I argue that the left is just as elite as the right. Hence all communist regimes have been dictatorships. Stalin killed more people than Hitler and Mao killed more people than both combined.
Being liberal has nothing to do with being left or right. Left or right refers to which socio-economic principles you adhere to, ie socialism or capitalism. Both socialists and capitalists can be liberal, just as both socialists and capitalists can be conservative.
There are three basic dimensions in describing someone's general political outlook:
A) Progressive or Reactionary. Someone who is progressive looks to change society for the better in the future. Some who is reactionary resists that change and attempts to preserve the status quo or return it to a previous state. Progressives look to the future for guidance, reactionaries look to the past for guidance.
B) Socialist or Capitalist. Someone who is socialist believes that individuals should be responsible for the betterment of society. Someone who is capitalist believes that individuals should be responsible for the betterment of themselves.
C) Autocratic or Tolerant. Autocratic people believe that they should be deciding how other people should live their lives. Tolerant people believe that other people should decide for themselves how to live their lives.
Generally speaking in our society a conservative is almost always a reactionary, and usually they are autocratic. Most are capitalists but there are many who are socialists as well (these would be your communists after they have taken power).
Liberals are usually progressive, almost always are tolerant, and generally around the center between socialism and capitalism.
There are other dimensions as well. Politics is a complex thing, it is not wise to try to pigeon hole people because there is a huge diversity between all those dimensions. No two people are exactly alike in their opinions and philosophy.