The Non-Linear Loophole?
By Bryan Caplan
Last month, I asked readers for a “Great Reconciliation” of three popular beliefs:
1. Risk mitigation should be directly proportional to risk severity.
2. Medically speaking, COVID is 2-5x as bad as flu.
3. Our COVID mitigation efforts should be much more than 5x our flu mitigation efforts.
The most theoretically compelling resolution I’ve encountered maintains that contra (1), our response to risk should be strongly non-linear.
On the surface, this is a plausible story. Consider: How much money would someone have to pay you to endure a 1% chance of death today? Suppose your answer is $100,000. Does logic compel you, then, to accept a 100% chance of death today for 100*$100,000=$10M?
That’s plainly absurd. Indeed, unless your loved ones prefer fat stacks to your continued company, dying for cash is an exercise in futility. And since the value of risk is clearly non-linear, the value of risk mitigation must be non-linear, too.
Should we infer, then, that the War on COVID is prudent after all? Hardly. Sure, non-linearity makes sense when you raise a high risk. But approximate linearity still makes sense when you raise a low risk. If you disvalue a 1% risk of death at $100,000, would you really require far more than $110,000 for a 1.1% risk? Would you really require far less than $90,000 for a .9% risk? Remember, non-linearity is symmetric: If X increases faster than linearly, X should also fall faster than linearly.
Remember, moreover, that you face a long list of risks. They add up to a scary sum, but taken individually, even broad risks (e.g. “all accidents” or “all contagious disease”) are typically modest. So while it might be wise to take great efforts to halve your total risk, taking great efforts to halve any specific risk remains foolish.
Indeed, assigning non-linear weights to specific risks readily leads you to choose higher overall risk over lower overall risk. Suppose you face three risks: death by accident, death by contagious disease, and death by other. These initial annual risks are .1%, .1%, and .8%, initially disvalued at $10,000, $10,000, and $80,000. Now suppose that doubling the first two risks (to .2% and .2%) will reduce the latter risk by three-eights (to .5%), slashing your overall death risk from 1% to .9%. If you value each specific risk quadratically, you will disvalue these three risks at $40,000, $40,000, and $31,250. Upshot: Non-linearity counter-productively leads you to disvalue the safer package over the riskier package, merely because of the composition of danger.
Too abstract? What would you think about someone who categorically refused to drive on rainy days because inclement weather raises his accident risk by 25%? “Eccentric,” if you’re kind.
If non-linear risk valuation doesn’t explain the gargantuan global response to COVID, what does? I’ve invoked them before, and I’ll invoke them again: hysteria and herding. Novel, vivid risks lead to wildly innumerate overreactions, especially when all the other kids are overreacting too.
Alas, that’s human nature. Yet you can and should rise above such feelings and calmly tell the herd: You will not stampede me. And take comfort in the fact that ADHD shall save us – indeed, is saving us already.