Kevin shares an intriguing problem from Pearl’s book on statistics about a baseball player with a higher batting average than his teammate overall but a lower average against both right-handed and left-handed pitchers. This paradox, known as Simpson’s Paradox, can be solved using the Z3 Theorem Prover tool. By setting constraints and running Z3, an example is generated that illustrates the paradox clearly. The key to understanding this paradox lies in the fact that the players faced different sets of pitchers, ultimately impacting their batting averages. This exercise sheds light on the complexities of statistics and causal inference.
https://kevinlynagh.com/z3-simpsons-paradox/