  A majority coloring of an undirected graph is a vertex coloring in which for
each vertex there are at least as many bi-chromatic edges containing that
vertex as monochromatic ones. It is known that for every countable graph a
majority 3-coloring always exists. The Unfriendly Partition Conjecture states
that every countable graph admits a majority 2-coloring. Since the 3-coloring
result extends to countable DAGs, a variant of the conjecture states that 2
colors are enough to majority color every countable DAG. We show that this is
false by presenting a DAG for which 3 colors are necessary. Presented
construction is strongly based on a StackExchange conversation regarding
labellings of infinite graphs that is linked in the references.
