Making decisions with imprecise probabilities is a risky business

The media tends to like to point out either the risks or the benefits of reopening the economy versus staying locked down. It is rare to see any news outlet take a systematic approach, which is what we hope policymakers are doing. We know stats nerds are. With much of the economy now reopening, we hope for the best but what can we be certain of in uncertain times? Math may have the answer.

Photo by Wikipedia User Alinaderi158 CCA-SA 4.0.

In my research on sensors, machine learning, and collaborative robotics, understanding how to make decisions when you don’t know what is going to happen is something I deal with all the time. Mathematics can tell us something about what we’re facing, even when there is so much we don’t know.

Every decision we make comes with an element of risk. Do I buy a Honda or a Toyota? Or should I save that money and take the bus? Is it safe to go to the grocery store or should I stay home and order in? Can I survive on unemployment checks until it is safer to work or should I go back now?

These decisions come with risks. They also come with uncertainty.

You can think of risks as the “known unknowns” and uncertainty as the “unknown unknowns” of life.

One big unknown unknowns that we are all dealing with right now is Coronavirus. I guarantee you that thousands of risk assessment meetings across countless boardrooms went on in late 2019 and early 2020 that made zero mention of a worldwide pandemic and global lockdowns. Could it have been accounted for? Possibly better than it was but not completely.

As a teenager, I was a huge Isaac Asimov fan. Asimov was best known for two things: his rules of robotics and the fictional science of psychohistory, the mathematics of predicting the future which he made a critical character in his _Foundation _series. Fundamentally, Asimov’s psychohistory was about decision making under uncertainty with the belief that large political movements could be predicted or at least managed.

Chaos theory tells us that we can’t do what Asimov wanted. There are too many unpredictable events that have out-sized impacts. In mathematical terms, they are sensitive to initial conditions. Even something as tiny and insignificant as a single change in a single strand of RNA in a single virus can have an enormous impact on human events. The “butterfly effect” means that nobody can predict even global events too far into the future.

Suppose, however, that there were a perfectly rational being in charge who could make decisions taking all factors into account and maximizing benefit at minimal cost. Knowing that the probabilities of any outcome are unknown and the benefits of certain actions also unknown, could even a super artificial intelligence make the right choice? What sort of mathematics could this being rely upon? What sort of strategy would such a being choose?

#uncertainty #policy #mathematics #decision-making #maximum-likelihood #go