> Yes, we do.

No, we don't. This is not an yes/no answer. This is the type of question that should be answered in terms of confidence intervals.

> right wing tweets actually got promoted more

In relation to what? What is a "right wing" tweet? What is a "left wing" tweet?

E.g, if the algorithm is focused on filtering out disparaging extreme messages, and it ends up filtering X amount of "non-extreme right wing content", 3X of "extreme right-wing content" and 5X of "extreme left-wing content", it satisfies the claim that "it promotes more right-wing content" while also silencing conservative voices.

This is not exclusive to Twitter, but here's a recent research papaer on the comparative advantage of "the right" in dissimination of information on social media.

The advantage of the right in social media news sharing: https://academic.oup.com/pnasnexus/article/1/3/pgac137/66516...

Upenn article summary: https://penntoday.upenn.edu/news/Penn-research-Twitter-gives...

yes, let us ask twitter for their opinion on whether they are doing improper things.

its like if a policeman is accused of wrongdoing, he gets to investigate if he did that himself.