> What features make a private website a public square?

* The fact that that's what these sites bill themselves as (a place to connect everyone).

* Their user base cross-cuts most demographics (even if the samplings are always representative).

> Would people feel differently if platforms were honest and direct about being a private club of some specific kind?

Yes. You don't hear much about the government wanting to regulate Reddit, do you? It has roughly comparable number of monthly active users in the US as Twitter (26.4 million vs. 68 million) but it's built around the idea of independently moderated virtual clubs.

> If Twitter came out and said they wanted to be a private club for people with progressive views to discuss politics and sundry, would that dampen the criticism of censorship?

I think people (and advertising revenue) would move to a different platform.

> I think people (and advertising revenue) would move to a different platform.

That may be, but that's not what I'm asking, I'm asking whether they would still be criticized for censorship. I think probably so?

Your point about reddit is an interesting one. You're right that they don't get much grief from lawmakers on the censorship question, but I suspect that has a lot to do with unfamiliarity. They have certainly gotten lots of grief from denizens of the internet for their moderation policies over time.

>The fact that that's what these sites bill themselves as (a place to connect everyone).

Companies never lie or have false advertising.

One definition could be that you become a public square when you benefit sufficiently from the society in which you operate that you must correspondingly take on civic responsibility to that society.

In terms of Facebook: they rake it in because millions of us chose their platform, over many others, for posting our cat photos. Accordingly, Facebook must pay something back to society. (Though perhaps the “pay something back” merely needs to be covered by corporation tax, rather than anything more special.)

If the local pub becomes the de facto meeting room for the village club, and makes a killing selling them beer as a result, maybe it should be obliged to provide free parking?

I think if you have over a billion members, you shouldn’t be classified as a private club.

I don't know about the rest of the people, but I definitely feel differently when it comes to being honest about being a private club.

Here is my analogy: I don't mind mods on r/thedonald kicking out anyone who isn't fully on board with the agenda, just like I agree with mods on r/latestagecapitalism or r/communism getting rid of those with dissenting opinions. But I do have issues with r/politics positioning themselves as a "neutral" sub to discuss politics, while essentially being an off-shoot of r/communism and r/DNC.