[ExI] Probability of being affected by terrorism [WAS Re: Mass transit]

[Anders Sandberg]

Richard Loosemore wrote:
> Keith Henson wrote:
>> As usual, airtight reasoning from Anders.
>
> Uh, not so fast.
Thanks Keith, and you're right, Richard. :-)

In fact, I have partially redone the calculations more carefully and 
found a few minor issues. I will post them on my blog a bit later (right 
now I am sitting on the London-Oxford bus, hardly the best place for 
getting probability theory stringent). Basically, it turns out that the 
risk of being harmed from a single-victim feral is a bit larger in small 
groups (avoid elevators!) because of the smaller pool of potential 
victims. And for power-law distributed terrorism there is a situation 
where there exist a finite most dangerous group size for a given 
probability of people being terrorists and for the damage exponent. But 
they hardly change my core conclusions.

>
> Terrorism (or feral actions, if you will) are often not designed to 
> target the individuals they hurt directly, but to target the 
> perceptions of the majority of society.

Yup. In many ways this is a good thing, since terrorists do not seem to 
maximize lethality.

>
> So, please redo the calculations and include the probability of "side 
> effects" such as these, which utterly dwarf the direct effects.
>
> (Hint:  correct answer is that the probabilities cannot be computed in 
> any meaningful way).

Depends on whether you are a subjectivist or not about probabilities. I 
see no problem with saying that the risk of being affected is = P(me 
affected|side effects) P(side effects|terrorism) P(terrorist act). The 
probabilities are going to be subjective estimates, largely set by 
experience and messy, unreliable intuition. A more elaborate model 
taking real world structure into account might even give better 
estimates, but it will still merely be a best guess. This entirely OKand 
rational as long as correctly update probabilities as I get new 
evidence; I might wish for the certainty of mathematics or firm 
empirical data, but in a world of unknowns and black swans this is what 
we have to make do with.

Actually, let's play around a bit with our assumptions and see what 
happens. I think we have a pretty good model of terrorism being power 
law distributed with exponent -2.5. The amount of effect a terrorist 
action has depends on 1) where it happens, 2) how big it is, 3) how 
outrageous it is. Who can name this week's terrorist actions without 
googling? They all happened in the usual far-away countries we tend to 
skim over in our news reading, and they happened to people we do not 
know. Conversely, 911 was an unusually big terrorist event - it is an 
outlier in the data, and the effect was of course amplified by happening 
in a major developed country and in an outrageous fashion (not all 
tragedies are equal). I would model this by saying the effect probably 
scales with the size X as X^k, where k>1. The proper thing would be to 
actually check the amount of coverage different terrorist actions have 
got as a function of their sizes, building a proper probability model. 
Finally, let's make a guesstimate of how the event effect influences the 
chance of it influencing me. I can see an argument for a threshold 
effect (small ones rarely matter, big ones have a high likeliehood): a 
simple model would be P(affected|effect)=(effect}^p where p is another 
exponent > 1, and we clamp the result to [0,1]. Now, putting all this 
together we get P(me affected|event size = X)=CX^(k+p-2.5) where C is 
the normalization factor.

This crude estimate already tells us something interesting. Unless 
k+p<2.5 (which is unlikely, since both are by assumption > 1) there is 
going to a be a critical terrorism size that affects everybody. This is 
in many ways the terrorist sweet spot: it is hard to make big X attacks, 
but if you reach a sufficient size you will get global effects - it 
actually doesn't pay making bigger attacks. If k+p<2.5 big attacks do 
not pay: too hard to do, and there is insufficient reaction to them. So 
other forms of "politics by other means" are needed. So if we want to 
reduce terrorism it might be interesting to consider *ignoring* it to a 
certain extent - overreactions play into the hands of terrorists (and 
anti-terrorists, of course).

(OK, this is as far as I could get between London and Oxford...)

Anders Sandberg,
Future of Humanity Institute
Philosophy Faculty of Oxford University