  We consider edge colorings of graphs. An edge coloring is a majority coloring
if for every vertex at most half of the edges incident with it are in one
color. And edge coloring is a distinguishing coloring if for every non-trivial
automorphism at least one edge changes its color. We consider these two notions
together. We show that every graph without pendant edges has a majority
distinguishing edge coloring with at most $\lceil\sqrt{\Delta}\rceil+5$ colors.
Moreover, we show results for some classes of graphs and a~general result for
symmetric digraphs.
