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Coalition dynamics

I hate to publicize this sort of thing, but two different people forwarded it to me, so I thought I should comment. It’s a paper by Peter Klimek, Rudolf Hanel, and Stefan Thurner:

The quality of governance of institutions, corporations and countries depends on the ability of efficient decision making within the respective boards or cabinets. Opinion formation processes within groups are size dependent. It is often argued – as now e.g. in the discussion of the future size of the European Commission – that decision making bodies of a size beyond 20 become strongly inefficient. We report empirical evidence that the performance of national governments declines with increasing membership and undergoes a qualitative change in behavior at a particular group size.

I admire the goal of doing empirical analysis, and the graphs are great, but I agree with the Arxiv blogger that their mathematical model of “a critical value of around 19-20 members” is “somewhat unconvincing” (except that I’d remove the “somewhat”). Do people really believe this sort of thing? It seems like numerology to me.

The problem with counting countries

Another problem, to my mind, is the reference to the number of countries in the European Union. I understand that these are sovereign states, but I don’t think it makes sense to count them equally. Applying a model in which all voters are equal doesn’t make sense to me.


I am unhappy with the authors’ attempts to imply that their work is relevant to actual politics. That said, I like the rest of the paper–it’s a fun model, and you have to start somewhere. After all, I wrote a paper on coalitions myself that had no empirical relevance. So I can hardly object to this sort of academic exercise.


  1. goodnessOfFit says:

    I wrote a more snarky comment but thought maybe a question would be better.

    Do you think there is anything that can be gleaned from mathematical modeling (be it axiomatic, simulation or ABM) of political process that tells us about the real world. Or are you just averse to ABM itself?

  2. goodnessOfFit says:

    (I hit return before I finished my post)

    Maybe a post on your view of the role of formal models and their intersection with empirical analysis would be interesting. Or maybe your feeling about the EITM movement in political science.

  3. Andrew says:

    I don't know what you mean by ABM or EITM, so I hesitate to offer any opinions on the matter.

  4. TO says:

    EITM is Empirical Implications of Theoretical Models, a movement in political science. I know not what ABM stands for.

  5. Corey says:

    Some googling seems to indicate that ABM is "agent-based modelling" and EITM is "empirical implications of theoretical modelling".

  6. goodnessOfFit says:

    Yeah, they got it. Sorry for the alphabet soup.

  7. goodnessOfFit says:

    I just realized that if you did not recognize the acronym EITM you may not know about it. Here is a quote from the website of the latest summer program:

    The scientific study of politics requires empirical evaluation of theoretical models, but theories too often proliferate without adequate testing, and empirical work too frequently applies sketchy and oversimplified theory. In EITM, researchers use recent advances in game theory and mathematical modeling to develop theoretical models of politics. These models are then subjected to rigorous tests that meet the highest standards of empirical research, including statistical analysis, experiments, and case studies. In some instances, researchers create new estimators designed to closely test the assumptions and predictions of the theoretical models. By integrating models and data, EITM is creating a new standard for theoretically grounded empirical research that yields cumulative advances to our understanding of politics.

  8. Antony Unwin says:

    "the graphs are great" Hmm. Common scaling should be used for the horizontal axes of Fig 1(b) and ideally be the same as in Fig 1(a). What is the "(a)" doing inside the plot in Fig 1(a)? Does the conclusion in the caption of Fig 6 hold for the Human Development Indicator? I know graphics standards in general are low, but I thought yours were higher!

  9. Andrew says:


    I like agent modeling. It's like probability modeling but more general. But I get off the bus when they start making claims such as "there is a phase transition when committee size reaches 20." This could be correct but it violates all my mathematical intuition.

    As for EITM, I don't know anything about it–but it sounds to me more like a slogan than a research program.


    Sure, the graphs as graphs could be improved. But I like them compared to the tables that one would likely see in a statistics article. The standards for presentation of results are higher in physics than in statistics, I believe. Physicists routinely use creative graphs, whereas statisticians too often use tables or else spit out formulaic graphs such as q-q plots.