Omitted Labels Induce Nontransitive Paradoxes in Causality
This addresses a fundamental issue in causality for specialized expert systems, though it appears incremental as it builds on known paradoxes like Simpson's paradox.
The paper tackles the problem of omitted label contexts in training data, where only a subset of possible labels is available, and shows that this leads to nontransitive paradoxes in causal conclusions, with a proof linking these structures to ranked-choice voting.
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.