I recently started reading “How Not To Be Wrong - The Power of Mathematical Thinking” by Jordan Ellenberg. It is an accessible book for people who have been out of touch from rigorous math.
Jordan provides examples of erroneous day to day headlines, and then points out issues in judgments made. Jordan does not try to provide rigorous proof, but is able to channel our intuition to make us comfortable with his conclusions.
There are two biases that I call out in this blog post.
Accommodating survivorship
Our observations of the world are misled when we only focus on what information we have available now, and assuming that existing information is representative of the entire system state (i.e. a random sample in statistics terms).
Instead, it is better to think about why and how did the present situation and or information come into being.
The example was quite poignant: In World war 2, armoring of air planes against bullets was one of key strategic initiatives in the American military.
Planes coming back from the battle field had few holes on the engine, and a higher number of bullet holes on the fuselage and the fuel system.
If we add more armor to the plane by raw hole counts, we may erroneously armor the fuselage and the fuel system. However, it is the engines that require the most protection, as lack of bullet holes in that area indicates that holes in the engine led to fatal crashes.
The reason our intuition is misled is that we think that planes coming back from the battle are a random sample of all planes (representing all bullet hole hits), and that is simply not true.
Being wary of false linearity
Humans are very good at linear thinking, i.e. simple cause and effect relationships. However, there are many relationships that are more complex.
A poignant example is the relationship between Government revenue and Taxation: popular belief is that lower taxation will provide economic activity boost that will increase revenues eventually.
However, this is a false assumption, as if it were true, then zero taxation would provide highest revenue, and this is clearly not the case. Indeed, there is a Laffer curve like relationship (quadratic).