Richard Posner has made a name for himself applying cost-benefit analysis to the law. In this book he asks how we should think about very very unlikely scenarios that are very, very bad.
In Catastrophe, Posner wonders what the law says / should say about very very bad things that are very very unlikely.
In American torts, “If someone has been hurt, then whoever harmed them has to pay.” That’s tough in many cases, like torrent downloads, and … unlikely catastrophes.
For example, the Relativistic Heavy Ion Collider. Built in New York state a decade before Geneva’s Large Hadron Collider, some worried that the Earth would be completely destroyed by RHIC’s experiments. Either a mini-black-hole would swallow us, or a strangelet (made of strange quarks) would rapidly accrete everything in the world onto itself, and in less than a second people, plants, and the molten iron core would be gone, gone, one: not with a bang but with a slurp.
Despite how awesome that would be, some people were against the idea. But how do you assess the chance that those high-energy physicists could destroy the rock we live on?
The judge in New York heard testimony from scientists who basically said, “These bombardments have been going on for æons on the moon, and the moon’s fine. We’re gonna be fine.” The Senate also convened hearings.
- Senator: So … are you guys going to destroy everything?
- Physicist: Nope.
- Senator: Um. Are you sure?
- Physicist: Yep.
- Senator: But … like … how sure are you? Sure sure? Or just sure?
- Physicist: I’m sure.
Turns out they were right. The RHIC ran without destroying the world and the LHC has also not destroyed the world. (Even though it would be so much cooler if one of them did.)
But, like, who are these scientists to testify about the fate of us all? And who is the judge to decide? Who is the US Senate to decide? At the very least, there are jurisdictional issues. New York probably shouldn’t preside over the fate of the world, even though most people in Manhattan aren’t aware that anybody outside New York actually exists.
And then, there’s the issue of risk preference. Suppose just one person was affected by a catastrophe. No bargaining or interpersonal tradeoffs necessary.
How should she weigh a
- 1‱ chance of losing $10,000 versus
- a .001‱ chance of losing $10M, versus
- a .000001‱ chance of losing her life?
Obviously she doesn’t want any of those things to happen, but .000001‱ is a pretty small chance. Maybe she should take it.
And the chance of many astronomical catastrophes is even smaller, like maybe 10^−50 or less. What’s even tougher to think about is: those probability numbers themselves have a probability attached to them! If a scientist tells you there’s a 5% chance of global warming, it’s not 100% chance that she’s correct; it’s some unknown % chance that she’s correct.
Another post, another time, about imprecise probabilities.
In the normal domain of values we encounter these problems in, people have common sense, adages, and experience to guide them.
- “What’s the worst that could happen?”
- “One in the hand is worth two in the bush.”
- “Even a once-in-a-century flood, still comes once a century.”
Measurements of Risk Aversion
People are averse to risk. They’re also averse to losses. (By risk I mean the chance of a loss; by loss I mean the certainty of a loss.)
They also mis-understand numerical probabilities. More about prospect theory in another post.
There are some estimates of the magnitudes of all this psychology. Definitely no measurements can be made about people’s real reaction to these galactically improbable events.
But suppose you knew every single person’s risk preference. Still, would that tell you how to weigh these choices?
Just fathoming this stuff is difficult. Trying to weigh the morality of the options is difficult.
Let’s pretend that all imprecision in climatologists’ estimate of the chances of global warming is erased tomorrow. Now we know exactly the chance of 1 degree global warming, of 2 degrees global warming, and so on. And we know exactly what x degrees of warming would mean for the livelihoods of Norwegians, Indonesians, Oregonians, Argentinians, everybody.
Still! What would you do? How could we come to an agreement? Even if people could agree on what’s the relative value of an Indonesian’s well-being versus an Oregonian’s? How. Would. You. Know. What to do.
How do you decide to pair unfathomably large damage with unfathomably small probability?