Bayesian Belief

I encountered Bayes Theorem in an undergraduate statistics course but never grasped its importance until this 9/12/16 article from Scott Alexander:

Scott’s blog used to have this as its slogan:

“P(A|B) = [P(A)*P(B|A)]/P(B), all the rest is commentary.

You read the formula as:  The probability of A given B is equal to the probability of A times the probability of B given A, all divided by the probability of B (the base rate).

After studying Chapter 5 of Steven Pinker’s Rationality (2021), Beliefs and Evidence (Bayesian Reasoning), you understand Bayes Theorem at a gut level.  He begins the chapter with a hat tip to the Rationality Community, “a heartening exception to the disdain for reason”. avers “you may want to learn about Bayes rule if you are a professional who uses statistics, a computer programmer, or a human being”.  It’s that important of a thing to know. 

Baysian reasoning is the essence of human cognition in a world of uncertainty and yet frequently flouted in everyday thinking.  Pinker explains how people neglect the base-rate or actively ignore certain information as “thought taboos”.  Bayes rule tells us how much credence we should give a hypothesis before we look at the evidence.  Prior credence is knowledge accumulated from all our experiences in the past.  In fact, the information from one round of looking at evidence can supply the prior probability for the next round, a cycle called Bayesian updating.  It’s the mindset of someone who wasn’t born yesterday.

Surprising new scientific findings have low probability of truth because our cumulative scientific understanding is not worthless.  That’s why an undergraduate physics textbook is 90% true, while the contents of a primary research journal of physics is 90% false.  Bayes taught us that we should be suspicious of new knowledge.  Pinker quotes Carl Sagan at the beginning of the chapter:  “Extraordinary claims require extraordinary evidence”.

In chapter 6 of Rationality, Risk and Reward (Rational Choice and Expected Utility), Pinker unfortunately recounts the frequently made but fallacious moral argument for coercive wealth redistribution on pg. 182, while discussing happiness:

The psychological meaning is obvious:  an extra $100 increases the happiness of a poor person more than the happiness of a rich person11 (This is the moral argument for redistribution:  transferring money from the rich to the poor increases the amount of happiness in the world, all things being equal.)

Pinker should know better.  Endnote 11 cites a 2008 academic paper on the economics of subjective well-being (happiness).  But Game Theory from the 1940s established that in a competitive, free world, THERE IS NO SUCH THING AS OVERALL MARGINAL UTILITY/HAPPINESS! 

Read my 7/27/21 post.  That’s not my opinion.  It’s the mathematical formalization of von Neumann and Morgenstern.

Next week, we plow through more statistical knowledge before arriving at Pinker’s chapter on Game Theory.

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