> - I do not know if there is a clean, ethical way to "run the social media"

My hand-wavy proposal:

1. there needs to be something akin to a constitution where all players involved (users of social media, social media companies) can express some shared set of values. For example kids shouldn't get depressed, data should be private, widely spread information should be reasonably accurate.

2. There needs to be a few institutions with enough power and checks and balances to be able to steer the system towards these values.