Further Reading

The research paper “Common Ecology Quantifies Human Insurgency” has generated a lot of interest from many different academic, political and media partners. The feedback and comments have proved very helpful and on this page we will address issues arising from these conversations. This page is a work in progress and will be updated over time and we always welcome further comments,  both positive and negative. We hope these comments will serve as the starting point for more research.

1. Beyond power-laws

Our Nature paper, in contrast to our earlier 2005 and 2006 preprints, specifically looks at features beyond a simple power-law. As in other areas of complex systems research, we feel it would be a shame if this fledgling field of conflict mathematics gets too bogged down in the subtleties of power-laws and their tests. Indeed, as reported in our Nature paper, additional information is contained in the deviations beyond power-law. In particular, the good fit between our model and these empirical deviations beyond power-law (Fig. 2), offers insight into subtle differences in the rules-of-engagement for these conflicts.

2. The ‘news’ in our model simply means any common information

In Fig. 4 of our Nature paper, we show a cartoon of news being broadcast. This ‘news’ simply means a common set of information – not necessarily a particular media source (e.g. CNN) or even type of media.  Indeed, we state in our Nature paper that: “Each group receives daily some common but limited information (for example, …opposition troop movements, a specific religious holiday, even a shift in weather patterns). The actual content is unimportant provided it becomes the primary input for the group’s decision-making process.” This common information acts as a coordinating effect. Even if it is incorrect or inaccurate, it acts to concentrate responses in a similar way. This crowding effect in strategy space is explained in detail, in the context of financial market burstiness, in one of the downloads from our website “chapter4.pdf”.

3. Alternative models to explain casualty data

As we state at the end of our Nature paper, “Other explanations of human insurgency are possible, though any competing theory would also need to replicate the results of Figs 1–3.” For example, just as in financial market models, certain types of stochastic process might generate similar statistical features – however, just as in the financial market field, it is well recognized that no deep understanding of market dynamics is offered by such models, other than the ability to replicate similar statistical patterns. By contrast, our model is based on reasonable mechanisms of the microscopic dynamics of insurgencies, with fairly minimal assumptions, and hence opens up the path to a wide range of uses (e.g. scenario testing, evaluation of different strategies, interpretation of the ‘change’ in a war through a surge etc.). In the future, once competing models are identified, the entire set of candidate models (including ours) can be cross-checked against more subtle measures of the empirical data.

4. Aggregation in Iraq data: Possible pitfalls

As stated specifically in our Nature paper, and also in depth in the Appendix of our 2006 preprint (Ref. 12 of our Nature paper), we were careful to remove large, artificially aggregated fatality ‘events’ such as morgue reports from our database.

Under this same topic, we would like to warn interested readers that an additional type of artificial ‘aggregation’ can arise in terms of the database classification ‘bodies found’. In particular, it can often happen that bodies are either found together at a particular time, or simply are recorded at a particular time – and hence are assigned as a discrete single event. In particular, we know of various examples of events in the range of 10-30 casualties, which were recorded as single events in earlier versions of the IBC database. Anyone carrying out an analysis on such an earlier database would therefore have an artificially high number of discrete events in the casualty range 10-30 for example. This may significantly corrupt the true distribution, and hence any power-law analysis, since such single events are actually a collection of smaller events. In terms of power-law testing, this is crucial: For example, if the estimated x_min happens to be smaller than these quantities (e.g. less than 10) then these extra events throw significant doubt on the accuracy of resulting power-law estimates.

5. Statistical Analysis: The rejection and acceptance of power-laws

As Clauset et al. warn in Ref. 9 of our Nature paper: “the MLE gives accurate answers when x_min is chosen exactly equal to the true value, but deviates rapidly below this point (because the distribution deviates from power-law) and more slowly above (because of dwindling sample size). It would probably be acceptable in this case for x_min to err a little on the high side (though not too much), but estimates that are too low could have severe consequences.” For this reason, we followed the method of estimating x_min described in Ref. 10 (and 9) of our Nature paper, i.e. we choose the value of x_min that makes the probability distributions of the measured data and the best-fit power-law model as similar as possible above x_min.

By contrast, however, any scheme that attempts to use a value of x_min which is unnecessarily small, will bias the analysis. In short, as stated explicitly by Clauset: “If we choose too low a value for x_min, we will get a biased estimate of the scaling parameter since we will be attempting to fit a power-law model to non-power-law data”. Most importantly, it may lead to the erroneous rejection of a power-law fit for data in the tail of the casualty distribution. For example, a scheme in which x_min is chosen as the minimum value such that a given hypothesis cannot be rejected with a certain confidence level beyond x_min, can result biased against possible support of a power-law. Compounding this analysis with a database in which ‘bodies found’ events are included as discrete events with magnitudes in the range 10-30 (see point 4. above) would likely produce erroneous conclusions.

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