The minimal example would be if each risk had 50% independent chance of happening: then the observable correlation coefficient would be -0.5 (not -1, since there is 1/3 chance to get neither risk; the possible outcomes are: no event, risk A, and risk B). If the probability of no disaster happening is N/(N+2) and the risks are equal 1/(N+2), then the correlation will be -1/(N+1).
I tried a slightly more elaborate model. Assume X and Y to be independent power-law distributed disasters (say war and pestillence outbreaks), and that if X+Y is larger than seven billion no observers will remain to see the outcome. If we ramp up their size (by multiplying X and Y with some constant) we get the following behaviour (for alpha=3):
As the situation gets more deadly the correlation becomes more negative. This also happens when allowing the exponent run from the very fat (alpha=1) to the thinner (alpha=3):
The same thing also happens if we multiply X and Y.
I like the phenomenon: it gives us a way to look for anthropic effects by looking for suspicious anticorrelations. In particular, for the same variable the correlation ought to shift from near zero for small cases to negative for large cases. One prediction might be that periods of high superpower tension would be anticorrelated with mishaps in the nuclear weapon control systems. Of course, getting the data might be another matter. We might start by looking at extant companies with multiple risk factors like insurance companies and see if capital risk becomes anticorrelated with insurance risk at the high end.
This weeks talkie in the scientific blogosphere is a tongue-in-cheek paper by Neil Hall, The Kardashian index: a measure of discrepant social media profile for scientists (Genome Biology 2014, 15:424). He suggests it as the ratio between actual twitter followers and the one predicted by the number of scientific citations a scholar has, . A higher value than 5 indicates scientists whose visibility exceeds their contributions.
Of course, not everybody took it well, and various debates erupted. Since I am not in the danger zone (just as my blood pressure, cholesterol and weight are all just barely in the normal range and hence entirely acceptable) I can laugh at it, while recognizing that some people may have huge K scores while actually being good scientists – in fact, part of being a good scientific citizen is to engage with the outside world. As Micah Allen at UCL said: “Wear your Kardashian index with pride.”
Incidentally, the paper gives further basis for my thinking about merit vs. fame. There has been debate over whether fame depends linearly on merit (measured by papers published) (Bagrow et al.) or increases exponentially (M.V. Simkin and V.P. Roychowdhury, subsequent paper). The above paper suggests a cube-root law, more dampened than Bagrow’s linear claim. However, Hall left out people on super-cited papers and may have used a small biased sample: I suspect, given other results, that there will be a heavy tail of super-followed scientists (Neil deGrasse Tyson, anyone?)
Here is a reason not to worry too much about Ebola… yet. I took the WHO data on Ebola outbreaks and plotted it. The distribution is not power-law distributed (looks bent on a loglog scale) but is decently exponential (straight on a semilog scale). The probability goes down fast with size.
However, when we add the final toll from the current outbreak (1603 suspected cases with 887 fatalities at August 1) it might turn out to be a “dragon-king” bucking the line: in that case we should expect that large international outbreaks follow an entirely new dynamic. This is mildly worrying. Still, it is early days.