Distribution Re-weighting and Voting Paradoxes.

We explore a specific type of distribution shift called domain expertise, in which training is limited to a subset of all possible labels. This setting is common among specialized human experts, or specific focused studies. We show how the standard approach to distribution shift, which involves re-weighting data, can result in paradoxical disagreements among differing domain expertise. We also demonstrate how standard adjustments for causal inference lead to the same paradox. We prove that the characteristics of these paradoxes exactly mimic another set of paradoxes which arise among sets of voter preferences.