On Simpson's Paradox and the Sure-Thing Principle

Abstract

Abstract This paradox is the possibility of P(A|B) <P(A|B') even though P(A|B)≥P(A| B') both under the additional condition C and under the complement C' of that condition. Details are given on why this can happen and how extreme the inequalities can be. An example shows that Savage's sure-thing principle (“If you would definitely prefer g to f, either knowing that the event C obtained, or knowing that C did not obtain, then you definitely prefer g to f.”) is not applicable to alternatives f and g that involve sequential operations.