Who's in charge of Twitter? I'm going to go with Twitter.

Well, it is a private company's site, so I would assume the corporation. If I walked into a Starbucks and started being rude to patrons, I can easily be removed on a whim. Just because it is a place that encourages social interactions does not mean that they have to allow interactions they do not like. I do not see the difference here.

Twitter is used for formal announcements because Trump himself has decided that it is a good place to make them, not because Twitter has placed themselves in that position. Granted, they make like being in that position and it probably benefits them greatly due to the increased ad revenue and engagement, but they can also make the decision that his presence is not worth the vitriol it generates. He can easily choose another avenue (Facebook, Reddit, News media, etc) to make announcements if it is no longer the best choice for him.

I was suddenly struck with an image of Trump angrily posting his updates on Hacker News.

Neither. The population are, or at least should be.

The population should be in charge of twitter? Doesn't that seem a little funny?

I believe this is called a nationalization. And here I was, thinking nothing Trump could pull would be surprising, but actually Trump nationalizing Twitter would do the trick.

I too would be very surprised to see a social media platform nationalized.