  We explore what we call ``omitted label contexts,'' in which training data is
limited to a subset of the possible labels. This setting is common among
specialized human experts or specific focused studies. We lean on well-studied
paradoxes (Simpson's and Condorcet) to illustrate the more general difficulties
of causal inference in omitted label contexts. Contrary to the fundamental
principles on which much of causal inference is built, we show that ``correct''
adjustments sometimes require non-exchangeable treatment and control groups.
These pitfalls lead us to the study networks of conclusions drawn from
different contexts and the structures the form, proving an interesting
connection between these networks and social choice theory.
