I’m a sociologist by training who has studied as much economics as sociology as well as a fair amount of physical science/applied mathematics. It seems to me that if it’s deemed that sociology ought to become more mathematical economics may not be the best model, at least not at the beginning. Perhaps the mathematics background one gets as a result of an undergraduate degree in physics or engineering might be the better way to go. Such students are required to take three semesters of calculus, differential equations, and linear algebra (often differential equations and linear algebra are part of the same course where the linear algebra part is focused on differential and difference equations). The math courses taken by these students may focus on derivations but tend not to focus very much (if at all) on the kinds of proofs found in pure mathematics and even theoretical economics. If we could get sociologists close to this type of mathematical background, either by requiring applicants to graduate programs to already have it or, perhaps more realistically, trying to provide as much of it as possible once students start graduate study in sociology programs, I think this relatively modest step would be a vast improvement. A way to do this once students start graduate study would be to require all PhD students in sociology to take at least a semester and perhaps a year of mathematics. The first semester could be a course in Mathematics for Sociologists and an ideal book for such a course might be Alpha C. Chiang’s Fundamental Methods of Mathematical Economics. Even though it has Economics in the title it covers areas of mathematics that are quite useful for sociologists too. I suspect that afinethorem might regard Chiang as not rigorous enough but remember I’m proposing something, at least as a start, that is more modest than what economics programs are trying to do. Thus, a book like Simon and Blume’s Mathematics for Economists, which I understand is often used for PhD students in economics. although a very good book, would, I suspect, be too difficult for what I have in mind. The second semester, if there is one, would be a course on mathematical modeling and a book like Giordano et al.’s A First Course in Mathematical Modeling would be an ideal text. Once students had the background they would obtain from these courses, then sociology programs could begin to teach their statistics courses differently, including more mathematical statistics and probability theory (intuitive not measure theoretic). I suspect that what I’m proposing would be controversial among sociologists. But it seems to me that economists, engineers, physicists, and others are doing a lot of work these days (consider the work on the small world problem and social networks more generally) on what, arguably, are sociological problems. Many of us (perhaps most of us) in the discipline don’t have the mathematical background required to understand this work and, perhaps, contribute to it, which I think is kind of shame. The proposal I’ve made won’t get us to a point where we will understand all of this work and other work similar to it—but I think it would be a start.

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]]>I politely accuse you of advocating a method that is inherently academic (that is, wrong).

In other words, please speak to the practical side of your argument.

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]]>@Amit: you can sign up here: http://www.sscnet.ucla.edu/soc/groups/mathsoc/index.php

Seriously, all those who expressed support for Fabio’s post: the ASA Math Soc section could really use some more members. Join the club…

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]]>It could happen. But other disciplines – such as biology – have a much more balanced approach to mathematical formalization, so I don’t see so great a danger in the horizon.

Economics, on the other hand, suffers from a severe case of physics envy.

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]]>And besides, I suck at math.

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]]>From my experience, I think the problem will be the opposition to this within sociology itself. There are too many academics that are maths-phobic, and resort to arrogant, yet incoherent arguments against modelling in sociology.

What if sociology looked at other (sub-)disciplines such as behavioural economics and institutional economics for insipiration? Aren’t these doing a lot of exciting ‘mixed’ methods work right now?

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]]>Trivers doesn’t say that Group Selection is isomorphic to Individual Selection. Trivers said that group selection – the idea that evolution operates at a higher level than the individual or their genes- is essentially wrong.

When he does mention the word isomorphic, he is disputing theorists who do claim group selection is isomorphic to individual selection. See part 2, 7 minutes 30 seconds. “Just because two languages are isomorphic – or can be made isomorphic – does not mean that they are equally useful in thinking about things.”

He then uses Kin selection to explain genetic imprinting, something which he claims group selection would take all sorts of exceptions and premises.

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]]>Of course not all analytic philosophy that is published meets these criteria, and certainly most of it is not mathematically precise, though results in logic, decision theory, and formal epistemology are. The discipline as a whole does strive to meet these criteria, though.

I don’t know much about sociology theory, so I don’t know whether there is a body of verbal theory in sociology that is alive to these concerns. But I think it’s important to keep in mind that verbal theory can strive for conceptual clarity, logical precision, and argumentative rigor.

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]]>The economic model is one way. In that model, you eject all work that is not mathematical and select students based on math ability. Then you get a group of people who are essentially doing applied math.

But there are other models. Demography is a good example. It’s a field where almost everybody knows some models and the models are low tech. It’s a field where even qualitative demographers are expected to have basic fluency in things like life tables and Markov processes. Some specialists do high tech, but most don’t. Since the models are low tech, you can teach them, people accept them, and they can see how they are motivated by real examples.

So there’s a successful model of formalization that is not the econ model. Now the question is professional. That’s the real stickler, in my view. Sociology is a field that people flee to because they are bad at math or scared of math.

Despite that problem, there has been success on some fronts. All students must take multiple regression. A lot of students take network analysis. Descriptive? Sure, but it shows that if properly packaged and connected to real world concerns, a lot of people are willing to give it a shot.

Also, graduate committees at most soc programs look at quantitative scores. Northwestern is atypical in that it’s a bastion of qualitative culture studies (#1 according to US News rankings). Most top 20 programs have a small, but noticable, trickle of math, econ, and engineering folks (I was one). Many leading sociologists have physical science degrees, such as James Coleman (chemistry) and Harrison White (PhD in physics and sociology). The potential is there.

Ultimately, what you need is a cohort of scholars who are willing to fight the good fight. It starts with building a language for formalization and then fighting it out in journals. I’ve read old economics journals. It wasn’t all fixed point theorems in 1910. It took decades to build the field. The same with sociology. We’ve got cool ideas, now it’s time for a new generation to build the tools. And if they can show success, it’ll be respected and built into the system.

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]]>Consider even basic theory results in economics. The proof of Nash existence in finite games, as far as I know, requires the use of a fixed point theorem. Just saying that Nash has an equilibrium because the requirements of Kakutani are satisfied surely wouldn’t be convincing to a lay sociologist. But the math behind why Kakutani works, though only at the level of a first year graduate course in mathematics, is far from trivial. And note that NE existence is a 60 year old, one-page-long paper: the really nice modern mathematical results in economics are often quite a bit more complicated.

Fields like economics essentially weed out the mathematically unprepared before graduate programs even begin…but it’s tough to imagine any sociology program rejecting a promising student because of their lack of Real Analysis. If that is the case, then, good journals in sociology need to decide between printing papers using a methodology inaccessible to much of the profession, or maintaining the fairly-unmathematical status quo. How could sociology get around this problem?

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