When leftist media platforms like Facebook ban news about BLM marxist founder buying mansions in white area is this liberal or authoritarian/fascist approach?
Facebook banning content on "their yard" does not hurt anyone because it's their property. Therefore on a spectrum this would be Right - Libertarian.
Conservative on the political spectrum states: Right-wing political ideologies are characterized by conservative views. Since the political compass asks us to isolate the left/right binary for economic preferences, right-wing economic policy often favors reducing taxes, limiting government spending, and fewer government-imposed restrictions on businesses.
Key: "fewer government-imposed restrictions on businesses"
By controlling what Facebook can/can't ban that's imposing a restriction, so the opposite of that makes this right-wing since FB is being allowed to censor whatever they choose.
Libertarian: People that hold a libertarian political identity often focus on the freedom of the individual. They believe that personal freedom should be maximized and they support the idea that government authority and control over their citizens should be displaced.5 Equality is of utmost importance for libertarians.
^ This, except lib/right consider companies/capitalism an extension of citizenship and give them more rights.
The left would probably demand more fairness/equalness since the left-wing side of the political spectrum says:
left-wing economic policy often favors higher taxes for wealthy individuals, stronger regulations for businesses, and government spending on social infrastructure.
So authoritarian/left would demand higher taxes and stronger regulations possibly it would also give the government final say in everything posted on facebook and require facebook to divulge the identity and data of any member it requests data on, court order or not.
As an aside I consider myself libertarian/left - as in I'd like less statist power (weaker federal govt, more freedom for individuals, but more oversight/regulations on businesses and corporations so they can't become countries unto themselves like Amazon and I believe egalitarianism is the most noble pursuit because we have enough resources and science to support everyone on earth - considering everything we waste daily, so why should anyone have to suffer if there's a way for them not to within our means if we just collectively desired that outcome?).
There is nothing libertarian about censoring someone.
Sure, you have the right to do that, given they're on your private property (on Facebook) but that screams authoritarianism: it's like Facebook is his own little country ruling on his citizens and limiting their freedom.
Now, the act of advocating for Facebook to be able to do what it is currently able to do is libertarian. An authoritarian measure would be, as you mention, regulating Facebook to force them to publish anything or giving exactly the same space / visibility to people of opposing viewpoints.
As an another aside, as an anarcho-capitalist (right libertarian), I've a lot of respect for your political viewpoint - that would be ideal but I think it's unachievable. Egalitarianism - or equality of outcomes - can't happen unless you force it with an authoritarian government or you have perfect people that share voluntarily everything. On top of this, as soon as you have an authoritarian government you'll start having corruption (we don't have perfect people) which will favour government officials over normal people, throwing in the bin your egalitarianism.
Instead of focusing on equality of outcomes, I think we should focus on reaching equality of opportunity; given we have imperfect people we need a system of incentives to keep people broadly aligned with what society wants. Therefore there should be no government (which is outside the market and corruptible) and all services (including protection, healthcare, lawmaking) should be provided by the market. I think this will bring us as close to egalitarianism as we can possibly get.
How does an anarcho-capitalist deal with issues like village commons, natural monopolies, winner-take-all business models, national borders, etc?
The general answer is, by mutual agreement among the affected persons, and by refusing to interact at all with people who cannot be trusted to abide by mutual agreements.
For a more detailed treatment, see, for example, David Friedman's The Machinery of Freedom.
Of course there is no simple, short path from where we are now to any feasible anarcho-capitalist society; the idea that we need governments to solve problems is becoming more and more firmly entrenched, even in the face of the terrible track record of governments at actually solving problems.
No, libertarians believe that actual people should have that right (subject to the non-aggression principle, which is actually more than just "doesn't physically infringe on another's freedoms"). Corporations are not actual people.
To a libertarian, corporations are tools that individual people can use if they want to work together to accomplish some common purpose. But most "corporations" in today's society are no such thing; certainly Facebook is not. Most stockholders in corporations today have no actual interest in what the corporation does or what common purpose it is serving; they view their stock as just a money-making asset. (Indeed, most "stockholders" in individual corporations today are mutual funds, not individual investors.) None of this is libertarian; it is due to government manipulation of the financial system and government regulation of corporations and investments. In a truly libertarian world something like Facebook could not even exist.
Liberalism is a tricky word, because Modern Liberalism or Social Liberalism (or just Liberalism in the USA) are almost the opposite of Classical Liberalism.
The Political Compass avoids the terms and use:
- Authoritarian (Fascism) - Libertarian (Anarchism): from "everything is controlled by a central entity" to "everything is decentralised" - Left (Communism) - Right (Neo-liberalism): from "everything is nationalised", to "everything is provided by the market"