Individualized Decision-Making Under Partial Identification: Three Perspectives, Two Optimality Results, and One Paradox

• URL: http://arxiv.org/abs/2110.10961v1
• Date: Thu, 21 Oct 2021 08:15:35 GMT
• Title: Individualized Decision-Making Under Partial Identification: Three Perspectives, Two Optimality Results, and One Paradox
• Authors: Yifan Cui
• Abstract summary: We argue that when faced with unmeasured confounding, one should pursue individualized decision-making using partial identification. We establish a formal link between individualized decision-making under partial identification and classical decision theory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Unmeasured confounding is a threat to causal inference and gives rise to biased estimates. In this article, we consider the problem of individualized decision-making under partial identification. Firstly, we argue that when faced with unmeasured confounding, 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, that is, individualized decision-making and unmeasured confounding. Although motivated by instrumental variable bounds, we emphasize that the general framework proposed in this article would in principle apply for a rich set of bounds that might be available under partial identification.

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