Recent advances in behavioral economics and quantum cognition and decision elucidated a number of deviations of actual human decisions and choices from mathematical principles of normative decision theory, which are referred to as “anomalies”. One of the prominent anomalies is that the violations of Savage’s sure-thing principle, which is the fundamental axiom of the rational theory of decision under uncertainty. It states that if prospect x is preferred to y knowing that Event A occurred, and if x is preferred to y knowing that A did not occur, then x should be preferred to y even when it is not known whether A occurred. I explicitly derive an inequality for testing the violations of Savage’s principle in behavioral experiments on decision under uncertainty. The derivation suggests that the violation of Savage’s sure-thing principle may be due to the violation of the rule of complementarity in probability theory. Future applications for behavioral and neuro- economics and quantum cognition and decision theory are discussed.
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