Unmeasured confounding is a threat to causal inference and gives rise to bi-ased estimates. In this paper, we consider the problem of individualized decision making under partial identiﬁcation. Firstly, we argue that when faced with unmeasured con-founding, one should pursue individualized decision making using partial identiﬁcation in a comprehensive manner. We establish a formal link between individualized decision making under partial identiﬁcation and classical decision theory by considering a lower bound perspective of value/utility function. Secondly, building on this uniﬁed framework, we provide a novel minimax solution (i.e., a rule that minimizes the maximum regret for so-called opportunists) for individualized decision making/policy assignment. Lastly, we provide an interesting paradox drawing on novel connections between two challenging domains, i.e., individualized decision making and unmeasured confounding. Although motivated by instrumental variable bounds, we emphasize that the general framework proposed in this paper would in principle apply for a rich set of bounds that might be available under partial identiﬁcation.
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