linear vs. combinatoric social science

In mathematics, there’s a very rough distinction between “linear” things and “combinatoric” things. We are all familiar with linear science, but combinatorics is more subtle. Combinatorics simply means the math you need in order to count different combinations of things. For example, you may ask, “if I have ten red balls and twenty green balls, and I randomly draw three balls, how many different combinations of red and green do I get?” That’s a combinatoric question – counting discrete things.

Social science has lots of tools that exploit linear models: utility maximization, regression analysis, scale construction, etc. But we don’t have a lot of tools that address the combinatoric side of social life. To see what I mean, consider the issue of policy formation – why does government make some policies and not others?

  • The linear answer (taken from the Median Voter Theorem in economics): Politicians offer policies designed to attract the median voter. Thus, the utility of a policy is approximated by how popular it is.
  • The combinatoric answer (taken from Agendas, Alternatives, and Public Policies): Nature produces a stream of political issues and actors. Think of nature as drawing them from a big box of issues and people. If nature happens to simultaneously choose an issue and actor that “match,” then a policy gets made.

These are not inconsistent views, but they require very different toolkits. The first is about studying distributions of voters. The second is an arrival process. Metaphorically, the first model is a world of smoothness with thresholds. The second is chunky. Over the last hundred years or so of quantitative social science, we have lots of tools for smooth things. We have a few tools for chunky discrete things, like network analysis, but not enough. Ambitious quantitative social science PhD students should carefully think about that last sentence.

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Written by fabiorojas

February 22, 2013 at 12:09 am

Posted in fabio, just theory

7 Responses

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  1. How would you contrast a combinatoric approach approach to a Fuzzy Set approach to analysis? It sounds like a lot of Boolean logic at work here.


    Grad Student

    February 22, 2013 at 1:27 am

  2. Fuzzy sets to me are a compromise. The Boolean logic is definitely combinatorics but the QCA methods end up linearizing the results by invoking continuos degrees of set membership.



    February 22, 2013 at 1:33 am

  3. Check out Ragin’s new book- there is a discussion of measurement vis-a-vis calibration which addresses this issue in detail.


    Chris Bail

    February 22, 2013 at 3:42 pm

  4. There’s also an important distinction between the logic of the model and the logic of fitting the model. I think that the model behind QCA is at heart combinatorial, whereas its estimation is frequently more linearly approached. In some ways the “compromise” you’re suggesting there is thus on the latter only. No? This may be what Chris Bail is pointing at, as I haven’t read the new book.


    jimi adams

    February 22, 2013 at 7:19 pm

  5. To me, the distinction between the linear and combinatoric approaches is really about a distinction between simple chain of causality and complex casual network. The “simultaneous choice” that characterizes the combinatoric approach means that there are two co-existing causal forces. Network analysis features a set of tools that abstract away the complex causal network in order to produce descriptors that are not overwhelmingly complicated. Structural equation modeling, particularly path analysis, can capture some of the simultaneous causalities, albeit with increased demand on data. Ultimately it’s a trade-off. You can choose to recognize the complex causal network in your model, but your estimation will have to pay for it. Or you can settle with a simplified causal model that your estimation can support. At some point, it might be better off going qualitative to retain the complexity and sacrifice potential generalizability. IMHO, the next generation of toolkits can be found if we carefully rethink these trade-offs.


    Chih Liu

    February 22, 2013 at 9:04 pm

  6. […] vs. combinatoric social science” … (not sure that I understood that […]


  7. […] linear vs. combinatoric social science ( […]


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