What is left-libertarianism?
Roughly...left libertarianism is the position that the political left have identified almost all the correct issues to worry about...but that they missed 1 fundamental point: the government is either the cause or the enabler of almost all the problems. If one combines actual liberal (as opposed to Democrat) sensibilities: anti-discrimination, opposition to corporate power, freedom of religion, tolerance of at least other tolerant cultures, distrust of police, anti-war, pro-drug, anti-exploitation, etc....and adds the public choice/marxist analysis that the government is AT BEST no solution to the problem, and usually a fundamental cause, and start providing examples....what comes out?
Well...19th century socialist/libertarian anarchism/communalism/mutualism is the rough answer, with a smattering of hegelian dialectic from the tradition of Sciabarra thrown in.
The question becomes how to create the world we would like, while recognizing that Mao was right: power flows from the barrel of a gun...and this is what ALL governments are founded upon, despite any pretty myths coming from American or European fantastic history.
We are clearly logically prohibited from voting, as a vote is ALWAYS a vote to use violence or threat of violence to make other people do what we want. And as per Patri, that's just morally wrong. Rather, the goal has to be to create alternative, non-violent institutions that solve problems. Much harder than the immediately attractive, but ultimately self-defeating proposition of trying to seize the power of the government (and its violence) to achieve your ends against the already existing power centers.
Where does that put one politically....opposed to everything. We are almost as opposed to the (vulgar) libertarian (effectively) pro-corporatist stance as to the Republican worship of state sponsored violence and status-quo-ism or the Democratic worship of the state's capacity to improve social circumstances.
The goal is to remove the state's influence from areas. So we might agree with the Republican that the 2nd amendment's first (and dependent) clause should be (largely) absolute, so as to get the government out of that area of life....and we might agree with the progressive that the government should not be in the business of regulating drugs...and we might hang with the cypherpunks in being pro-strong crypto...and we might prefer the cash economy, and the grey or darker markets we see...and we might violently agree with the liberal claims of obvious and odious discrimination from having a obscenely large black prison population...etc.
The most obvious (IMO) place of departure for the left-libertarian from the non-left libertarian would be to suggest starting to dismantle the state locally by abolishing the government police. Privatize crime fighting first.