I just finished reading through the main paper on [Mexican Drug cartel sizes in Science]() (I still really need to read the supplement, which is where all the actual details are…). One of the things I love about Science and Nature is that they will publish “preambles” or “contexualizers” for articles. [In this case, there is a lengthy preamble by Caulkins, Kilmer, and Reuter]() that – I suspect – was the result of a review of this paper that pointed out a number of issues that would be impossible to resolve. In addition to pointing out what seems to be a fairly large hole in the specific justification (e.g. that the result is indeterminate because it’s a ratio), it attacks the entire mathematical modeling edifice itself as too crude an approximation for the complex dynamics involved in cartels “Cartel members are not billard balls or atoms locked into mechanistic reactions to external shocks”. Yet, while this is done with concise and technical precision – the rebuttal is ultimately laudatory and accurate captures the ambition and scope of the effort. It’s nice to see people agree on the utility of big ideas and insights even if they may have huge disagreements on the details – and it’s also nice that Science tries to support this style of debate.

Now, for my own take, I think the objections to the mathematical modeling have the potential to be overblown. The goal with this type of mathematical modeling is to capture just enough of the truth to be useful. In this case, it seems any more detailed modeling would be impossible to do. e.g. the problem with more complicated agent based models is that it’s hard to know if you have baked in any effect due to the extremely large number of choices they require and establishing the this is not so is often problematic and time consuming.