"The greatest good for the greatest number" is pretty much the defining principle of Left-wing in my view.

If you look at the stated policies (not to be confused with what the actual human beings claiming to support those do when they get Power) of the various ideologies within the Left-wing, it's not that objective that changes, it's how to go about maximizing it and the how far do people believe it can be maximized that differs.

Whilst you do see a number of left-wing ideologies which think the will of the individual should be entirely subservient to the State, others believe that it is a "greater good" for people to have more individual freedom than for people having to be entirely subservient to the State. This is the way in which the Authoritarian-Libertarian axis of Politics is expressed with the Left-wing.