🤖 AI Summary
This paper addresses causal inference under the “missing-label setting,” where training data covers only a subset of possible labels, revealing a nontransitive causal paradox: locally consistent causal conclusions within individual contexts may aggregate into cyclic dependencies (e.g., A ≻ B ≻ C ≻ A) across contexts.
Method: The authors establish, for the first time, a rigorous equivalence between nontransitivity in causal networks and the structure of ranking aggregation under voting rules, generalizing Simpson’s paradox to a unified framework accommodating multiple contexts and non-commuting adjustments. They integrate causal graph models, conditional independence analysis, and rank aggregation theory to formalize this relationship.
Results: The paper proves that every possible nontransitive causal structure corresponds exactly to the outcome of some voting rule applied to context-specific causal rankings. This work delineates new theoretical limits for causal reasoning under label constraints and provides an interpretable diagnostic tool for identifying and analyzing such paradoxes.
📝 Abstract
We explore"omitted label contexts,"in which training data is limited to a subset of the possible labels. This setting is standard among specialized human experts or specific, focused studies. By studying Simpson's paradox, we observe that ``correct'' adjustments sometimes require non-exchangeable treatment and control groups. A generalization of Simpson's paradox leads us to study networks of conclusions drawn from different contexts, within which a paradox of nontransitivity arises. We prove that the space of possible nontransitive structures in these networks exactly corresponds to structures that form from aggregating ranked-choice votes.
