An interesting definition of socialism certainly "a bit less right wing than the other right wing party". One of the strange things about American politics is that the US has not had a left wing part for a long time, if ever. The UK is like that now (Corbyn aside) and it seems the way things are going.
Neil Kinnock, the former leader of the British Labour party told a story in an interview about an American woman you looked at him in astonishment and said "You can't be socialists, you're too nice".
A lot of the world (most of Europe for a start) has had numerous socialist governments without any more murder than under right wing governments. Oh, you mean communists? Different from socialists, and no American government has been anywhere near being either.