Omitted Labels Induce Nontransitive Paradoxes in Causality

Bijan Mazaheri, Siddharth Jain, Matthew Cook, Jehoshua Bruck

Keywords: Paradoxes, Simpson's Paradox, Condorcet Paradox, Social Choice, Decision Fusion, Nontransitivity

TL;DR: We study networks of causal quantities computed on subsets of labels and observe a paradox of nontransitivity, which we present as a generalization of Simpson's Paradox.

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.

Submission Number: 59