In the past I have used the term Lefty Fundamentalists. I am about to change my terminology to Lefty Sentimentalist.
The reason is straightforward. The peak of Lefty historic triumph and the point at which the Left's values were most widely accepted in the world was 1959. See my blog on the subject.
Thus Lefties are people looking back sentimentally to the day when 90% of the world was governed by communist or socialist central governments, all new postcolonial governments including the new revolutionary Cuba were socialist. Unions in the United States were at their peak. Nearly all major corporations in Europe were owned by the state.
Those were the glory days for Lefties.
Lefties are sentimental for those long gone days of their greatest achievements.