  We propose the notion of a majority $k$-edge-coloring of a graph $G$, which
is an edge-coloring of $G$ with $k$ colors such that, for every vertex $u$ of
$G$, at most half the edges of $G$ incident with $u$ have the same color. We
show the best possible results that every graph of minimum degree at least $2$
has a majority $4$-edge-coloring, and that every graph of minimum degree at
least $4$ has a majority $3$-edge-coloring. Furthermore, we discuss a natural
variation of majority edge-colorings and some related open problems.
