lines of “why would you even bother doing this?” But I’m not sure I can find sources for that. Any kind of “controversy” will do if there are people who have written things disagreeing with each other.

–Pam

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As a former math modeler, I would say there has been a decades controversy over the potential usefulness of math models for sociology. In the 1970’s math modeling was claimed to be the big next answer to sociology. Obviously this has not occurred. Still many in the ASA math modeling section still claim that math models has great promise for sociology.

Chris Winship

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Can you point me to someone who has written that math models have proven to be a waste of time, or disappointing or some such?

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Another would be whether parsimonious models are necessary or merely preferable. Macy takes the strong pro-parsimony position. I’m not sure who has argued explicitly for thick models but I’ve certainly seen examples (eg, Moody’s unpublished simulation of the sociology labor market).

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Gabriel, I’d argue that we shouldn’t value parsimony per se, but that we will often end up finding ourselves preferring more parsimonious models because we benefit more from a deeper understanding of something parsimonious than a more shallow understanding of something more complex/realistic.

Math models to be simulated or solved analytically are different from statistical models to be fit to real data, but some of the arguments Andrew Gelman makes against parsimony are relevant: http://andrewgelman.com/2005/04/against_parsimo_1/

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Not sure if this is squarely within mathematical sociology, but there is certainly an ongoing debate and controversy about the use of dyadic data to make inferences about social influence (e.g., Christakis and Fowler) as compared to the contagion models that concentrate network influences to the individual level (this may describe several approaches: Marsden & Friedkin 1993, roommates – Sacerdote 2001, propensity score and matched sample estimation – Aral, Muchnik & Sundararajan 2009).

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There is, of course, the rational choice theory vs. anti-rational choice theory debate. Can’t we just admit that there is insight to be had from multiple approaches? (ok, that still requires debating how much insight of what kinds come from different approaches.)

I don’t recall hearing a debate between RCT and other mathematical modeling strategies but it has to exist somewhere because I’ve had the debate informally a few times.

Here are some of my relevant blog posts:

http://permut.wordpress.com/2009/10/21/mathematical-models-why-and-what-for/

http://permut.wordpress.com/2009/10/27/paul-krugman-on-metaphors-and-models/

http://permut.wordpress.com/2009/11/01/performativity-barely-scratching-the-surface/

http://permut.wordpress.com/2009/11/10/forced-to-defend-rational-choice-theory/

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Another debate: simulation (programming) vs. analytic (paper and pencil) approach to mathematical models.

Fabio has come down on analytic side in multiple blog posts. I think we should like both.

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Yes, closed-form analytical models vs. emergent agent-based models seems like a decent split, though I don’t know if it’s a controversy or not.

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I wouldn’t call it a “controversy”, but there have also been discussions of forward vs. backwards-looking rationality that might be about the right scope for an undergraduate paper.

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The most important controversy in mathematical sociology is the difference between parsimony and simulation. Simulators want complex and more accurate simulations of reality. in contrast parsimony modelers focus on a few variables. Complex models are hard to understand but accurate. Simple models are easy-to-understand but less accurate.

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I’m not sure that this would fit in a neat pro/con controversy, but writing about the nature of racial residential segregation using agent-based models is one area of active research using mathematical sociology. Based on Schelling’s tipping point model, a great deal of research investigates both the formal model (e.g., Bruch and Mare, Fossett) and the theoretical underpinnings that hold up or challenge some of the assumptions of mathematical sociology (W.A.V. Clark, Krysan, Farley). There are several debates within this, but they all center around Schelling’s mathematical model.

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I always get a little uncomfortable when people assert that simulation=complex and mathematical modeling=parsimonious. Simulations can be very simple, and their results can approximate the same solutions one would get from, say, an interactive Markov model. Though of course, part of the appeal of simulation is that one can formally investigate problems for which there are no closed-form solutions.

That having been said, my sense is that micro-macro (as opposed to macro-macro) simulations–even ones that include many dimensions in an attempt to accurately represent reality–are rarely accurate. It took the MIDAS project (http://www.nigms.nih.gov/Research/FeaturedPrograms/MIDAS/) ten years (and god knows how many millions of dollars) to develop their model of flu epidemics, which is now being used to make policy decisions. This extremely complicated model was built up over time from a set of much simpler models.

My view is that mathematical modeling has certain advantages over simulation: you can see the whole universe of potential solutions to a problem. It’s easy to miss multiple equilibrium in simulation models, and also harder to identify basins of attraction. However, there are a lot of questions that mathematical models cannot answer. They can’t include a lot of population heterogeneity, they are pretty limited in the number of focal attributes, they cannot take into account spatial relationships, etc.

Geek addendum: One concern I have with mathematical models is that they assume a continuous world when in fact we live in a discrete world. Math models–at least the ones I work with–distribute individuals probabilistically over potential outcomes which imposes a “smoothing” of reality. Agent-based models force agents to make a 0/1 decision. This might make a big difference, especially in situations where group size is small (and thus the entry or exit of one person from a group can have a significant effect on group composition).

Elizabeth

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great comment!

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on the smoothing point, i see this as one of the insights of Granovetter AJS 1978 (one of my favorite papers). in it he notes that if there is any discontinuity in the micro threshold distribution you’ll stop the diffusion in its tracks. of course this is something you only see if you

drawfrom a distribution (as in a simulation) rather than using the distribution itself (as often w math). more recently i’ve also noticed that there’s a lot of math literature on all-pay auctions that I find less interesting than Tullock lotteries (the noisy form of all-pay).aside from better being able to handle noise, lumpiness, etc, the other reason I prefer simulations is pretty practical, which is that lots of sociologists are decent programmers and thus could very easily start doing simulations whereas few of us have done proofs since high school. this isn’t an issue to the extent that math/sims is an area for specialists, but is to the extent that we think it should scale up to wider use throughout the discipline. obviously this could change (it did in econ after Samuelson) but in the short to medium run, math has a ceiling whereas we could very rapidly scale up use of simulations.

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