A test of (weak) certainty independence

We provide a test of the axioms of certainty and weak certainty independence in models of decision-making under subjective uncertainty. We show that it is through these two weakenings of the classic independence axiom that prominent ambiguity models retain properties that stand in conflict with the ambiguity-sensitive behavior that is revealed in our experiment. Our findings suggest that this conflict may be of a more fundamental nature than what most of these models can accommodate. Our results call for the use of ambiguity models that can accommodate an ambiguity attitude which depends on the chances of winning.