The logic of Simpson's paradox

There are three distinct questions associated with Simpson’s paradox. (i) Why or in what sense is Simpson’s paradox a paradox? (ii) What is the proper analysis of the paradox? (iii) How one should proceed when confronted with a typical case of the paradox?We propose a “formal” answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding Simpson’s paradox. Our account contrasts sharply with Pearl’s causal (and questionable) account of the first two questions. We argue that the “how to proceed question?” does not have a unique response, and that it depends on the context of the problem. We evaluate an objection to our account by comparing ours with Blyth’s account of the paradox. Our research on the paradox suggests that the “how to proceed question” needs to be divorced from what makes Simpson’s paradox “paradoxical.” Davin Nelson was a former student of Montana State University. P. S. Bandyoapdhyay (B) · G. Brittan Department of History & Philosophy & Affiliate to Astrobiology Biogeocatalysis Research Center, Montana State University, Bozeman, MT, USA e-mail: [email protected] G. Brittan e-mail: [email protected] D. Nelson Department of History & Philosophy, Montana State University, Bozeman, MT, USA M. Greenwood · J. Berwald Department of Mathematical Sciences, Montana State University, Bozeman, MT, USA e-mail: [email protected] J. Berwald e-mail: [email protected]