The 2-coloring conjecture for countable acyclic digraphs

Let $D$ be a countable acyclic digraph. A vertex coloring of $D$ is a majority coloring if, at every vertex, at most half of its outgoing edges are bad, meaning that their endpoints receive the same color. Acyclic digraph majority-coloring conjecture. Every countable acyclic digraph is majority $2$-colorable. Finite acyclic digraphs are easily majority $2$-colorable, and the conjecture is known with three colors for countable acyclic digraphs, but the two-color assertion remains open.