The Black swan fallacy is all the rage, but nobody talks about its less-sexy, far-too-neglected cousin: the rare events fallacy. There’s no link because I couldn’t find one! The mind-numbingly obvious point is that rare events happen. Like, all the time. People for some reason think that pointing out how exceedingly unlikely it is for an average person to be the victim of a violent attack at any point in time somehow constitutes an argument. Taken at face value, it would imply that one should never worry about rare events at all; this misses the point that probability accumulates over many trials.[Update: Come to think of it, I suppose an appropriate link might be Zeno’s paradox: how do all those negligible, infinitesimal points add up to a segment of positive length?]
C’mon, folks. Do you lock your door when you leave the house? Given how statistically rare home break-ins are where you live, that’s probably effort wasted. Do you buckle up in your car? (I know I do — the damn thing won’t stop beeping until I click in the belt.) What are your odds of having an accident on this very trip? Screening for various rare diseases — what are you, a hypochondriac?
In slightly more mathematical language, the rare events fallacy rests on the faulty premise of an improperly defined probability space. The right question to ask is not, “What is the probability of X happening to me right now?” Rather the question should be something like, “Over a lifetime of actions, is my expected utility higher if I consistently perform action X rather than its alternative?”