Be a Good Bayesian and Save the World

 "‘Bayesian epistemology’ became an epistemological movement in the 20th century, though its two main features can be traced back to the eponymous Reverend Thomas Bayes (c. 1701–61). Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic. The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization." (From The Stanford Encyclopedia of Philosophy). 

Quantifying and formalizing inductive logic is of the utmost importance these days, since so many questions abound about the reliability of information and the very nature of what is actually happening in the world. Fascists and other types of authoritarian demagogues have long known that one of the fundamental precursors to controlling what people think is to discredit the very idea of information. One of the salutary ways to counter this general mistrust in all sources of information is to deploy a Bayesian framework of conditional likelihood, and remain open to new beliefs based on new evidence. I just published this Medium piece today that also recommends healthy use of Occam's Razor and Hanlon's Razor.  Truly, simplicity is best, and stupidity has much stronger priors than dastardly but complex cleverness. These are simply facts out of history. 

Anyway, the great insight of Reverend Bayes was that information changes our degree of confidence in the likelihood of an outcome. Standard probability gives odds as a ratio of a particular outcome to the total number of possible outcomes. Bayesian probability does this but assigns an different "weight" to the total number of possible outcomes based on prior information. An example would be choosing a student at random from a student population who is an art major. Standard probability would be to take the total number of art majors and divide by the total student population. But what if it's Tuesday, and Tuesday happens to be when only 20% of all of the art majors have a class on campus? Clearly, that makes it less likely that one would choose an art major at random. 

This trivial example points to the much more significant reality that, if we have pre-existing knowledge, we can often apply that knowledge to an estimate of the likelihood of a particular claim. When I first encountered Chump's tweet about being COVID positive, I think my level of belief was at about 30% confidence or perhaps lower. The Washington Post estimates that Chump has lied 25,000 times since being elected, so I'm justified in not accepting his tweet, really. It would be foolish to take it at face value, given my prior information. On the other hand, as more evidence came in from other sources, my confidence in the claim increased. I think this is a reasonable and healthy way to operate in the world. It would be weird for me to cling to my doubts and start developing some kind of elaborate conspiracy theory and widespread cover up idea, in the face of more reliable evidence. 

It seems that holding beliefs lightly, allowing for new, contradictory evidence, and re-evaluating one's confidence in one's beliefs are all skills that could save the world. They are also skills that could save a long term relationship, a marriage, a work situation, or any other area where we are deploying inductive logic and belief functions. Connected with a spirit of openness to new evidence, a willingness to sincerely investigate is very important. It's not enough for me to just wait passively for new evidence. Sometimes I have to go in search of it, especially when I recognize that I have a high level of confidence in a weird proposition. 

For example, maybe a coworker has not replied to a friendly email for days. I might start believing fairly confidently that said coworker hates me, or found the email stupid, or just does not want to reply. In such situations, it's important for me to be mindful and pursue more information. It's compassionate, it is reality therapy, and it is liberating for me to seek communication with this coworker and investigate my beliefs. The spirit of investigation makes a great many things possible that we shut doors on. 

I'm thinking of buying a stationary bicycle, for example, since the air quality is so bad here in LA that cardio really should be indoors, with filtered air. The thought first arose and then was immediately shot down, due to my imagination that stationary bikes are prohibitively expensive. It turns out they really are not, especially via a used equipment store. There's even a cool thing that includes a desk, so I could conceivably be doing cardio and grading or lesson planning. 

Anyway, it's Sunday. It's nap time. Life's weird.