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On Simpson's Paradox and the Sure-Thing Principle

Colin R. Blyth
Journal of the American Statistical Association
Vol. 67, No. 338 (Jun., 1972), pp. 364-366
DOI: 10.2307/2284382
Stable URL: http://www.jstor.org/stable/2284382
Page Count: 3
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On Simpson's Paradox and the Sure-Thing Principle
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Abstract

This paradox is the possibility of $P(A \mid B) < P(A \mid B\prime)$ 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.

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