The Monty Hall paradox appears in many introductory books on probability theory (e.g., Grinstead and Snell, 1998, p. 136; Lindley, 2014, p. 201). The equivalent “three prisoners dilemma” was used to demonstrate the inadequacy of non-Bayesian approaches in Pearl (1988, pp. 58–62).
Tierney (July 21, 1991) and Crockett (2015) tell the amazing story of vos Savant’s column on the Monty Hall paradox; Crockett gives several other entertaining and embarrassing comments that vos Savant received from so-called experts. Tierney’s article tells what Monty Hall himself thought of the fuss — an interesting human-interest angle! An extensive account of the history of Simpson’s paradox is given in Pearl (2009, pp. 174–182), including many attempts by statisticians and philosophers to resolve it without invoking causation. A more recent account, geared for educators, is given in Pearl (2014).
Savage (2009), Julious and Mullee (1994), and Appleton, French, and Vanderpump (1996) give the three real-world examples of Simpson’s paradox mentioned in the text (relating to baseball, kidney stones, and smoking, respectively).
Savage’s sure-thing principle (Savage, 1954) is treated in Pearl (2016b), and its corrected causal version is derived in Pearl (2009, pp. 181–182).
Versions of Lord’s paradox (Lord, 1967) are described in Glymour (2006); Hernández-Díaz, Schisterman, and Hernán (2006); Senn (2006); Wainer (1991). A comprehensive analysis can be found in Pearl (2016a).
Paradoxes invoking counterfactuals are not included in this chapter but are no less intriguing. For a sample, see Pearl (2013).
Appleton, D., French, J., and Vanderpump, M. (1996). Ignoring a covariate: An example of Simpson’s paradox. American Statistician 50: 340–341.
Crockett, Z. (2015). The time everyone “corrected” the world’s smartest woman. Priceonomics. Available at: http://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest (posted: February 19, 2015).
Glymour, M. M. (2006). Using causal diagrams to understand common problems in social epidemiology. In Methods in Social Epidemiology. John Wiley and Sons, San Francisco, CA, 393–428.
Grinstead, C. M., and Snell, J. L. (1998). Introduction to Probability.
2nd rev. ed. American Mathematical Society, Providence, RI. Hernández-Díaz, S., Schisterman, E., and Hernán, M. (2006). The birth weight “paradox” uncovered? American Journal of Epidemiology 164: 1115–1120.
Julious, S., and Mullee, M. (1994). Confounding and Simpson’s paradox. British Medical Journal 309: 1480–1481.